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Class 11 Physics (India)
Unit 9: lesson 1.
- Types of forces and free body diagrams
Introduction to free body diagrams
- Introduction to forces and free body diagrams review
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Solving Force Problems in Physics by Using Free-Body Diagrams
Physics i: 501 practice problems for dummies (+ free online practice).
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In physics, force problems typically ask you to predict what will happen when you apply force to an object, and usually there’s no handy illustration to help you visualize what’s being described. Fortunately, you can create your own diagram so you can better picture what a question is asking you. Follow this seven-step method to solve force problems:
Draw each of the objects you’re interested in.
Here’s an example:
Identify the forces acting on each object.
For each force acting on one of the objects from Step 1, draw an arrow that indicates the direction of the force, as shown in the following figure. Note that the tail of the arrow indicates which part of the object the force is acting on.
Draw a free-body diagram for each object.
If you’re following this step-by-step guide, you’ve already drawn a free-body diagram. It’s listed separately because it’s the most important step!
Choose a coordinate system for each object.
Usually you draw the x -direction horizontally and the y -direction vertically, as shown in the following figure. However, when dealing with inclined planes, sometimes you want to choose your coordinate axes parallel and perpendicular to the plane.
For each object, write down each component of Newton’s second law.
For angular motion problems, choose an axis of rotation and write down the angular version of Newton’s second law.
Include any constraints.
Sometimes you have more variables than equations at this point. Write down any other information you know. For example, if a car is driving on a flat road, you know that the vertical component of its acceleration is zero.
Solve the equations.
Now that you’ve used all your physics knowledge, all you have to do is the algebra.
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Free Body Diagram
What is a Free Body Diagram?
Free Body Diagrams (FBD) are useful aids for representing the relative magnitude and direction of all forces acting upon an object in a given situation. The first step in analyzing and describing most physical phenomena involves the careful drawing of a free-body diagram. In a free body diagram, the size of the arrow denotes the magnitude of the force while the direction of the arrow denotes the direction in which the force acts.
A free body diagram is defined as:
A free-body diagram is a graphic, dematerialized, symbolic representation of the body (structure, element or segment of an element) in which all connecting “pieces” have been removed.
Features of Free Body Diagram
A free-body diagram is a diagram that is modified as the problem is solved. Normally, a free body diagram consists of the following components:
- A simplified version of the body (most commonly a box)
- A coordinate system
- Forces are represented as arrows pointing in the direction they act on the body
- Moments showed as curved arrows pointing in the direction they act on the body
The number of forces acting on a body depends on the specific problem and the assumptions made. Commonly, air resistance and friction are neglected.
Exclusions in Free Body Diagram
Some of the things that a free body diagram excludes are as follows:
- Bodies other than the free body diagram
- Constraints
- Internal Forces
- Velocity and Acceleration Vectors
What is the purpose of a free body diagram?
Free body diagrams are tools that are used to visualize the force and moments applied to a body and to calculate the resulting reactions in many types of mechanics problems.
How to make a free body diagram?
In the section, we will explain the step-by-step procedure of drawing a free body diagram:
1. Identify the Contact Forces
To identify the forces acting on the body, draw an outline of the object with dotted lines as shown in the figure. Make sure to draw a dot when something touches the object. When there is a dot, it indicates that there is at least one contact force acting on the body. Draw the force vectors at the contact points to represent how they push or pull on the object.
2. After identifying the contact forces, draw a dot to represent the object that we are interested in. Here, we are only interested in determining the forces acting on our object.
3. Draw a coordinate system and label positive directions.
4. Draw the contact forces on the dot with an arrow pointing away from the dot. The arrow lengths should be relatively proportional to each other. Label all forces.
5. Draw and label our long-range forces. This will usually be weight unless there is an electric charge or magnetism involved.
6. If there is acceleration in the system, then draw and label the acceleration vector.
Free Body Diagram Examples
In this section, we have listed free diagrams considered under different scenarios.
1. A bottle is resting on a tabletop. Draw the forces acting on the bottle.
2. An egg is free-falling from a nest in a tree, neglecting the air resistance, what would the free body diagram look like?
3. If a rightward force is applied to a book in order to move it across a desk at a constant velocity. Considering only the frictional forces and neglecting air resistance. A free-body diagram for this situation looks like this:
4. A skydiver is descending at a constant velocity. Considering the air resistance, the free body diagram for this situation would like the following:
Free Body Diagram Solved Problem
Example: Draw a free body diagram of three blocks placed one over the other as shown in the figure.
The forces acting on the individual elements of the system are shown below:
Description of Forces acting on each block:
The forces on block “C” are:
W C =m C g= its weight, acting downward
N B = normal reaction on “C” due to the upper surface of block B, acting upward
The forces on block “B” are:
W B =m B g= its weight, acting downward
N B = normal reaction on “B” due to the lower surface of block C, acting downward
N A = normal reaction on “B” due to the upper surface of block A, acting upward
The forces on the block “A” are :
W A =m A g= its weight, acting downward
N A = normal reaction on “A” due to the lower surface of block B, acting downward
N O = normal reaction on “A” due to horizontal surface, acting upward
The FBD of the blocks as points with external forces are shown here.
Frequently Asked Questions on Free Body Diagram
What is the definition of a free body diagram.
A free-body diagram is a graphic, dematerialized, symbolic representation of the body (structure, element or segment of an element) in which all connecting “pieces” have been removed.
What does a free body diagram represent?
Free-body diagrams represent the relative magnitude and direction of all forces acting upon an object in a given situation.
How to draw a free body diagram?
While drawing a free body diagram, we draw the object of interest by drawing all the forces acting on it and resolve all force vectors into x– and y-components. Separate free body diagrams should be drawn for each object in the problem.
What is the free body diagram indicative of?
Free body diagrams are used to visualize the forces and moments applied to a body and to calculate the resulting reactions in many types of mechanics problems.
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5 Steps to Help Solve any Free Body Diagram Problem (3:59)
5 Newton’s Laws of Motion
5.7 Drawing Free-Body Diagrams
Learning objectives.
By the end of the section, you will be able to:
- Explain the rules for drawing a free-body diagram
- Construct free-body diagrams for different situations
The first step in describing and analyzing most phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams have been used in examples throughout this chapter. Remember that a free-body diagram must only include the external forces acting on the body of interest. Once we have drawn an accurate free-body diagram, we can apply Newton’s first law if the body is in equilibrium (balanced forces; that is, [latex]{F}_{\text{net}}=0[/latex]) or Newton’s second law if the body is accelerating (unbalanced force; that is, [latex]{F}_{\text{net}}\ne 0[/latex]).
In Forces , we gave a brief problem-solving strategy to help you understand free-body diagrams. Here, we add some details to the strategy that will help you in constructing these diagrams.
Problem-Solving Strategy: Constructing Free-Body Diagrams
Observe the following rules when constructing a free-body diagram:
- Draw the object under consideration; it does not have to be artistic. At first, you may want to draw a circle around the object of interest to be sure you focus on labeling the forces acting on the object. If you are treating the object as a particle (no size or shape and no rotation), represent the object as a point. We often place this point at the origin of an xy -coordinate system.
- Include all forces that act on the object, representing these forces as vectors. Consider the types of forces described in Common Forces —normal force, friction, tension, and spring force—as well as weight and applied force. Do not include the net force on the object. With the exception of gravity, all of the forces we have discussed require direct contact with the object. However, forces that the object exerts on its environment must not be included. We never include both forces of an action-reaction pair.
- Convert the free-body diagram into a more detailed diagram showing the x – and y -components of a given force (this is often helpful when solving a problem using Newton’s first or second law). In this case, place a squiggly line through the original vector to show that it is no longer in play—it has been replaced by its x – and y -components.
- If there are two or more objects, or bodies, in the problem, draw a separate free-body diagram for each object.
Note: If there is acceleration, we do not directly include it in the free-body diagram; however, it may help to indicate acceleration outside the free-body diagram. You can label it in a different color to indicate that it is separate from the free-body diagram.
Let’s apply the problem-solving strategy in drawing a free-body diagram for a sled. In Figure (a), a sled is pulled by force P at an angle of [latex]30^\circ[/latex]. In part (b), we show a free-body diagram for this situation, as described by steps 1 and 2 of the problem-solving strategy. In part (c), we show all forces in terms of their x – and y -components, in keeping with step 3.
Two Blocks on an Inclined Plane
Construct the free-body diagram for object A and object B in Figure .
We follow the four steps listed in the problem-solving strategy.
We start by creating a diagram for the first object of interest. In Figure (a), object A is isolated (circled) and represented by a dot.
We now include any force that acts on the body. Here, no applied force is present. The weight of the object acts as a force pointing vertically downward, and the presence of the cord indicates a force of tension pointing away from the object. Object A has one interface and hence experiences a normal force, directed away from the interface. The source of this force is object B, and this normal force is labeled accordingly. Since object B has a tendency to slide down, object A has a tendency to slide up with respect to the interface, so the friction [latex]{f}_{\text{BA}}[/latex] is directed downward parallel to the inclined plane.
As noted in step 4 of the problem-solving strategy, we then construct the free-body diagram in Figure (b) using the same approach. Object B experiences two normal forces and two friction forces due to the presence of two contact surfaces. The interface with the inclined plane exerts external forces of [latex]{N}_{\text{B}}[/latex] and [latex]{f}_{\text{B}}[/latex], and the interface with object B exerts the normal force [latex]{N}_{\text{AB}}[/latex] and friction [latex]{f}_{\text{AB}}[/latex]; [latex]{N}_{\text{AB}}[/latex] is directed away from object B, and [latex]{f}_{\text{AB}}[/latex] is opposing the tendency of the relative motion of object B with respect to object A.
Significance
The object under consideration in each part of this problem was circled in gray. When you are first learning how to draw free-body diagrams, you will find it helpful to circle the object before deciding what forces are acting on that particular object. This focuses your attention, preventing you from considering forces that are not acting on the body.
Two Blocks in Contact
A force is applied to two blocks in contact, as shown.
Draw a free-body diagram for each block. Be sure to consider Newton’s third law at the interface where the two blocks touch.
Significance[latex]{\mathbf{\overset{\to }{A}}}_{21}[/latex] is the action force of block 2 on block 1. [latex]{\mathbf{\overset{\to }{A}}}_{12}[/latex] is the reaction force of block 1 on block 2. We use these free-body diagrams in Applications of Newton’s Laws .
Block on the Table (Coupled Blocks)
A block rests on the table, as shown. A light rope is attached to it and runs over a pulley. The other end of the rope is attached to a second block. The two blocks are said to be coupled. Block [latex]{m}_{2}[/latex] exerts a force due to its weight, which causes the system (two blocks and a string) to accelerate.
We assume that the string has no mass so that we do not have to consider it as a separate object. Draw a free-body diagram for each block.
Each block accelerates (notice the labels shown for [latex]{\mathbf{\overset{\to }{a}}}_{1}[/latex] and [latex]{\mathbf{\overset{\to }{a}}}_{2}[/latex]); however, assuming the string remains taut, they accelerate at the same rate. Thus, we have [latex]{\mathbf{\overset{\to }{a}}}_{1}={\mathbf{\overset{\to }{a}}}_{2}[/latex]. If we were to continue solving the problem, we could simply call the acceleration [latex]\mathbf{\overset{\to }{a}}[/latex]. Also, we use two free-body diagrams because we are usually finding tension T , which may require us to use a system of two equations in this type of problem. The tension is the same on both [latex]{m}_{1}\,\text{and}\,{m}_{2}[/latex].
Check Your Understanding
(a) Draw the free-body diagram for the situation shown. (b) Redraw it showing components; use x -axes parallel to the two ramps.
Figure a shows a free body diagram of an object on a line that slopes down to the right. Arrow T from the object points right and up, parallel to the slope. Arrow N1 points left and up, perpendicular to the slope. Arrow w1 points vertically down. Arrow w1x points left and down, parallel to the slope. Arrow w1y points right and down, perpendicular to the slope. Figure b shows a free body diagram of an object on a line that slopes down to the left. Arrow N2 from the object points right and up, perpendicular to the slope. Arrow T points left and up, parallel to the slope. Arrow w2 points vertically down. Arrow w2y points left and down, perpendicular to the slope. Arrow w2x points right and down, parallel to the slope.
View this simulation to predict, qualitatively, how an external force will affect the speed and direction of an object’s motion. Explain the effects with the help of a free-body diagram. Use free-body diagrams to draw position, velocity, acceleration, and force graphs, and vice versa. Explain how the graphs relate to one another. Given a scenario or a graph, sketch all four graphs.
- To draw a free-body diagram, we draw the object of interest, draw all forces acting on that object, and resolve all force vectors into x – and y -components. We must draw a separate free-body diagram for each object in the problem.
- A free-body diagram is a useful means of describing and analyzing all the forces that act on a body to determine equilibrium according to Newton’s first law or acceleration according to Newton’s second law.
Key Equations
Conceptual questions.
In completing the solution for a problem involving forces, what do we do after constructing the free-body diagram? That is, what do we apply?
If a book is located on a table, how many forces should be shown in a free-body diagram of the book? Describe them.
Two forces of different types: weight acting downward and normal force acting upward
A ball of mass m hangs at rest, suspended by a string. (a) Sketch all forces. (b) Draw the free-body diagram for the ball.
A car moves along a horizontal road. Draw a free-body diagram; be sure to include the friction of the road that opposes the forward motion of the car.
A runner pushes against the track, as shown. (a) Provide a free-body diagram showing all the forces on the runner. ( Hint: Place all forces at the center of his body, and include his weight.) (b) Give a revised diagram showing the xy -component form.
The traffic light hangs from the cables as shown. Draw a free-body diagram on a coordinate plane for this situation.
Additional Problems
Two small forces, [latex]{\mathbf{\overset{\to }{F}}}_{1}=-2.40\mathbf{\hat{i}}-6.10t\mathbf{\hat{j}}[/latex] N and [latex]{\mathbf{\overset{\to }{F}}}_{2}=8.50\mathbf{\hat{i}}-9.70\mathbf{\hat{j}}[/latex] N, are exerted on a rogue asteroid by a pair of space tractors. (a) Find the net force. (b) What are the magnitude and direction of the net force? (c) If the mass of the asteroid is 125 kg, what acceleration does it experience (in vector form)? (d) What are the magnitude and direction of the acceleration?
Two forces of 25 and 45 N act on an object. Their directions differ by [latex]70^\circ[/latex]. The resulting acceleration has magnitude of [latex]10.0\,{\text{m/s}}^{2}.[/latex] What is the mass of the body?
A force of 1600 N acts parallel to a ramp to push a 300-kg piano into a moving van. The ramp is inclined at [latex]20^\circ[/latex]. (a) What is the acceleration of the piano up the ramp? (b) What is the velocity of the piano when it reaches the top if the ramp is 4.0 m long and the piano starts from rest?
Draw a free-body diagram of a diver who has entered the water, moved downward, and is acted on by an upward force due to the water which balances the weight (that is, the diver is suspended).
For a swimmer who has just jumped off a diving board, assume air resistance is negligible. The swimmer has a mass of 80.0 kg and jumps off a board 10.0 m above the water. Three seconds after entering the water, her downward motion is stopped. What average upward force did the water exert on her?
(a) Find an equation to determine the magnitude of the net force required to stop a car of mass m , given that the initial speed of the car is [latex]{v}_{0}[/latex] and the stopping distance is x . (b) Find the magnitude of the net force if the mass of the car is 1050 kg, the initial speed is 40.0 km/h, and the stopping distance is 25.0 m.
a. [latex]{F}_{\text{net}}=\frac{m({v}^{2}-{v}_{0}{}^{2})}{2x}[/latex]; b. 2590 N
A sailboat has a mass of [latex]1.50\times {10}^{3}[/latex] kg and is acted on by a force of [latex]2.00\times {10}^{3}[/latex] N toward the east, while the wind acts behind the sails with a force of [latex]3.00\times {10}^{3}[/latex] N in a direction [latex]45^\circ[/latex] north of east. Find the magnitude and direction of the resulting acceleration.
Find the acceleration of the body of mass 10.0 kg shown below.
[latex]\begin{array}{cc} {\mathbf{\overset{\to }{F}}}_{\text{net}}=4.05\mathbf{\hat{i}}+12.0\mathbf{\hat{j}}\text{N}\hfill \\ {\mathbf{\overset{\to }{F}}}_{\text{net}}=m\mathbf{\overset{\to }{a}}\Rightarrow \mathbf{\overset{\to }{a}}=0.405\mathbf{\hat{i}}+1.20\mathbf{\hat{j}}\,{\text{m/s}}^{2}\hfill \end{array}[/latex]
A body of mass 2.0 kg is moving along the x -axis with a speed of 3.0 m/s at the instant represented below. (a) What is the acceleration of the body? (b) What is the body’s velocity 10.0 s later? (c) What is its displacement after 10.0 s?
Force [latex]{\mathbf{\overset{\to }{F}}}_{\text{B}}[/latex] has twice the magnitude of force [latex]{\mathbf{\overset{\to }{F}}}_{\text{A}}.[/latex] Find the direction in which the particle accelerates in this figure.
[latex]\begin{array}{cc} {\mathbf{\overset{\to }{F}}}_{\text{net}}={\mathbf{\overset{\to }{F}}}_{\text{A}}+{\mathbf{\overset{\to }{F}}}_{\text{B}}\hfill \\ {\mathbf{\overset{\to }{F}}}_{\text{net}}=A\mathbf{\hat{i}}+(-1.41A\mathbf{\hat{i}}-1.41A\mathbf{\hat{j}})\hfill \\ {\mathbf{\overset{\to }{F}}}_{\text{net}}=A(-0.41\mathbf{\hat{i}}-1.41\mathbf{\hat{j}})\hfill \\ \theta =254^\circ\hfill \end{array}[/latex]
(We add [latex]180^\circ[/latex], because the angle is in quadrant IV.)
Shown below is a body of mass 1.0 kg under the influence of the forces [latex]{\mathbf{\overset{\to }{F}}}_{A}[/latex], [latex]{\mathbf{\overset{\to }{F}}}_{B}[/latex], and [latex]m\mathbf{\overset{\to }{g}}[/latex]. If the body accelerates to the left at [latex]20\,{\text{m/s}}^{2}[/latex], what are [latex]{\mathbf{\overset{\to }{F}}}_{A}[/latex] and [latex]{\mathbf{\overset{\to }{F}}}_{B}[/latex]?
A force acts on a car of mass m so that the speed v of the car increases with position x as [latex]v=k{x}^{2}[/latex], where k is constant and all quantities are in SI units. Find the force acting on the car as a function of position.
[latex]F=2kmx[/latex]; First, take the derivative of the velocity function to obtain [latex]a=2kx[/latex]. Then apply Newton’s second law [latex]F=ma=m(2kx)=2kmx[/latex].
A 7.0-N force parallel to an incline is applied to a 1.0-kg crate. The ramp is tilted at [latex]20^\circ[/latex] and is frictionless. (a) What is the acceleration of the crate? (b) If all other conditions are the same but the ramp has a friction force of 1.9 N, what is the acceleration?
Two boxes, A and B, are at rest. Box A is on level ground, while box B rests on an inclined plane tilted at angle [latex]\theta[/latex] with the horizontal. (a) Write expressions for the normal force acting on each block. (b) Compare the two forces; that is, tell which one is larger or whether they are equal in magnitude. (c) If the angle of incline is [latex]10^\circ[/latex], which force is greater?
a. For box A, [latex]{N}_{\text{A}}=mg[/latex] and [latex]{N}_{\text{B}}=mg\,\text{cos}\,\theta[/latex]; b. [latex]{N}_{\text{A}} \gt {N}_{\text{B}}[/latex] because for [latex]\theta \lt 90^\circ[/latex], [latex]\text{cos}\,\theta \lt 1[/latex]; c. [latex]{N}_{\text{A}} \gt {N}_{\text{B}}[/latex] when [latex]\theta =10^\circ[/latex]
As shown below, two identical springs, each with the spring constant 20 N/m, support a 15.0-N weight. (a) What is the tension in spring A? (b) What is the amount of stretch of spring A from the rest position?
a. 8.66 N; b. 0.433 m
Shown below is a 30.0-kg block resting on a frictionless ramp inclined at [latex]60^\circ[/latex] to the horizontal. The block is held by a spring that is stretched 5.0 cm. What is the force constant of the spring?
In building a house, carpenters use nails from a large box. The box is suspended from a spring twice during the day to measure the usage of nails. At the beginning of the day, the spring stretches 50 cm. At the end of the day, the spring stretches 30 cm. What fraction or percentage of the nails have been used?
0.40 or 40%
A force is applied to a block to move it up a [latex]30^\circ[/latex] incline. The incline is frictionless. If [latex]F=65.0\,\text{N}[/latex] and [latex]M=5.00\,\text{kg}[/latex], what is the magnitude of the acceleration of the block?
Two forces are applied to a 5.0-kg object, and it accelerates at a rate of [latex]2.0\,{\text{m/s}}^{2}[/latex] in the positive y -direction. If one of the forces acts in the positive x -direction with magnitude 12.0 N, find the magnitude of the other force.
The block on the right shown below has more mass than the block on the left ([latex]{m}_{2} \gt {m}_{1}[/latex]). Draw free-body diagrams for each block.
Challenge Problems
If two tugboats pull on a disabled vessel, as shown here in an overhead view, the disabled vessel will be pulled along the direction indicated by the result of the exerted forces. (a) Draw a free-body diagram for the vessel. Assume no friction or drag forces affect the vessel. (b) Did you include all forces in the overhead view in your free-body diagram? Why or why not?
b. No; [latex]{\mathbf{\overset{\to }{F}}}_{\text{R}}[/latex] is not shown, because it would replace [latex]{\mathbf{\overset{\to }{F}}}_{1}[/latex] and [latex]{\mathbf{\overset{\to }{F}}}_{2}[/latex]. (If we want to show it, we could draw it and then place squiggly lines on [latex]{\mathbf{\overset{\to }{F}}}_{1}[/latex] and [latex]{\mathbf{\overset{\to }{F}}}_{2}[/latex] to show that they are no longer considered.
A 10.0-kg object is initially moving east at 15.0 m/s. Then a force acts on it for 2.00 s, after which it moves northwest, also at 15.0 m/s. What are the magnitude and direction of the average force that acted on the object over the 2.00-s interval?
On June 25, 1983, shot-putter Udo Beyer of East Germany threw the 7.26-kg shot 22.22 m, which at that time was a world record. (a) If the shot was released at a height of 2.20 m with a projection angle of [latex]45.0^\circ[/latex], what was its initial velocity? (b) If while in Beyer’s hand the shot was accelerated uniformly over a distance of 1.20 m, what was the net force on it?
a. 14.1 m/s; b. 601 N
A body of mass m moves in a horizontal direction such that at time t its position is given by [latex]x(t)=a{t}^{4}+b{t}^{3}+ct,[/latex] where a , b , and c are constants. (a) What is the acceleration of the body? (b) What is the time-dependent force acting on the body?
A body of mass m has initial velocity [latex]{v}_{0}[/latex] in the positive x -direction. It is acted on by a constant force F for time t until the velocity becomes zero; the force continues to act on the body until its velocity becomes [latex]\text{−}{v}_{0}[/latex] in the same amount of time. Write an expression for the total distance the body travels in terms of the variables indicated.
[latex]\frac{F}{m}{t}^{2}[/latex]
The velocities of a 3.0-kg object at [latex]t=6.0\,\text{s}[/latex] and [latex]t=8.0\,\text{s}[/latex] are [latex](3.0\mathbf{\hat{i}}-6.0\mathbf{\hat{j}}+4.0\mathbf{\hat{k}})\,\text{m/s}[/latex] and [latex](-2.0\mathbf{\hat{i}}+4.0\mathbf{\hat{k}})\,\text{m/s}[/latex], respectively. If the object is moving at constant acceleration, what is the force acting on it?
A 120-kg astronaut is riding in a rocket sled that is sliding along an inclined plane. The sled has a horizontal component of acceleration of [latex]5.0\,\text{m}\text{/}{\text{s}}^{2}[/latex] and a downward component of [latex]3.8\,\text{m}\text{/}{\text{s}}^{2}[/latex]. Calculate the magnitude of the force on the rider by the sled. ( Hint : Remember that gravitational acceleration must be considered.)
Two forces are acting on a 5.0-kg object that moves with acceleration [latex]2.0\,{\text{m/s}}^{2}[/latex] in the positive y -direction. If one of the forces acts in the positive x -direction and has magnitude of 12 N, what is the magnitude of the other force?
Suppose that you are viewing a soccer game from a helicopter above the playing field. Two soccer players simultaneously kick a stationary soccer ball on the flat field; the soccer ball has mass 0.420 kg. The first player kicks with force 162 N at [latex]9.0^\circ[/latex] north of west. At the same instant, the second player kicks with force 215 N at [latex]15^\circ[/latex] east of south. Find the acceleration of the ball in [latex]\mathbf{\hat{i}}[/latex] and [latex]\mathbf{\hat{j}}[/latex] form.
[latex]\mathbf{\overset{\to }{a}}=-248\mathbf{\hat{i}}-433\mathbf{\hat{j}}\text{m}\text{/}{\text{s}}^{2}[/latex]
A 10.0-kg mass hangs from a spring that has the spring constant 535 N/m. Find the position of the end of the spring away from its rest position. (Use [latex]g=9.80\,{\text{m/s}}^{2}[/latex].)
A 0.0502-kg pair of fuzzy dice is attached to the rearview mirror of a car by a short string. The car accelerates at constant rate, and the dice hang at an angle of [latex]3.20^\circ[/latex] from the vertical because of the car’s acceleration. What is the magnitude of the acceleration of the car?
[latex]0.548\,{\text{m/s}}^{2}[/latex]
At a circus, a donkey pulls on a sled carrying a small clown with a force given by [latex]2.48\mathbf{\hat{i}}+4.33\mathbf{\hat{j}}\,\text{N}[/latex]. A horse pulls on the same sled, aiding the hapless donkey, with a force of [latex]6.56\mathbf{\hat{i}}+5.33\mathbf{\hat{j}}\,\text{N}[/latex]. The mass of the sled is 575 kg. Using [latex]\mathbf{\hat{i}}[/latex] and [latex]\mathbf{\hat{j}}[/latex] form for the answer to each problem, find (a) the net force on the sled when the two animals act together, (b) the acceleration of the sled, and (c) the velocity after 6.50 s.
Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m , and they are equally spaced by a distance d , as shown. The angles labeled [latex]\theta[/latex] describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal, labeled [latex]\varphi[/latex]. Let [latex]{T}_{1}[/latex] be the tension in the leftmost section of the string, [latex]{T}_{2}[/latex] be the tension in the section adjacent to it, and [latex]{T}_{3}[/latex] be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables m , g , and [latex]\theta[/latex]. (b) Find the angle [latex]\varphi[/latex] in terms of the angle [latex]\theta[/latex]. (c) If [latex]\theta =5.10^\circ[/latex], what is the value of [latex]\varphi[/latex]? (d) Find the distance x between the endpoints in terms of d and [latex]\theta[/latex].
a. [latex]{T}_{1}=\frac{2mg}{\text{sin}\,\theta }[/latex], [latex]{T}_{2}=\frac{mg}{\text{sin}(\text{arctan}(\frac{1}{2}\text{tan}\,\theta ))}[/latex], [latex]{T}_{3}=\frac{2mg}{\text{tan}\,\theta };[/latex] b. [latex]\varphi =\text{arctan}(\frac{1}{2}\text{tan}\,\theta )[/latex]; c. [latex]2.56^\circ[/latex]; (d) [latex]x=d(2\,\text{cos}\,\theta +2\,\text{cos}(\text{arctan}(\frac{1}{2}\text{tan}\,\theta ))+1)[/latex]
A bullet shot from a rifle has mass of 10.0 g and travels to the right at 350 m/s. It strikes a target, a large bag of sand, penetrating it a distance of 34.0 cm. Find the magnitude and direction of the retarding force that slows and stops the bullet.
An object is acted on by three simultaneous forces: [latex]{\mathbf{\overset{\to }{F}}}_{1}=(-3.00\mathbf{\hat{i}}+2.00\mathbf{\hat{j}})\,\text{N}[/latex], [latex]{\mathbf{\overset{\to }{F}}}_{2}=(6.00\mathbf{\hat{i}}-4.00\mathbf{\hat{j}})\,\text{N}[/latex], and [latex]{\mathbf{\overset{\to }{F}}}_{3}=(2.00\mathbf{\hat{i}}+5.00\mathbf{\hat{j}})\,\text{N}[/latex]. The object experiences acceleration of [latex]4.23\,{\text{m/s}}^{2}[/latex]. (a) Find the acceleration vector in terms of m . (b) Find the mass of the object. (c) If the object begins from rest, find its speed after 5.00 s. (d) Find the components of the velocity of the object after 5.00 s.
a. [latex]\mathbf{\overset{\to }{a}}=(\frac{5.00}{m}\mathbf{\hat{i}}+\frac{3.00}{m}\mathbf{\hat{j}})\,\text{m}\text{/}{\text{s}}^{2};[/latex] b. 1.38 kg; c. 21.2 m/s; d. [latex]\mathbf{\overset{\to }{v}}=(18.1\mathbf{\hat{i}}+10.9\mathbf{\hat{j}})\,\text{m}\text{/}{\text{s}}^{2}[/latex]
In a particle accelerator, a proton has mass [latex]1.67\times {10}^{-27}\,\text{kg}[/latex] and an initial speed of [latex]2.00\times {10}^{5}\,\text{m}\text{/}\text{s.}[/latex] It moves in a straight line, and its speed increases to [latex]9.00\times {10}^{5}\,\text{m}\text{/}\text{s}[/latex] in a distance of 10.0 cm. Assume that the acceleration is constant. Find the magnitude of the force exerted on the proton.
A drone is being directed across a frictionless ice-covered lake. The mass of the drone is 1.50 kg, and its velocity is [latex]3.00\mathbf{\hat{i}}\text{m}\text{/}\text{s}[/latex]. After 10.0 s, the velocity is [latex]9.00\mathbf{\hat{i}}+4.00\mathbf{\hat{j}}\text{m}\text{/}\text{s}[/latex]. If a constant force in the horizontal direction is causing this change in motion, find (a) the components of the force and (b) the magnitude of the force.
a. [latex]0.900\mathbf{\hat{i}}+0.600\mathbf{\hat{j}}\,\text{N}[/latex]; b. 1.08 N
5.7 Drawing Free-Body Diagrams Copyright © 2016 by OpenStax. All Rights Reserved.
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- 5.7 Drawing Free-Body Diagrams
- Introduction
- 1.1 The Scope and Scale of Physics
- 1.2 Units and Standards
- 1.3 Unit Conversion
- 1.4 Dimensional Analysis
- 1.5 Estimates and Fermi Calculations
- 1.6 Significant Figures
- 1.7 Solving Problems in Physics
- Key Equations
- Conceptual Questions
- Additional Problems
- Challenge Problems
- 2.1 Scalars and Vectors
- 2.2 Coordinate Systems and Components of a Vector
- 2.3 Algebra of Vectors
- 2.4 Products of Vectors
- 3.1 Position, Displacement, and Average Velocity
- 3.2 Instantaneous Velocity and Speed
- 3.3 Average and Instantaneous Acceleration
- 3.4 Motion with Constant Acceleration
- 3.5 Free Fall
- 3.6 Finding Velocity and Displacement from Acceleration
- 4.1 Displacement and Velocity Vectors
- 4.2 Acceleration Vector
- 4.3 Projectile Motion
- 4.4 Uniform Circular Motion
- 4.5 Relative Motion in One and Two Dimensions
- 5.2 Newton's First Law
- 5.3 Newton's Second Law
- 5.4 Mass and Weight
- 5.5 Newton’s Third Law
- 5.6 Common Forces
- 6.1 Solving Problems with Newton’s Laws
- 6.2 Friction
- 6.3 Centripetal Force
- 6.4 Drag Force and Terminal Speed
- 7.2 Kinetic Energy
- 7.3 Work-Energy Theorem
- 8.1 Potential Energy of a System
- 8.2 Conservative and Non-Conservative Forces
- 8.3 Conservation of Energy
- 8.4 Potential Energy Diagrams and Stability
- 8.5 Sources of Energy
- 9.1 Linear Momentum
- 9.2 Impulse and Collisions
- 9.3 Conservation of Linear Momentum
- 9.4 Types of Collisions
- 9.5 Collisions in Multiple Dimensions
- 9.6 Center of Mass
- 9.7 Rocket Propulsion
- 10.1 Rotational Variables
- 10.2 Rotation with Constant Angular Acceleration
- 10.3 Relating Angular and Translational Quantities
- 10.4 Moment of Inertia and Rotational Kinetic Energy
- 10.5 Calculating Moments of Inertia
- 10.6 Torque
- 10.7 Newton’s Second Law for Rotation
- 10.8 Work and Power for Rotational Motion
- 11.1 Rolling Motion
- 11.2 Angular Momentum
- 11.3 Conservation of Angular Momentum
- 11.4 Precession of a Gyroscope
- 12.1 Conditions for Static Equilibrium
- 12.2 Examples of Static Equilibrium
- 12.3 Stress, Strain, and Elastic Modulus
- 12.4 Elasticity and Plasticity
- 13.1 Newton's Law of Universal Gravitation
- 13.2 Gravitation Near Earth's Surface
- 13.3 Gravitational Potential Energy and Total Energy
- 13.4 Satellite Orbits and Energy
- 13.5 Kepler's Laws of Planetary Motion
- 13.6 Tidal Forces
- 13.7 Einstein's Theory of Gravity
- 14.1 Fluids, Density, and Pressure
- 14.2 Measuring Pressure
- 14.3 Pascal's Principle and Hydraulics
- 14.4 Archimedes’ Principle and Buoyancy
- 14.5 Fluid Dynamics
- 14.6 Bernoulli’s Equation
- 14.7 Viscosity and Turbulence
- 15.1 Simple Harmonic Motion
- 15.2 Energy in Simple Harmonic Motion
- 15.3 Comparing Simple Harmonic Motion and Circular Motion
- 15.4 Pendulums
- 15.5 Damped Oscillations
- 15.6 Forced Oscillations
- 16.1 Traveling Waves
- 16.2 Mathematics of Waves
- 16.3 Wave Speed on a Stretched String
- 16.4 Energy and Power of a Wave
- 16.5 Interference of Waves
- 16.6 Standing Waves and Resonance
- 17.1 Sound Waves
- 17.2 Speed of Sound
- 17.3 Sound Intensity
- 17.4 Normal Modes of a Standing Sound Wave
- 17.5 Sources of Musical Sound
- 17.7 The Doppler Effect
- 17.8 Shock Waves
- B | Conversion Factors
- C | Fundamental Constants
- D | Astronomical Data
- E | Mathematical Formulas
- F | Chemistry
- G | The Greek Alphabet
Learning Objectives
By the end of this section, you will be able to:
- Explain the rules for drawing a free-body diagram
- Construct free-body diagrams for different situations
The first step in describing and analyzing most phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams have been used in examples throughout this chapter. Remember that a free-body diagram must only include the external forces acting on the body of interest. Once we have drawn an accurate free-body diagram, we can apply Newton’s first law if the body is in equilibrium (balanced forces; that is, F net = 0 F net = 0 ) or Newton’s second law if the body is accelerating (unbalanced force; that is, F net ≠ 0 F net ≠ 0 ).
In Forces , we gave a brief problem-solving strategy to help you understand free-body diagrams. Here, we add some details to the strategy that will help you in constructing these diagrams.
Problem-Solving Strategy
Constructing free-body diagrams.
Observe the following rules when constructing a free-body diagram:
- Draw the object under consideration; it does not have to be artistic. At first, you may want to draw a circle around the object of interest to be sure you focus on labeling the forces acting on the object. If you are treating the object as a particle (no size or shape and no rotation), represent the object as a point. We often place this point at the origin of an xy -coordinate system.
- Include all forces that act on the object, representing these forces as vectors. Consider the types of forces described in Common Forces —normal force, friction, tension, and spring force—as well as weight and applied force. Do not include the net force on the object. With the exception of gravity, all of the forces we have discussed require direct contact with the object. However, forces that the object exerts on its environment must not be included. We never include both forces of an action-reaction pair.
- Convert the free-body diagram into a more detailed diagram showing the x - and y -components of a given force (this is often helpful when solving a problem using Newton’s first or second law). In this case, place a squiggly line through the original vector to show that it is no longer in play—it has been replaced by its x - and y -components.
- If there are two or more objects, or bodies, in the problem, draw a separate free-body diagram for each object.
Note: If there is acceleration, we do not directly include it in the free-body diagram; however, it may help to indicate acceleration outside the free-body diagram. You can label it in a different color to indicate that it is separate from the free-body diagram.
Let’s apply the problem-solving strategy in drawing a free-body diagram for a sled. In Figure 5.31 (a), a sled is pulled by force P at an angle of 30 ° 30 ° . In part (b), we show a free-body diagram for this situation, as described by steps 1 and 2 of the problem-solving strategy. In part (c), we show all forces in terms of their x - and y -components, in keeping with step 3.
Example 5.14
Two blocks on an inclined plane.
We now include any force that acts on the body. Here, no applied force is present. The weight of the object acts as a force pointing vertically downward, and the presence of the cord indicates a force of tension pointing away from the object. Object A has one interface and hence experiences a normal force, directed away from the interface. The source of this force is object B, and this normal force is labeled accordingly. Since object B has a tendency to slide down, object A has a tendency to slide up with respect to the interface, so the friction f BA f BA is directed downward parallel to the inclined plane.
As noted in step 4 of the problem-solving strategy, we then construct the free-body diagram in Figure 5.32 (b) using the same approach. Object B experiences two normal forces and two friction forces due to the presence of two contact surfaces. The interface with the inclined plane exerts external forces of N B N B and f B f B , and the interface with object B exerts the normal force N AB N AB and friction f AB f AB ; N AB N AB is directed away from object B, and f AB f AB is opposing the tendency of the relative motion of object B with respect to object A.
Significance
Example 5.15, two blocks in contact.
Example 5.16
Block on the table (coupled blocks).
Check Your Understanding 5.10
(a) Draw the free-body diagram for the situation shown. (b) Redraw it showing components; use x -axes parallel to the two ramps.
Interactive
Engage the simulation below to predict, qualitatively, how an external force will affect the speed and direction of an object’s motion. Explain the effects with the help of a free-body diagram. Use free-body diagrams to draw position, velocity, acceleration, and force graphs, and vice versa. Explain how the graphs relate to one another. Given a scenario or a graph, sketch all four graphs.
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- Book title: University Physics Volume 1
- Publication date: Sep 19, 2016
- Location: Houston, Texas
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Problem-Solving Flowchart: A Visual Method to Find Perfect Solutions
Reading time: about 7 min
Posted by: Lucid Content Team
“People ask me questions Lost in confusion Well, I tell them there's no problem Only solutions” —John Lennon, “Watching the Wheels”
Despite John Lennon’s lyrics, nobody is free from problems, and that’s especially true in business. Chances are that you encounter some kind of problem at work nearly every day, and maybe you’ve had to “put out a fire” before lunchtime once or twice in your career.
But perhaps what Lennon’s saying is that, no matter what comes our way, we can find solutions. How do you approach problems? Do you have a process in place to ensure that you and your co-workers come to the right solution?
In this article, we will give you some tips on how to find solutions visually through a problem-solving flowchart and other methods.
What is visual problem-solving?
If you are a literal thinker, you may think that visual problem-solving is something that your ophthalmologist does when your vision is blurry. For the rest of us, visual problem-solving involves executing the following steps in a visual way:
- Define the problem.
- Brainstorm solutions.
- Pick a solution.
- Implement solutions.
- Review the results.
Learn more about the steps involved in the problem-solving process .
How to make your problem-solving process more visual
Words pack a lot of power and are very important to how we communicate on a daily basis. Using words alone, you can brainstorm, organize data, identify problems, and come up with possible solutions. The way you write your ideas may make sense to you, but it may not be as easy for other team members to follow.
When you use flowcharts, diagrams, mind maps, and other visuals, the information is easier to digest. Your eyes dart around the page quickly gathering information, more fully engaging your brain to find patterns and make sense of the data.
Identify the problem with mind maps
So you know there is a problem that needs to be solved. Do you know what that problem is? Is there only one problem? Is the problem sum total of a bunch of smaller problems?
You need to ask these kinds of questions to be sure that you are working on the root of the issue. You don’t want to spend too much time and energy solving the wrong problem.
To help you identify the problem, use a mind map. Mind maps can help you visually brainstorm and collect ideas without a strict organization or structure. A mind map more closely aligns with the way a lot of our brains work—participants can bounce from one thought to the next defining the relationships as they go.
Mind mapping to solve a problem includes, but is not limited to, these relatively easy steps:
- In the center of the page, add your main idea or concept (in this case, the problem).
- Branch out from the center with possible root causes of the issue. Connect each cause to the central idea.
- Branch out from each of the subtopics with examples or additional details about the possible cause. As you add more information, make sure you are keeping the most important ideas closer to the main idea in the center.
- Use different colors, diagrams, and shapes to organize the different levels of thought.
Alternatively, you could use mind maps to brainstorm solutions once you discover the root cause. Search through Lucidchart’s template library or add the mind map shape library to quickly start your own mind map.
Create a problem-solving flowchart
A mind map is generally a good tool for non-linear thinkers. However, if you are a linear thinker—a person who thinks in terms of step-by-step progression making a flowchart may work better for your problem-solving strategy. A flowchart is a graphical representation of a workflow or process with various shapes connected by arrows representing each step.
Whether you are trying to solve a simple or complex problem, the steps you take to solve that problem with a flowchart are easy and straightforward. Using boxes and other shapes to represent steps, you connect the shapes with arrows that will take you down different paths until you find the logical solution at the end.
Flowcharts or decision trees are best used to solve problems or answer questions that are likely to come up multiple times. For example, Yoder Lumber , a family-owned hardwood manufacturer, built decision trees in Lucidchart to demonstrate what employees should do in the case of an injury.
To start your problem-solving flowchart, follow these steps:
- Draw a starting shape to state your problem.
- Draw a decision shape where you can ask questions that will give you yes-or-no answers.
- Based on the yes-or-no answers, draw arrows connecting the possible paths you can take to work through the steps and individual processes.
- Continue following paths and asking questions until you reach a logical solution to the stated problem.
- Try the solution. If it works, you’re done. If it doesn’t work, review the flowchart to analyze what may have gone wrong and rework the flowchart until you find the solution that works.
If your problem involves a process or workflow , you can also use flowcharts to visualize the current state of your process to find the bottleneck or problem that’s costing your company time and money.
Lucidchart has a large library of flowchart templates to help you analyze, design, and document problem-solving processes or any other type of procedure you can think of.
Draw a cause-and-effect diagram
A cause-and-effect diagram is used to analyze the relationship between an event or problem and the reason it happened. There is not always just one underlying cause of a problem, so this visual method can help you think through different potential causes and pinpoint the actual cause of a stated problem.
Cause-and-effect diagrams, created by Kaoru Ishikawa, are also known as Ishikawa diagrams, fishbone diagrams , or herringbone diagrams (because they resemble a fishbone when completed). By organizing causes and effects into smaller categories, these diagrams can be used to examine why things went wrong or might go wrong.
To perform a cause-and-effect analysis, follow these steps.
1. Start with a problem statement.
The problem statement is usually placed in a box or another shape at the far right of your page. Draw a horizontal line, called a “spine” or “backbone,” along the center of the page pointing to your problem statement.
2. Add the categories that represent possible causes.
For example, the category “Materials” may contain causes such as “poor quality,” “too expensive,” and “low inventory.” Draw angled lines (or “bones”) that branch out from the spine to these categories.
3. Add causes to each category.
Draw as many branches as you need to brainstorm the causes that belong in each category.
Like all visuals and diagrams, a cause-and-effect diagram can be as simple or as complex as you need it to be to help you analyze operations and other factors to identify causes related to undesired effects.
Collaborate with Lucidchart
You may have superior problem-solving skills, but that does not mean that you have to solve problems alone. The visual strategies above can help you engage the rest of your team. The more involved the team is in the creation of your visual problem-solving narrative, the more willing they will be to take ownership of the process and the more invested they will be in its outcome.
In Lucidchart, you can simply share the documents with the team members you want to be involved in the problem-solving process. It doesn’t matter where these people are located because Lucidchart documents can be accessed at any time from anywhere in the world.
Whatever method you decide to use to solve problems, work with Lucidchart to create the documents you need. Sign up for a free account today and start diagramming in minutes.
Start diagramming with Lucidchart today—try it for free!
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About lucidchart.
Lucidchart is the intelligent diagramming application that empowers teams to clarify complexity, align their insights, and build the future—faster. With this intuitive, cloud-based solution, everyone can work visually and collaborate in real time while building flowcharts, mockups, UML diagrams, and more.
The most popular online Visio alternative , Lucidchart is utilized in over 180 countries by millions of users, from sales managers mapping out target organizations to IT directors visualizing their network infrastructure.
Related posts:
How You Can Use Creative Problem Solving at Work
Dialogue Mapping 101: How to Solve Problems Through Visuals
5 Newton’s Laws of Motion
5.7 drawing free-body diagrams, learning objectives.
By the end of the section, you will be able to:
- Explain the rules for drawing a free-body diagram
- Construct free-body diagrams for different situations
The first step in describing and analyzing most phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams have been used in examples throughout this chapter. Remember that a free-body diagram must only include the external forces acting on the body of interest. Once we have drawn an accurate free-body diagram, we can apply Newton’s first law if the body is in equilibrium (balanced forces; that is, [latex] {F}_{\text{net}}=0 [/latex]) or Newton’s second law if the body is accelerating (unbalanced force; that is, [latex] {F}_{\text{net}}\ne 0 [/latex]).
In Forces , we gave a brief problem-solving strategy to help you understand free-body diagrams. Here, we add some details to the strategy that will help you in constructing these diagrams.
Problem-Solving Strategy: Constructing Free-Body Diagrams
Observe the following rules when constructing a free-body diagram:
- Draw the object under consideration; it does not have to be artistic. At first, you may want to draw a circle around the object of interest to be sure you focus on labeling the forces acting on the object. If you are treating the object as a particle (no size or shape and no rotation), represent the object as a point. We often place this point at the origin of an xy -coordinate system.
- Include all forces that act on the object, representing these forces as vectors. Consider the types of forces described in Common Forces —normal force, friction, tension, and spring force—as well as weight and applied force. Do not include the net force on the object. With the exception of gravity, all of the forces we have discussed require direct contact with the object. However, forces that the object exerts on its environment must not be included. We never include both forces of an action-reaction pair.
- Convert the free-body diagram into a more detailed diagram showing the x – and y -components of a given force (this is often helpful when solving a problem using Newton’s first or second law). In this case, place a squiggly line through the original vector to show that it is no longer in play—it has been replaced by its x – and y -components.
- If there are two or more objects, or bodies, in the problem, draw a separate free-body diagram for each object.
Note: If there is acceleration, we do not directly include it in the free-body diagram; however, it may help to indicate acceleration outside the free-body diagram. You can label it in a different color to indicate that it is separate from the free-body diagram.
Let’s apply the problem-solving strategy in drawing a free-body diagram for a sled. In (Figure) (a), a sled is pulled by force P at an angle of [latex] 30\text{°} [/latex]. In part (b), we show a free-body diagram for this situation, as described by steps 1 and 2 of the problem-solving strategy. In part (c), we show all forces in terms of their x – and y -components, in keeping with step 3.
Figure 5.31 (a) A moving sled is shown as (b) a free-body diagram and (c) a free-body diagram with force components.
Two Blocks on an Inclined Plane
Construct the free-body diagram for object A and object B in (Figure) .
We follow the four steps listed in the problem-solving strategy.
We start by creating a diagram for the first object of interest. In (Figure) (a), object A is isolated (circled) and represented by a dot.
Figure 5.32 (a) The free-body diagram for isolated object A. (b) The free-body diagram for isolated object B. Comparing the two drawings, we see that friction acts in the opposite direction in the two figures. Because object A experiences a force that tends to pull it to the right, friction must act to the left. Because object B experiences a component of its weight that pulls it to the left, down the incline, the friction force must oppose it and act up the ramp. Friction always acts opposite the intended direction of motion.
We now include any force that acts on the body. Here, no applied force is present. The weight of the object acts as a force pointing vertically downward, and the presence of the cord indicates a force of tension pointing away from the object. Object A has one interface and hence experiences a normal force, directed away from the interface. The source of this force is object B, and this normal force is labeled accordingly. Since object B has a tendency to slide down, object A has a tendency to slide up with respect to the interface, so the friction [latex] {f}_{\text{BA}} [/latex] is directed downward parallel to the inclined plane.
As noted in step 4 of the problem-solving strategy, we then construct the free-body diagram in (Figure) (b) using the same approach. Object B experiences two normal forces and two friction forces due to the presence of two contact surfaces. The interface with the inclined plane exerts external forces of [latex] {N}_{\text{B}} [/latex] and [latex] {f}_{\text{B}} [/latex], and the interface with object B exerts the normal force [latex] {N}_{\text{AB}} [/latex] and friction [latex] {f}_{\text{AB}} [/latex]; [latex] {N}_{\text{AB}} [/latex] is directed away from object B, and [latex] {f}_{\text{AB}} [/latex] is opposing the tendency of the relative motion of object B with respect to object A.
Significance
The object under consideration in each part of this problem was circled in gray. When you are first learning how to draw free-body diagrams, you will find it helpful to circle the object before deciding what forces are acting on that particular object. This focuses your attention, preventing you from considering forces that are not acting on the body.
Two Blocks in Contact
A force is applied to two blocks in contact, as shown.
Draw a free-body diagram for each block. Be sure to consider Newton’s third law at the interface where the two blocks touch.
Significance[latex] {\overset{\to }{A}}_{21} [/latex] is the action force of block 2 on block 1. [latex] {\overset{\to }{A}}_{12} [/latex] is the reaction force of block 1 on block 2. We use these free-body diagrams in Applications of Newton’s Laws .
Block on the Table (Coupled Blocks)
A block rests on the table, as shown. A light rope is attached to it and runs over a pulley. The other end of the rope is attached to a second block. The two blocks are said to be coupled. Block [latex] {m}_{2} [/latex] exerts a force due to its weight, which causes the system (two blocks and a string) to accelerate.
We assume that the string has no mass so that we do not have to consider it as a separate object. Draw a free-body diagram for each block.
Each block accelerates (notice the labels shown for [latex] {\overset{\to }{a}}_{1} [/latex] and [latex] {\overset{\to }{a}}_{2} [/latex]); however, assuming the string remains taut, they accelerate at the same rate. Thus, we have [latex] {\overset{\to }{a}}_{1}={\overset{\to }{a}}_{2} [/latex]. If we were to continue solving the problem, we could simply call the acceleration [latex] \overset{\to }{a} [/latex]. Also, we use two free-body diagrams because we are usually finding tension T , which may require us to use a system of two equations in this type of problem. The tension is the same on both [latex] {m}_{1}\,\text{and}\,{m}_{2} [/latex].
Check Your Understanding
(a) Draw the free-body diagram for the situation shown. (b) Redraw it showing components; use x -axes parallel to the two ramps.
View this simulation to predict, qualitatively, how an external force will affect the speed and direction of an object’s motion. Explain the effects with the help of a free-body diagram. Use free-body diagrams to draw position, velocity, acceleration, and force graphs, and vice versa. Explain how the graphs relate to one another. Given a scenario or a graph, sketch all four graphs.
- To draw a free-body diagram, we draw the object of interest, draw all forces acting on that object, and resolve all force vectors into x – and y -components. We must draw a separate free-body diagram for each object in the problem.
- A free-body diagram is a useful means of describing and analyzing all the forces that act on a body to determine equilibrium according to Newton’s first law or acceleration according to Newton’s second law.
Key Equations
Conceptual questions.
In completing the solution for a problem involving forces, what do we do after constructing the free-body diagram? That is, what do we apply?
If a book is located on a table, how many forces should be shown in a free-body diagram of the book? Describe them.
A ball of mass m hangs at rest, suspended by a string. (a) Sketch all forces. (b) Draw the free-body diagram for the ball.
A car moves along a horizontal road. Draw a free-body diagram; be sure to include the friction of the road that opposes the forward motion of the car.
A runner pushes against the track, as shown. (a) Provide a free-body diagram showing all the forces on the runner. ( Hint: Place all forces at the center of his body, and include his weight.) (b) Give a revised diagram showing the xy -component form.
The traffic light hangs from the cables as shown. Draw a free-body diagram on a coordinate plane for this situation.
Additional Problems
Two small forces, [latex] {\overset{\to }{F}}_{1}=-2.40\hat{i}-6.10t\hat{j} [/latex] N and [latex] {\overset{\to }{F}}_{2}=8.50\hat{i}-9.70\hat{j} [/latex] N, are exerted on a rogue asteroid by a pair of space tractors. (a) Find the net force. (b) What are the magnitude and direction of the net force? (c) If the mass of the asteroid is 125 kg, what acceleration does it experience (in vector form)? (d) What are the magnitude and direction of the acceleration?
Two forces of 25 and 45 N act on an object. Their directions differ by [latex] 70\text{°} [/latex]. The resulting acceleration has magnitude of [latex] 10.0\,{\text{m/s}}^{2}. [/latex] What is the mass of the body?
A force of 1600 N acts parallel to a ramp to push a 300-kg piano into a moving van. The ramp is inclined at [latex] 20\text{°} [/latex]. (a) What is the acceleration of the piano up the ramp? (b) What is the velocity of the piano when it reaches the top if the ramp is 4.0 m long and the piano starts from rest?
Draw a free-body diagram of a diver who has entered the water, moved downward, and is acted on by an upward force due to the water which balances the weight (that is, the diver is suspended).
For a swimmer who has just jumped off a diving board, assume air resistance is negligible. The swimmer has a mass of 80.0 kg and jumps off a board 10.0 m above the water. Three seconds after entering the water, her downward motion is stopped. What average upward force did the water exert on her?
(a) Find an equation to determine the magnitude of the net force required to stop a car of mass m , given that the initial speed of the car is [latex] {v}_{0} [/latex] and the stopping distance is x . (b) Find the magnitude of the net force if the mass of the car is 1050 kg, the initial speed is 40.0 km/h, and the stopping distance is 25.0 m.
a. [latex] {F}_{\text{net}}=\frac{m({v}^{2}-{v}_{0}{}^{2})}{2x} [/latex]; b. 2590 N
A sailboat has a mass of [latex] 1.50\,×\,{10}^{3} [/latex] kg and is acted on by a force of [latex] 2.00\,×\,{10}^{3} [/latex] N toward the east, while the wind acts behind the sails with a force of [latex] 3.00\,×\,{10}^{3} [/latex] N in a direction [latex] 45\text{°} [/latex] north of east. Find the magnitude and direction of the resulting acceleration.
Find the acceleration of the body of mass 10.0 kg shown below.
A body of mass 2.0 kg is moving along the x -axis with a speed of 3.0 m/s at the instant represented below. (a) What is the acceleration of the body? (b) What is the body’s velocity 10.0 s later? (c) What is its displacement after 10.0 s?
Force [latex] {\overset{\to }{F}}_{\text{B}} [/latex] has twice the magnitude of force [latex] {\overset{\to }{F}}_{\text{A}}. [/latex] Find the direction in which the particle accelerates in this figure.
(We add [latex] 180\text{°} [/latex], because the angle is in quadrant IV.)
Shown below is a body of mass 1.0 kg under the influence of the forces [latex] {\overset{\to }{F}}_{A} [/latex], [latex] {\overset{\to }{F}}_{B} [/latex], and [latex] m\overset{\to }{g} [/latex]. If the body accelerates to the left at [latex] 20\,{\text{m/s}}^{2} [/latex], what are [latex] {\overset{\to }{F}}_{A} [/latex] and [latex] {\overset{\to }{F}}_{B} [/latex]?
A force acts on a car of mass m so that the speed v of the car increases with position x as [latex] v=k{x}^{2} [/latex], where k is constant and all quantities are in SI units. Find the force acting on the car as a function of position.
[latex] F=2kmx [/latex]; First, take the derivative of the velocity function to obtain [latex] a=2kx [/latex]. Then apply Newton’s second law [latex] F=ma=m(2kx)=2kmx [/latex].
A 7.0-N force parallel to an incline is applied to a 1.0-kg crate. The ramp is tilted at [latex] 20\text{°} [/latex] and is frictionless. (a) What is the acceleration of the crate? (b) If all other conditions are the same but the ramp has a friction force of 1.9 N, what is the acceleration?
Two boxes, A and B, are at rest. Box A is on level ground, while box B rests on an inclined plane tilted at angle [latex] \theta [/latex] with the horizontal. (a) Write expressions for the normal force acting on each block. (b) Compare the two forces; that is, tell which one is larger or whether they are equal in magnitude. (c) If the angle of incline is [latex] 10\text{°} [/latex], which force is greater?
a. For box A, [latex] {N}_{\text{A}}=mg [/latex] and [latex] {N}_{\text{B}}=mg\,\text{cos}\,\theta [/latex]; b. [latex] {N}_{\text{A}}>{N}_{\text{B}} [/latex] because for [latex] \theta <90\text{°} [/latex], [latex] \text{cos}\,\theta <1 [/latex]; c. [latex] {N}_{\text{A}}>{N}_{\text{B}} [/latex] when [latex] \theta =10\text{°} [/latex]
As shown below, two identical springs, each with the spring constant 20 N/m, support a 15.0-N weight. (a) What is the tension in spring A? (b) What is the amount of stretch of spring A from the rest position?
Shown below is a 30.0-kg block resting on a frictionless ramp inclined at [latex] 60\text{°} [/latex] to the horizontal. The block is held by a spring that is stretched 5.0 cm. What is the force constant of the spring?
In building a house, carpenters use nails from a large box. The box is suspended from a spring twice during the day to measure the usage of nails. At the beginning of the day, the spring stretches 50 cm. At the end of the day, the spring stretches 30 cm. What fraction or percentage of the nails have been used?
0.40 or 40%
A force is applied to a block to move it up a [latex] 30\text{°} [/latex] incline. The incline is frictionless. If [latex] F=65.0\,\text{N} [/latex] and [latex] M=5.00\,\text{kg} [/latex], what is the magnitude of the acceleration of the block?
Two forces are applied to a 5.0-kg object, and it accelerates at a rate of [latex] 2.0\,{\text{m/s}}^{2} [/latex] in the positive y -direction. If one of the forces acts in the positive x -direction with magnitude 12.0 N, find the magnitude of the other force.
The block on the right shown below has more mass than the block on the left ([latex] {m}_{2}>{m}_{1} [/latex]). Draw free-body diagrams for each block.
Challenge Problems
If two tugboats pull on a disabled vessel, as shown here in an overhead view, the disabled vessel will be pulled along the direction indicated by the result of the exerted forces. (a) Draw a free-body diagram for the vessel. Assume no friction or drag forces affect the vessel. (b) Did you include all forces in the overhead view in your free-body diagram? Why or why not?
Show Solution
b. No; [latex] {\overset{\to }{F}}_{\text{R}} [/latex] is not shown, because it would replace [latex] {\overset{\to }{F}}_{1} [/latex] and [latex] {\overset{\to }{F}}_{2} [/latex]. (If we want to show it, we could draw it and then place squiggly lines on [latex] {\overset{\to }{F}}_{1} [/latex] and [latex] {\overset{\to }{F}}_{2} [/latex] to show that they are no longer considered.
A 10.0-kg object is initially moving east at 15.0 m/s. Then a force acts on it for 2.00 s, after which it moves northwest, also at 15.0 m/s. What are the magnitude and direction of the average force that acted on the object over the 2.00-s interval?
On June 25, 1983, shot-putter Udo Beyer of East Germany threw the 7.26-kg shot 22.22 m, which at that time was a world record. (a) If the shot was released at a height of 2.20 m with a projection angle of [latex] 45.0\text{°} [/latex], what was its initial velocity? (b) If while in Beyer’s hand the shot was accelerated uniformly over a distance of 1.20 m, what was the net force on it?
a. 14.1 m/s; b. 601 N
A body of mass m moves in a horizontal direction such that at time t its position is given by [latex] x(t)=a{t}^{4}+b{t}^{3}+ct, [/latex] where a , b , and c are constants. (a) What is the acceleration of the body? (b) What is the time-dependent force acting on the body?
A body of mass m has initial velocity [latex] {v}_{0} [/latex] in the positive x -direction. It is acted on by a constant force F for time t until the velocity becomes zero; the force continues to act on the body until its velocity becomes [latex] \text{−}{v}_{0} [/latex] in the same amount of time. Write an expression for the total distance the body travels in terms of the variables indicated.
[latex] \frac{F}{m}{t}^{2} [/latex]
The velocities of a 3.0-kg object at [latex] t=6.0\,\text{s} [/latex] and [latex] t=8.0\,\text{s} [/latex] are [latex] (3.0\hat{i}-6.0\hat{j}+4.0\hat{k})\,\text{m/s} [/latex] and [latex] (-2.0\hat{i}+4.0\hat{k})\,\text{m/s} [/latex], respectively. If the object is moving at constant acceleration, what is the force acting on it?
A 120-kg astronaut is riding in a rocket sled that is sliding along an inclined plane. The sled has a horizontal component of acceleration of [latex] 5.0\,\text{m}\text{/}{\text{s}}^{2} [/latex] and a downward component of [latex] 3.8\,\text{m}\text{/}{\text{s}}^{2} [/latex]. Calculate the magnitude of the force on the rider by the sled. ( Hint : Remember that gravitational acceleration must be considered.)
Two forces are acting on a 5.0-kg object that moves with acceleration [latex] 2.0\,{\text{m/s}}^{2} [/latex] in the positive y -direction. If one of the forces acts in the positive x -direction and has magnitude of 12 N, what is the magnitude of the other force?
Suppose that you are viewing a soccer game from a helicopter above the playing field. Two soccer players simultaneously kick a stationary soccer ball on the flat field; the soccer ball has mass 0.420 kg. The first player kicks with force 162 N at [latex] 9.0\text{°} [/latex] north of west. At the same instant, the second player kicks with force 215 N at [latex] 15\text{°} [/latex] east of south. Find the acceleration of the ball in [latex] \hat{i} [/latex] and [latex] \hat{j} [/latex] form.
[latex] [/latex][latex] \overset{\to }{a}=-248\hat{i}-433\hat{j}\text{m}\text{/}{\text{s}}^{2} [/latex]
A 10.0-kg mass hangs from a spring that has the spring constant 535 N/m. Find the position of the end of the spring away from its rest position. (Use [latex] g=9.80\,{\text{m/s}}^{2} [/latex].)
A 0.0502-kg pair of fuzzy dice is attached to the rearview mirror of a car by a short string. The car accelerates at constant rate, and the dice hang at an angle of [latex] 3.20\text{°} [/latex] from the vertical because of the car’s acceleration. What is the magnitude of the acceleration of the car?
[latex] 0.548\,{\text{m/s}}^{2} [/latex]
At a circus, a donkey pulls on a sled carrying a small clown with a force given by [latex] 2.48\hat{i}+4.33\hat{j}\,\text{N} [/latex]. A horse pulls on the same sled, aiding the hapless donkey, with a force of [latex] 6.56\hat{i}+5.33\hat{j}\,\text{N} [/latex]. The mass of the sled is 575 kg. Using [latex] \hat{i} [/latex] and [latex] \hat{j} [/latex] form for the answer to each problem, find (a) the net force on the sled when the two animals act together, (b) the acceleration of the sled, and (c) the velocity after 6.50 s.
Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m , and they are equally spaced by a distance d , as shown. The angles labeled [latex] \theta [/latex] describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal, labeled [latex] \varphi [/latex]. Let [latex] {T}_{1} [/latex] be the tension in the leftmost section of the string, [latex] {T}_{2} [/latex] be the tension in the section adjacent to it, and [latex] {T}_{3} [/latex] be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables m , g , and [latex] \theta [/latex]. (b) Find the angle [latex] \varphi [/latex] in terms of the angle [latex] \theta [/latex]. (c) If [latex] \theta =5.10\text{°} [/latex], what is the value of [latex] \varphi [/latex]? (d) Find the distance x between the endpoints in terms of d and [latex] \theta [/latex].
A bullet shot from a rifle has mass of 10.0 g and travels to the right at 350 m/s. It strikes a target, a large bag of sand, penetrating it a distance of 34.0 cm. Find the magnitude and direction of the retarding force that slows and stops the bullet.
An object is acted on by three simultaneous forces: [latex] {\overset{\to }{F}}_{1}=(-3.00\hat{i}+2.00\hat{j})\,\text{N} [/latex], [latex] {\overset{\to }{F}}_{2}=(6.00\hat{i}-4.00\hat{j})\,\text{N} [/latex], and [latex] {\overset{\to }{F}}_{3}=(2.00\hat{i}+5.00\hat{j})\,\text{N} [/latex]. The object experiences acceleration of [latex] 4.23\,{\text{m/s}}^{2} [/latex]. (a) Find the acceleration vector in terms of m . (b) Find the mass of the object. (c) If the object begins from rest, find its speed after 5.00 s. (d) Find the components of the velocity of the object after 5.00 s.
a. [latex] \overset{\to }{a}=(\frac{5.00}{m}\hat{i}+\frac{3.00}{m}\hat{j})\,\text{m}\text{/}{\text{s}}^{2}; [/latex] b. 1.38 kg; c. 21.2 m/s; d. [latex] \overset{\to }{v}=(18.1\hat{i}+10.9\hat{j})\,\text{m}\text{/}{\text{s}}^{2} [/latex]
In a particle accelerator, a proton has mass [latex] 1.67\,×\,{10}^{-27}\,\text{kg} [/latex] and an initial speed of [latex] 2.00\,×\,{10}^{5}\,\text{m}\text{/}\text{s.} [/latex] It moves in a straight line, and its speed increases to [latex] 9.00\,×\,{10}^{5}\,\text{m}\text{/}\text{s} [/latex] in a distance of 10.0 cm. Assume that the acceleration is constant. Find the magnitude of the force exerted on the proton.
A drone is being directed across a frictionless ice-covered lake. The mass of the drone is 1.50 kg, and its velocity is [latex] 3.00\hat{i}\text{m}\text{/}\text{s} [/latex]. After 10.0 s, the velocity is [latex] 9.00\hat{i}+4.00\hat{j}\text{m}\text{/}\text{s} [/latex]. If a constant force in the horizontal direction is causing this change in motion, find (a) the components of the force and (b) the magnitude of the force.
a. [latex] 0.900\hat{i}+0.600\hat{j}\,\text{N} [/latex]; b. 1.08 N
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Example on solving with free body diagramsA ball is rolling at 6.00 m/s and takes 6.00 m to come to a stop as it rolls across the floor.
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Construct the free-body diagram for object A and object B in Figure 5.8. 1. Strategy We follow the four steps listed in the problem-solving strategy. Solution We start by creating a diagram for the first object of interest. In Figure 5.8. 2 a, object A is isolated (circled) and represented by a dot.
Introduction to free body diagrams Google Classroom A block of cheese B B hangs from the ceiling by rope 1 1. A wheel of cheese W W hangs from the block of cheese by rope 2 2. What is the correct free body diagram for the wheel of cheese W W? Choose 1 answer: A B C D Stuck? Use a hint. Report a problem 7 4 1 x x y y \theta θ \pi π 8 5 2 0 9 6 3
Solving Force Problems in Physics by Using Free-Body Diagrams By: The Experts at Dummies Updated: 03-26-2016 From The Book: Physics I: 501 Practice Problems For Dummies (+ Free Online Practice) Physics I: 501 Practice Problems For Dummies (+ Free Online Practice) Explore Book Buy On Amazon
As illustrated in Newton's Laws of Motion, the system of interest depends on the question we need to answer. Only forces are shown in free-body diagrams, not acceleration or velocity. We have drawn several free-body diagrams in previous worked examples. Figure 6.2.1c shows a free-body diagram for the system of interest.
Sketch the situation, using arrows to represent all forces. Determine the system of interest. The result is a free-body diagram that is essential to solving the problem. Apply Newton's second law to solve the problem. If necessary, apply appropriate kinematic equations from the chapter on motion along a straight line.
Once a free-body diagram is drawn, we apply Newton's second law. This is done in Figure(d) for a particular situation. In general, once external forces are clearly identified in free-body diagrams, it should be a straightforward task to put them into equation form and solve for the unknown, as done in all previous examples.
Free Body Simulation ( Simulations ) | Physics | CK-12 Foundation. Free Body Simulation. Learn how to draw free body diagrams. Full Screen.
the problem statements not only did not facilitate problem solving, but also impeded it significantly. Particularly large between group differences, in favor of the group not provided with FBDs, were detected for problems that required use of free-body diagrams showing resolution of forces into components. The results of our study indicate
A free-body diagram is a diagram that is modified as the problem is solved. Normally, a free body diagram consists of the following components: A simplified version of the body (most commonly a box) A coordinate system Forces are represented as arrows pointing in the direction they act on the body
Learn how to solve problems that have Free Body Diagrams! This is an AP Physics 1 topic. Content Times: 0:15 Step 1) Draw the Free Body Diagram 0:50 Step 2) Break Forces into Components 1:37 Step 3) Redraw the Free Body Diagram 2:15 Step 4) Sum the Forces 2:45 Step 5) Sum the Forces (again) 3:13 Review the 5 Steps Multilingual? Please help translate Flipping Physics videos!
From Free-Body Diagram to Solution Drawing a free-body diagram is the first step in determining the acceleration of a mass using Newton's second law: Σ F = ma. Sometimes, a problem will...
Problem Solving Using Free Body Diagrams Problem Solving 1 Loading... Found a content error? Tell us Notes/Highlights Image Attributions Show Details Show Resources Was this helpful? Yes No
A free body diagram is a tool used to solve engineering mechanics problems. As the name suggests, the purpose of the diagram is to "free" the body from all other objects and surfaces around it so that it can be studied in isolation.
Construct the free-body diagram for object A and object B in Figure. Strategy We follow the four steps listed in the problem-solving strategy. Solution We start by creating a diagram for the first object of interest. In Figure (a), object A is isolated (circled) and represented by a dot.
Learn how to draw a free-body diagram for use in solving physics problems. Every problem in physics begins with drawing a free body diagram because that is how we represent all...
Learn about Newton's Third Law, force calculations in two dimensions, and the interaction of multiple objects in the context of a horse pulling a cart using our interactive simulation. Horse and Cart (Free Body Diagrams, Problem Solving Using Free Body Diagrams) | Physics | CK-12 Exploration Series
Use free-body diagrams to draw position, velocity, acceleration, and force graphs, and vice versa. Explain how the graphs relate to one another. Given a scenario or a graph, sketch all four graphs. Click to view content Previous Next Order a print copy As an Amazon Associate we earn from qualifying purchases. Citation/Attribution
Free body diagram solver - Math can be a challenging subject for many students. But there is help available in the form of Free body diagram solver. ... Learn how to solve problems that have Free Body Diagrams! This is an AP Physics 1 topic. Calculating forces using free. This lab activity helps students explore the concept of free body ...
To solve free body diagrams all forces in any direction must be taken into consideration. Start with identifying the north and south vectors or y-components. One acts in the positive...
Mind mapping to solve a problem includes, but is not limited to, these relatively easy steps: In the center of the page, add your main idea or concept (in this case, the problem). Branch out from the center with possible root causes of the issue. Connect each cause to the central idea.
Let's apply the problem-solving strategy in drawing a free-body diagram for a sled. In (Figure) (a), a sled is pulled by force P at an angle of 30° 30 °. In part (b), we show a free-body diagram for this situation, as described by steps 1 and 2 of the problem-solving strategy. In part (c), we show all forces in terms of their x - and y ...
Learn how to solve problems that have Free Body Diagrams! This is an AP Physics 1 topic. More ways to get app. Construction of Free Example on solving with free body diagramsA ball is rolling at 6.00 m/s and takes 6.00 m to come to a stop as it rolls across the floor. Calculating forces using free ...