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Problems & Exercises

1.2 physical quantities and units.

The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?

A car is traveling at a speed of 33 m/s 33 m/s size 12{"33"" m/s"} {} . (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h 90 km/h size 12{"90"" km/h"} {} speed limit?

Show that 1 . 0 m/s = 3 . 6 km/h 1 . 0 m/s = 3 . 6 km/h size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {} . Hint: Show the explicit steps involved in converting 1 . 0 m/s = 3 . 6 km/h. 1 . 0 m/s = 3 . 6 km/h. size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {}

American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)

What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)

Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)

The speed of sound is measured to be 342 m/s 342 m/s size 12{"342"" m/s"} {} on a certain day. What is this in km/h?

Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

(a) Refer to Table 1.3 to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?

1.3 Accuracy, Precision, and Significant Figures

Express your answers to problems in this section to the correct number of significant figures and proper units.

Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?

(a) A car speedometer has a 5.0 % 5.0 % size 12{5.0%} {} uncertainty. What is the range of possible speeds when it reads 90 km/h 90 km/h size 12{"90"" km/h"} {} ? (b) Convert this range to miles per hour. 1 km = 0.6214 mi 1 km = 0.6214 mi size 12{"1 km" "=" "0.6214 mi"} {}

An infant’s pulse rate is measured to be 130 ± 5 130 ± 5 size 12{"130" +- 5} {} beats/min. What is the percent uncertainty in this measurement?

(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

A can contains 375 mL of soda. How much is left after 308 mL is removed?

State how many significant figures are proper in the results of the following calculations: (a) 106 . 7 98 . 2 / 46 . 210 1 . 01 106 . 7 98 . 2 / 46 . 210 1 . 01 size 12{ left ("106" "." 7 right ) left ("98" "." 2 right )/ left ("46" "." "210" right ) left (1 "." "01" right )} {} (b) 18 . 7 2 18 . 7 2 size 12{ left ("18" "." 7 right ) rSup { size 8{2} } } {} (c) 1 . 60 × 10 − 19 3712 1 . 60 × 10 − 19 3712 size 12{ left (1 "." "60" times "10" rSup { size 8{ - "19"} } right ) left ("3712" right )} {} .

(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?

(a) If your speedometer has an uncertainty of 2 . 0 km/h 2 . 0 km/h size 12{2 "." 0" km/h"} {} at a speed of 90 km/h 90 km/h size 12{"90"" km/h"} {} , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h 60 km/h size 12{"60"" km/h"} {} , what is the range of speeds you could be going?

(a) A person’s blood pressure is measured to be 120 ± 2 mm Hg 120 ± 2 mm Hg size 12{"120" +- 2" mm Hg"} {} . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg 80 mm Hg size 12{"80"" mm Hg"} {} ?

A person measures his or her heart rate by counting the number of beats in 30 s 30 s size 12{"30"" s"} {} . If 40 ± 1 40 ± 1 size 12{"40" +- 1} {} beats are counted in 30 . 0 ± 0 . 5 s 30 . 0 ± 0 . 5 s size 12{"30" "." 0 +- 0 "." 5" s"} {} , what is the heart rate and its uncertainty in beats per minute?

What is the area of a circle 3 . 102 cm 3 . 102 cm size 12{3 "." "102"" cm"} {} in diameter?

If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon?

A marathon runner completes a 42 . 188 -km 42 . 188 -km size 12{"42" "." "188""-km"} {} course in 2 h 2 h size 12{2" h"} {} , 30 min, and 12 s 12 s size 12{"12"" s"} {} . There is an uncertainty of 25 m 25 m size 12{"25"" m"} {} in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

The sides of a small rectangular box are measured to be 1 . 80 ± 0 . 01 cm 1 . 80 ± 0 . 01 cm size 12{1 "." "80" +- 0 "." "01"" cm"} {} , {} 2 . 05 ± 0 . 02 cm, and 3 . 1 ± 0 . 1 cm 2 . 05 ± 0 . 02 cm, and 3 . 1 ± 0 . 1 cm size 12{2 "." "05" +- 0 "." "02"" cm, and 3" "." 1 +- 0 "." "1 cm"} {} long. Calculate its volume and uncertainty in cubic centimeters.

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where 1 lbm = 0 . 4539 kg 1 lbm = 0 . 4539 kg size 12{1" lbm"=0 "." "4539"`"kg"} {} . (a) If there is an uncertainty of 0 . 0001 kg 0 . 0001 kg size 12{0 "." "0001"`"kg"} {} in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

The length and width of a rectangular room are measured to be 3 . 955 ± 0 . 005 m 3 . 955 ± 0 . 005 m size 12{3 "." "955" +- 0 "." "005"" m"} {} and 3 . 050 ± 0 . 005 m 3 . 050 ± 0 . 005 m size 12{3 "." "050" +- 0 "." "005"" m"} {} . Calculate the area of the room and its uncertainty in square meters.

A car engine moves a piston with a circular cross section of 7 . 500 ± 0 . 002 cm 7 . 500 ± 0 . 002 cm size 12{7 "." "500" +- 0 "." "002"`"cm"} {} diameter a distance of 3 . 250 ± 0 . 001 cm 3 . 250 ± 0 . 001 cm size 12{3 "." "250" +- 0 "." "001"`"cm"} {} to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.

1.4 Approximation

How many heartbeats are there in a lifetime?

A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?

How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of 10 − 22  s 10 − 22  s size 12{"10" rSup { size 8{ - "22"} } " s"} {} .)

Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of 10 − 27  kg 10 − 27  kg size 12{"10" rSup { size 8{ - "27"} } " kg"} {} and the mass of a bacterium is on the order of 10 − 15  kg. 10 − 15  kg. size 12{"10" rSup { size 8{ - "15"} } "kg"} {} )

Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?

(a) What fraction of Earth’s diameter is the greatest ocean depth? (b) The greatest mountain height?

(a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?

Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?

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• Authors: Paul Peter Urone, Roger Hinrichs
• Publisher/website: OpenStax
• Book title: College Physics
• Publication date: Jun 21, 2012
• Location: Houston, Texas
• Book URL: https://openstax.org/books/college-physics/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units
• Section URL: https://openstax.org/books/college-physics/pages/1-problems-exercises

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1.1: The Basics of Physics

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Introduction: Physics and Matter

Physics is a study of how the universe behaves.

learning objectives

• Apply physics to describe the function of daily life

Physics is a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the study of nature in an attempt to understand how the universe behaves.

What is Physics? : Mr. Andersen explains the importance of physics as a science. History and virtual examples are used to give the discipline context.

Physics uses the scientific method to help uncover the basic principles governing light and matter, and to discover the implications of those laws. It assumes that there are rules by which the universe functions, and that those laws can be at least partially understood by humans. It is also commonly believed that those laws could be used to predict everything about the universe’s future if complete information was available about the present state of all light and matter.

Matter is generally considered to be anything that has mass and volume. Many concepts integral to the study of classical physics involve theories and laws that explain matter and its motion. The law of conservation of mass, for example, states that mass cannot be created or destroyed. Further experiments and calculations in physics, therefore, take this law into account when formulating hypotheses to try to explain natural phenomena.

Physics aims to describe the function of everything around us, from the movement of tiny charged particles to the motion of people, cars, and spaceships. In fact, almost everything around you can be described quite accurately by the laws of physics. Consider a smart phone; physics describes how electricity interacts with the various circuits inside the device. This knowledge helps engineers select the appropriate materials and circuit layout when building the smart phone. Next, consider a GPS system; physics describes the relationship between the speed of an object, the distance over which it travels, and the time it takes to travel that distance. When you use a GPS device in a vehicle, it utilizes these physics equations to determine the travel time from one location to another. The study of physics is capable of making significant contributions through advances in new technologies that arise from theoretical breakthroughs.

Global Positioning System : GPS calculates the speed of an object, the distance over which it travels, and the time it takes to travel that distance using equations based on the laws of physics.

Physics and Other Fields

Physics is the foundation of many disciplines and contributes directly to chemistry, astronomy, engineering, and most scientific fields.

• Explain why the study of physics is integral to the study of other sciences

Physics and Other Disciplines

Physics is the foundation of many important disciplines and contributes directly to others. Chemistry deals with the interactions of atoms and molecules, so it is rooted in atomic and molecular physics. Most branches of engineering are applied physics. In architecture, physics is at the heart of structural stability and is involved in acoustics, heating, lighting, and the cooling of buildings. Parts of geology rely heavily on physics, such as the radioactive dating of rocks, earthquake analysis, and heat transfer in the Earth. Some disciplines, such as biophysics and geophysics, are hybrids of physics and other disciplines.

Physics in Chemistry : The study of matter and electricity in physics is fundamental towards the understanding of concepts in chemistry, such as the covalent bond.

Physics has many applications in the biological sciences. On the microscopic level, it helps describe the properties of cell walls and cell membranes. On the macroscopic level, it can explain the heat, work, and power associated with the human body. Physics is involved in medical diagnostics, such as X-rays, magnetic resonance imaging (MRI), and ultrasonic blood flow measurements. Medical therapy sometimes directly involves physics: cancer radiotherapy uses ionizing radiation, for instance. Physics can also explain sensory phenomena, such as how musical instruments make sound, how the eye detects color, and how lasers can transmit information.

The boundary between physics and the other sciences is not always clear. For instance, chemists study atoms and molecules, which are what matter is built from, and there are some scientists who would be equally willing to call themselves physical chemists or chemical physicists. It might seem that the distinction between physics and biology would be clearer, since physics seems to deal with inanimate objects. In fact, almost all physicists would agree that the basic laws of physics that apply to molecules in a test tube work equally well for the combination of molecules that constitutes a bacterium. What differentiates physics from biology is that many of the scientific theories that describe living things ultimately result from the fundamental laws of physics, but cannot be rigorously derived from physical principles.

It is not necessary to formally study all applications of physics. What is most useful is the knowledge of the basic laws of physics and skill in the analytical methods for applying them. The study of physics can also improve your problem-solving skills. Furthermore, physics has retained the most basic aspects of science, so it is used by all of the sciences. The study of physics makes other sciences easier to understand.

Models, Theories, and Laws

The terms model , theory , and law have exact meanings in relation to their usage in the study of physics.

• Define the terms model, theory, and law

Definition of Terms: Model, Theory, Law

In colloquial usage, the terms model , theory , and law are often used interchangeably or have different interpretations than they do in the sciences. In relation to the study of physics, however, each term has its own specific meaning.

The laws of nature are concise descriptions of the universe around us. They are not explanations, but human statements of the underlying rules that all natural processes follow. They are intrinsic to the universe; humans did not create them and we cannot change them. We can only discover and understand them. The cornerstone of discovering natural laws is observation; science must describe the universe as it is, not as we may imagine it to be. Laws can never be known with absolute certainty, because it is impossible to perform experiments to establish and confirm a law in every possible scenario without exception. Physicists operate under the assumption that all scientific laws and theories are valid until a counterexample is observed. If a good-quality, verifiable experiment contradicts a well-established law, then the law must be modified or overthrown completely.

A model is a representation of something that is often too difficult (or impossible) to display directly. While a model’s design is justified using experimental information, it is only accurate under limited situations. An example is the commonly used “planetary model” of the atom, in which electrons are pictured as orbiting the nucleus, analogous to the way planets orbit the Sun. We cannot observe electron orbits directly, but the mental image helps explain the observations we can make, such as the emission of light from hot gases. Physicists use models for a variety of purposes. For example, models can help physicists analyze a scenario and perform a calculation, or they can be used to represent a situation in the form of a computer simulation.

Planetary Model of an Atom : The planetary model of the atom in which electrons are pictured as orbiting the nucleus, analogous to the way planets orbit the Sun

A theory is an explanation for patterns in nature that is supported by scientific evidence and verified multiple times by various groups of researchers. Some theories include models to help visualize phenomena, whereas others do not . Newton’s theory of gravity, for example, does not require a model or mental image, because we can observe the objects directly with our own senses. The kinetic theory of gases, on the other hand, makes use of a model in which a gas is viewed as being composed of atoms and molecules. Atoms and molecules are too small to be observed directly with our senses—thus, we picture them mentally to understand what our instruments tell us about the behavior of gases.

A law uses concise language to describe a generalized pattern in nature that is supported by scientific evidence and repeated experiments. Often, a law can be expressed in the form of a single mathematical equation. Laws and theories are similar in that they are both scientific statements that result from a tested hypothesis and are supported by scientific evidence. However, the designation law is reserved for a concise and very general statement that describes phenomena in nature, such as the law that energy is conserved during any process, or Newton’s second law of motion, which relates force, mass, and acceleration by the simple equation \(F=ma\). A theory, in contrast, is a less concise statement of observed phenomena. For example, the Theory of Evolution and the Theory of Relativity cannot be expressed concisely enough to be considered a law. The biggest difference between a law and a theory is that a law is much more complex and dynamic, and a theory is more explanatory. A law describes a single observable point of fact, whereas a theory explains an entire group of related phenomena. And, whereas a law is a postulate that forms the foundation of the scientific method, a theory is the end result of that process.

• Physics is a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force.
• Matter is generally considered to be anything that has mass and volume.
• Scientific laws and theories express the general truths of nature and the body of knowledge they encompass. These laws of nature are rules that all natural processes appear to follow.
• Many scientific disciplines, such as biophysics, are hybrids of physics and other sciences.
• The study of physics encompasses all forms of matter and its motion in space and time.
• The application of physics is fundamental towards significant contributions in new technologies that arise from theoretical breakthroughs.
• Concepts in physics cannot be proven, they can only be supported or disproven through observation and experimentation.
• A model is an evidence-based representation of something that is either too difficult or impossible to display directly.
• A theory is an explanation for patterns in nature that is supported by scientific evidence and verified multiple times by various groups of researchers.
• A law uses concise language, often expressed as a mathematical equation, to describe a generalized pattern in nature that is supported by scientific evidence and repeated experiments.
• matter : The basic structural component of the universe. Matter usually has mass and volume.
• scientific method : A method of discovering knowledge about the natural world based in making falsifiable predictions (hypotheses), testing them empirically, and developing peer-reviewed theories that best explain the known data.
• application : the act of putting something into operation
• Model : A representation of something difficult or impossible to display directly
• Law : A concise description, usually in the form of a mathematical equation, used to describe a pattern in nature
• theory : An explanation for patterns in nature that is supported by scientific evidence and verified multiple times by various groups of researchers

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Check Your Understanding

Answer: d = 1720 m

Answer: a = 8.10 m/s/s

Answers: d = 33.1 m and v f = 25.5 m/s

Answers: a = 11.2 m/s/s and d = 79.8 m

Answer: t = 1.29 s

Answers: a = 243 m/s/s

Answer: a = 0.712 m/s/s

Answer: d = 704 m

Answer: d = 28.6 m

Answer: v i = 7.17 m/s

Answer: v i = 5.03 m/s and hang time = 1.03 s (except for in sports commericals)

Answer: a = 1.62*10 5 m/s/s

Answer: d = 48.0 m

Answer: t = 8.69 s

Answer: a = -1.08*10^6 m/s/s

Answer: d = -57.0 m (57.0 meters deep) 

Answer: v i = 47.6 m/s

Answer: a = 2.86 m/s/s and t = 30. 8 s

Answer: a = 15.8 m/s/s

Answer: v i = 94.4 mi/hr

Solutions to Above Problems

d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s 2 )*(32.8 s) 2

Return to Problem 1

110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s) 2

110 m = (13.57 s 2 )*a

a = (110 m)/(13.57 s 2 )

a = 8.10 m/ s 2

Return to Problem 2

d = (0 m/s)*(2.60 s)+ 0.5*(-9.8 m/s 2 )*(2.60 s) 2

d = -33.1 m (- indicates direction)

v f = v i + a*t

v f = 0 + (-9.8 m/s 2 )*(2.60 s)

v f = -25.5 m/s (- indicates direction)

Return to Problem 3

a = (46.1 m/s - 18.5 m/s)/(2.47 s)

a = 11.2 m/s 2

d = v i *t + 0.5*a*t 2

d = (18.5 m/s)*(2.47 s)+ 0.5*(11.2 m/s 2 )*(2.47 s) 2

d = 45.7 m + 34.1 m

(Note: the d can also be calculated using the equation v f 2 = v i 2 + 2*a*d)

Return to Problem 4

-1.40 m = (0 m/s)*(t)+ 0.5*(-1.67 m/s 2 )*(t) 2

-1.40 m = 0+ (-0.835 m/s 2 )*(t) 2

(-1.40 m)/(-0.835 m/s 2 ) = t 2

1.68 s 2 = t 2

Return to Problem 5

a = (444 m/s - 0 m/s)/(1.83 s)

a = 243 m/s 2

d = (0 m/s)*(1.83 s)+ 0.5*(243 m/s 2 )*(1.83 s) 2

d = 0 m + 406 m

Return to Problem 6

(7.10 m/s) 2 = (0 m/s) 2 + 2*(a)*(35.4 m)

50.4 m 2 /s 2 = (0 m/s) 2 + (70.8 m)*a

(50.4 m 2 /s 2 )/(70.8 m) = a

a = 0.712 m/s 2

Return to Problem 7

(65 m/s) 2 = (0 m/s) 2 + 2*(3 m/s 2 )*d

4225 m 2 /s 2 = (0 m/s) 2 + (6 m/s 2 )*d

(4225 m 2 /s 2 )/(6 m/s 2 ) = d

Return to Problem 8

d = (22.4 m/s + 0 m/s)/2 *2.55 s

d = (11.2 m/s)*2.55 s

Return to Problem 9

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(2.62 m)

0 m 2 /s 2 = v i 2 - 51.35 m 2 /s 2

51.35 m 2 /s 2 = v i 2

v i = 7.17 m/s

Return to Problem 10

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(1.29 m)

0 m 2 /s 2 = v i 2 - 25.28 m 2 /s 2

25.28 m 2 /s 2 = v i 2

v i = 5.03 m/s

To find hang time, find the time to the peak and then double it.

0 m/s = 5.03 m/s + (-9.8 m/s 2 )*t up

-5.03 m/s = (-9.8 m/s 2 )*t up

(-5.03 m/s)/(-9.8 m/s 2 ) = t up

t up = 0.513 s

hang time = 1.03 s

Return to Problem 11

(521 m/s) 2 = (0 m/s) 2 + 2*(a)*(0.840 m)

271441 m 2 /s 2 = (0 m/s) 2 + (1.68 m)*a

(271441 m 2 /s 2 )/(1.68 m) = a

a = 1.62*10 5 m /s 2

Return to Problem 12

• (NOTE: the time required to move to the peak of the trajectory is one-half the total hang time - 3.125 s.)

First use:  v f  = v i  + a*t

0 m/s = v i  + (-9.8  m/s 2 )*(3.13 s)

0 m/s = v i  - 30.7 m/s

v i  = 30.7 m/s  (30.674 m/s)

Now use:  v f 2  = v i 2  + 2*a*d

(0 m/s) 2  = (30.7 m/s) 2  + 2*(-9.8  m/s 2 )*(d)

0 m 2 /s 2  = (940 m 2 /s 2 ) + (-19.6  m/s 2 )*d

-940  m 2 /s 2  = (-19.6  m/s 2 )*d

(-940  m 2 /s 2 )/(-19.6  m/s 2 ) = d

Return to Problem 13

-370 m = (0 m/s)*(t)+ 0.5*(-9.8 m/s 2 )*(t) 2

-370 m = 0+ (-4.9 m/s 2 )*(t) 2

(-370 m)/(-4.9 m/s 2 ) = t 2

75.5 s 2 = t 2

Return to Problem 14

(0 m/s) 2 = (367 m/s) 2 + 2*(a)*(0.0621 m)

0 m 2 /s 2 = (134689 m 2 /s 2 ) + (0.1242 m)*a

-134689 m 2 /s 2 = (0.1242 m)*a

(-134689 m 2 /s 2 )/(0.1242 m) = a

a = -1.08*10 6 m /s 2

(The - sign indicates that the bullet slowed down.)

Return to Problem 15

d = (0 m/s)*(3.41 s)+ 0.5*(-9.8 m/s 2 )*(3.41 s) 2

d = 0 m+ 0.5*(-9.8 m/s 2 )*(11.63 s 2 )

d = -57.0 m

(NOTE: the - sign indicates direction)

Return to Problem 16

(0 m/s) 2 = v i 2 + 2*(- 3.90 m/s 2 )*(290 m)

0 m 2 /s 2 = v i 2 - 2262 m 2 /s 2

2262 m 2 /s 2 = v i 2

v i = 47.6 m /s

Return to Problem 17

( 88.3 m/s) 2 = (0 m/s) 2 + 2*(a)*(1365 m)

7797 m 2 /s 2 = (0 m 2 /s 2 ) + (2730 m)*a

7797 m 2 /s 2 = (2730 m)*a

(7797 m 2 /s 2 )/(2730 m) = a

a = 2.86 m/s 2

88.3 m/s = 0 m/s + (2.86 m/s 2 )*t

(88.3 m/s)/(2.86 m/s 2 ) = t

t = 30. 8 s

Return to Problem 18

( 112 m/s) 2 = (0 m/s) 2 + 2*(a)*(398 m)

12544 m 2 /s 2 = 0 m 2 /s 2 + (796 m)*a

12544 m 2 /s 2 = (796 m)*a

(12544 m 2 /s 2 )/(796 m) = a

a = 15.8 m/s 2

Return to Problem 19

v f 2 = v i 2 + 2*a*d

(0 m/s) 2 = v i 2 + 2*(-9.8 m/s 2 )*(91.5 m)

0 m 2 /s 2 = v i 2 - 1793 m 2 /s 2

1793 m 2 /s 2 = v i 2

v i = 42.3 m/s

Now convert from m/s to mi/hr:

v i = 42.3 m/s * (2.23 mi/hr)/(1 m/s)

v i = 94.4 mi/hr

Return to Problem 20

25+ Most Important Physics Topics For Students

          “Physics: the mysterious subject for students.”

It is great to make a command on basics first if you want to master that subject. It is the scenario with every field of study. Someone who wants to study physics must clear his/her basic concepts and be familiar with its topics like kinetic energy, potential energy, statistical mechanics, etc.

    “Curiosity is the road that leads you to learn physics.”

In this blog, we will tell you what physics is and some important physics topics that will help in your daily life. We will tell you what physics is and how you can understand it.

Physics students learn about important physics topics by reading this blog. So, hang on and know everything about physics!

Get experts help to get top-notch Physics help online that will help you to improve your grades on your assignment.

What Is Physics?

Table of Contents

When we look at the things around us, many questions are in our minds. Physics gives the answers to all these questions. You all must have heard about chemistry and biology. There are a lot of applications of physics with different aspects of nature.

Chemistry tells us about the results of things, and biology studies the processes of real life. But only physics tells us how things work. And if you need chemistry assignment help , you can contact our experts. 

For example: As you look at a car running on the road, the question comes to your mind how does this car run on the road, how does its engine work, and how does a small brake pedal stop the entire car? The answer to all these questions is physics. Also, angular momentum is part of physics.

Physics tells us how things work. Many physics topics help us to understand the concept of nature and the universe. From the galaxy to the small atom, we can understand all these through physics.

The term physics is derived from the Greek word PHUSIKE, which means nature and its study. Energy, force, light, and time are all very basic concepts that we study in physics.

What Are The Topics Of Basic Physics?

These are the following topics of basic physics, and it is such as;

Subject Matter Topics for Introductory Physics

The following are the subject matter topics for introductory physics. It is also the best Physics topics for College students.

Reasons: Why do students choose to study physics in their higher education?

A physics degree helps you explore the world in every aspect- from the galaxy and the small atom with electronic structure. It equips you with techniques that help you to solve complex problems. It lets you know about some beautiful things and the plain ugly truth that rule our world. In reality, analyzing physics provides you with a deep knowledge of how the world works.

With the help of physics knowledge, many students want to pursue it by taking a postgraduate course related to it. It describes the various physics mysteries. 

Five reasons to study physics at college-

• Experimental Physics encourages you to know the world around you and answer your curiosity.
• Analyzing physics improves your problem-solving and critical-thinking skills.
• Versatility is the essence of physicists, which opens a broad range of future careers.
• Physics is applied everywhere and gives you a chance to work internationally.
• Physics encourages technological progress, influencing society, the economy, and the environment.

List Of Important School Physics Topics

• History of quantum mechanics
• Newton’s Laws Of Motion
• Vectors And Projectiles
• Work And Energy
• Circular Motion And Gravitation

Electric Circuits

Thermal physics.

• Vibrations And Waves
• Refraction And Lenses

There are many branches of Physics, one of which is named Mechanics, and Mechanics has three branches, one of which is named Kinematics. Kinematics is one of the most important physics topics.

Kinematics means describing the motion of an object. In kinematics, we only study the object’s motion, why that object, and who brings it into action is not related to kinematics.

Kinematics also has four parameters: velocity, displacement, acceleration, and time. With the help of these four parameters, we can describe motion in kinematics. For any assignment or homework above the kinematics subject, you can take help from our experts.

Newton’s Laws of Motion

Newton’s Law is One of the Most Important Physics Topics. Newton’s Law of Motion consists of three laws, based on which all things related to motion can be known. Newton’s law of motion consists of three laws. From these laws, we can know all things related to motion.

The first law of Newton’s law states Uniform Motion and is also called the Law of inertia. In the second Newton’s Law, the force is said to be, which is directly proportional to the square of acceleration. And in the third Newton’s law, it is said that every action has an equal and opposite reaction.

These three newton’s law of motion is a very important part of physics topics. If you are studying physics, then definitely read this topic, if any problem arises, you can take help related to physics assignments and homework from our experts.

Vectors and Projectiles

Vectors and Projectiles are one of the third most important physics topics. Vectors and projectiles both have different meanings, but they are related to each other, only then they are considered to be the same topic.

Arrows represent vectors. The length of the Arrow is Proportional to the Magnitude, and the Direction of the Arrow is to be the Direction of the Vector that defines the vector. And projectile means that after throwing any object, it goes down due to gravity.

This is a very interesting topic, if you are a student of physics, then you must read this topic, and if you need help with any assignment or homework related to it, then you can take it from our experts.

Work and Energy

Work and energy are the two words that we often use in everyday life, but this is a very important physics topic. Work and energy have different meanings in physics.

Work means that energy is transferred by force, and energy means the ability to work. Each other’s words are fulfilling the meaning of these two. It is a very interesting physics topic, on top of which you can also write many assignments.

Circular Motion and Gravitation

Circular Motion and Gravitation are very interesting physics topics. It is said that forces can be used in circular motion and gravitation.

Circular motion means when a body moves in a circular path at a content speed and constant direction. And gravitation means that if we throw an object upwards, that object will go back to the top of the force according to the Cause of Gravity.

Electric circuits are one of the physics topics that tell us in detail about electric circuits. Both positive and negative are electric field circuits. This is explained by what works and how they work.

Electric circuits refer to the positive current coming out of a cell and generator with a wire connected to the negative circuit with the help of a wire. This is a very interesting chapter for physics students and can also offer many models and assignments on this topic.

Thermal physics is also a very important part of physics topics. Thermal physics is a topic that exposes students to many new things.

The study of thermal physics is done by heat. Heat energy and thermal energies are the motions and vibrations of molecules in terms of the energy activity of any substance or system. If there are more molecules in it, the same energy will be found in it. This is a very interesting topic for students, and many assignments can be made on it.

Vibrations and Waves

Vibrations and Waves On hearing this word, your mind must have heard thoughts related to the sound. But vibrations and waves are also part of physics topics. Vibrations and waves are very important in physics. Also, know How do convex mirrors impact your reflection?

Vibrations mean that if we shake with a big pay force, then that body keeps vibrating for some time due to that force, that vibration is called vibration. A wave can be described as a disturbance that travels from one medium to another through a medium. They are both from advance quantum physics , and students can make many models and assignments on them to get the aim of physics.

Refraction and Lenses

Refraction and lenses are some of the most interesting and important physics topics. All this topic is based on refraction and lenses. Students need to know how light lanes affect refraction through their theoretical physicist.

We can determine whether the light will reflect or refract by placing the ray of light on the lens in the refraction and lenses. It is also one of the interesting topics for the students, and with the help of this topic, students can also make many physics assignments.

Bonus point: list of interesting topics for a physics research project-

Here we mention some physics research topics that you can take and prepare a project on it-

• Nanoscience and Nanotechnology
• Optical Physics and Quantum Information Science
• Astrophysics, Fusion, and Plasma Physics
• Create a project on physics history
• Climate-related topic
• Linear motion.
• Circular and Rotational Motion.
• Interactions and Force. 
• Motion in Two-Dimensions.

Physics topics for assignment

Follow the below-given physics topics list for the assignment.

• Unit dimensions and Error.
• Conservation of Momentum.
• Laws of Motion.
• Circular Motion.
• Motion in two dimensions.
• Work power and energy.

What is the best topic for physics project?

The best topic for the physics project for science and engineering practices: analyzing and s below.

Physics Topics Grade 11

Following are the topics in physics with their chapter name.

Physics topics for Class 12

Following are the physics topics are given below for the 12th grade.

Which topic is best for research in physics?

Follow the below-given points to know the physics topics for research.

• Optical Physics and Quantum Information Science.
• Astrophysics, Fusion, and Plasma Physics.
• Microfluidics and Microsystems.
• Nanoscience and Nanotechnology. 
• Condensed Matter and Materials Physics.
• Energy Systems. 
• Biophysics. 

Interesting topics for physics presentation

Best physics topics on mcat.

These are the following best physics topics for MCAT.

• Electrostatics.
• Atomic and Nuclear Phenomena.
• Kinematics.
• Light and Optics.
• Thermodynamics.

How is physics used in daily life?

Physics captures our daily life. It explains the motion, forces, and internal energy behind ordinary works. For example, various actions like driving a car, walking, or using a phone call include advances in physics.

Let’s understand it through examples-

1. Example of heat

Heat is a kind of energy that carries from a warm object to a cold object. For example, when you use the stove for cooking, the flame transfers the heat to the utensil put on top of it. As a result, food gets heat from utensils. Physical optics must account for the more subtle properties of visible light in its waveform.

2. Example of a ballpoint pen

The use of a ballpoint pen is inevitable whether you are in school or at the workplace. If physics is not there, then you are not able to write on paper. The physics topics of gravity come when we talk about writing through a ballpoint pen.

As you press the pen on the paper to write, the ball turns, or gravity pushes the ink down on the ball top, from where it is transferred to the paper.

Useful point for students-

Job opportunities after studying physics-

A physics degree opens the door to various post for students-

• Academic researcher
• Acoustic consultant
• Clinical scientist, medical physics
• Geophysicist
• Higher education lecturer
• Metallurgist
• Meteorologist
• Nanotechnologist
• Radiation protection practitioner
• Research scientist (physical sciences)
• Secondary school teacher
• Sound engineer
• Technical author

What are the 5 laws of physics?

These are the 5 laws of physics, it is given below.

• Pascal’s Law 
• Newton’s Laws 
• Coulomb’s Law 
• Stefan’s Law
• Avagadro’s Law

Quick Links

• A Brief Knowledge Of Kinematics Physics Equations
• The Definitive Guide On What Is Cartesian Equation

In this blog, we have explained what Physics means and which important Physics topics are there, which students can study with great interest. These all are 20th century physics topics. Moreover, many such physics topics have been told about which students can make their physics assignments and research projects. Moreover, if you need help with physics assignments, our experts offer Physics assignment help or physics homework help online free at very low prices.

Who is the father of physics?

The title “father of physics” has not been assigned to a particular person. Galileo Galilei, Sir Isaac, Albert Einstein, and Newton have all been considered the father of physics in western cultures.

What are the physics concepts everyone should know?

1. Classical mechanics (the laws of motion) 2. Electromagnetism 3. Relativity 4. Thermodynamics

What are the three main topics of physics?

The three main topics of physics are given below. Circular Motion (one-dimensional motion, two-dimensional motion, random motion, Harmonic motion) and Gravitation. Electric Circuits. Refraction and Lenses.

Which topic is hard in physics?

The hardest topic of physics is Quantum physics, pressure, and energy, work, etc.

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Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force.

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Browse Course Material

Course info.

• Prof. Markus Klute

Departments

As taught in.

• Nuclear Physics
• Particle Physics

Learning Resource Types

Introduction to nuclear and particle physics, assignments, problem sets, paper presentation.

Below is a list of seminal papers in nuclear and particle physics. You are asked to form a team of two and pick a paper (first come first served). Please review the paper and prepare a 20-minute presentation summarizing the paper and also setting it into context. You can also suggest a paper not listed below.

Parity Violation

Experimental Test of Parity Conservation in Beta Decays

CP Violation

Evidence for the \(2\pi\) Decays of the \(K_2^0\) Meson

Observation of Single Isolated Electrons of High Transverse Momentum in Events with Missing Transverse Energy at the CERN pp Collider

Experimental Observation of Lepton Pairs of Invariant Mass around 95 GeV/c 2 at the CERN SPS Collider

Neutrino Oscillations

Evidence for Oscillation of Atmospheric Neutrinos

Higgs Boson

Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC

Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC

Possible Existence of a Neutron

Fermi’s Theory of Beta Decay

Fermi’s Theory of Beta Decay (PDF)

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Why Study Physics?

Want to know “how” and “why” learn physics..

Physics is crucial to understanding the world around us, the world inside us, and the world beyond us. It is the most fundamental science.

Physics challenges our imaginations with concepts like relativity and string theory. It leads to great discoveries that, in turn, bring life-changing technologies, like computers, GPS, and lasers. Physicists also work to solve some of the greatest challenges of our times by finding ways to cure cancer, heal joints, or develop solutions for sustainable energy.

Learn more about the work that physicists do by reading stories from real physicists on our Physicists Profiles and Career Options pages.

If you’re an educator looking for resources to incorporate into your middle or high school classroom, review APS’s PhysicsQuest and STEP UP projects.

Like science? It begins with physics

Physics encompasses the study of the universe from the largest galaxies to the smallest (subatomic!) particles.

Moreover, physics is the basis for many other sciences, including chemistry, oceanography, seismology, and astronomy, as well as the applied sciences, like the various branches of engineering. The principles of physics are also applied in many areas of biology and biomedical science. Advanced education in all of these areas — and more! — is possible with a bachelor’s degree in physics.

Want to learn real-world skills? Study physics!

Physicists are problem solvers. Their analytical skills make them versatile and adaptable, so physicists often work interesting jobs in interesting places. You can find physicists in industrial and government labs, on college campuses, in the astronaut corps, and consulting for the special effects in TV shows and movies. In addition, many physics grads work for engineering or consulting firms, at newspapers and magazines, in government, for non-profits, in data science and app development roles, and even on Wall Street — places where their ability to think analytically is a great asset.

In general, though, most physics majors continue in STEM-related careers or careers that require strong problem-solving skills. Data shows that nearly 4 in 10 physics majors continue in engineering professions, while 1 in 4 go into computer or information systems. Another 1 in 4 physics majors continue in another STEM pathway or a non-STEM career where they regularly solve technical problems.

Want a job? People hire physicists

Physics brings a broad perspective to any problem. Because physicists learn how to critically analyze and breakdown even the most complex problems, they are not bound by context. This form of inventive thinking makes physicists desirable in any field. A bachelor’s degree in physics is a great foundation for careers in:

• Computer Science
• Data Science
• Engineering

Want a good salary? Physics tops the sciences

Even when the job market is slow, physicists get well-paying job offers. Employers know that a physicist brings additional skills and expertise — and they pay accordingly! That's why physics graduates can expect career salaries similar to those of computer science and engineering majors.

As of 2020, data shows the mean starting salary for a physics major taking a job in the STEM private sector was about $65k annually, with students who chose non-STEM technical pathways earning slightly less, at about $50k. But some physics majors, depending on their interests and skills acquired during college, start at much higher salaries — $80k or more.

Like most fields of STEM, if you pursue advanced education, your salary increases . After completing a master’s degree, physicists earn an average of about $90k annually, and after a doctorate, physicists earn a starting salary of roughly $120k.

View physics career statistical data

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Spectrometer

Spectrometer is a spectroscope equipped with devices for measuring the frequencies of the radiation observed by it. Spectrometers were developed in early studies of physics, astronomy, and chemistry. It is the study of interactions between light and matter, and the reactions and measurements of radiation intensity and wavelength. The concept of a spectrometer now encompasses instruments that do not examine light.

While it provided a theoretical backing to early quantum research in radiation and atomic structure, it also has a staggering number of other applied uses; Magnetic Resonance Imaging (MRI) and X-ray machines utilise a form of radio-frequency spectroscopy, we measure the unique makeup and physical properties of distant astral bodies through their spectra and wavelength, and it’s even used to test doping in sports.

Spectrometers the chief instrument used in spectrometric analysis, which are specialised pieces of equipment that measure radiation types and wavelength. Spectrometers separate particles, atoms, and molecules by their mass, momentum, or energy. These types of spectrometers are used in chemical analysis and particle physics.

Types of Spectrometer

There are multiple fields of spectroscopy. Some of the potential fields and applications include:

Mass Spectronomy – Sorts and measures masses within a chemical sample through their mass-to-charge ratio. This is usually done by ionizing the particles with a shower of electrons, then passing them through a magnetic field to separate them into different stages of deflection.

Once the particles are separated, they’re measured by an electron multiplier, and we can identify the makeup of the sample through the weight of each ion’s mass. Practical uses of Mass Spectronomy include isotope dating and protein characterisation. Independant roving space exploration robots such as the Mars Phoenix Lander also carry mass spectrometers for analysis of foreign soils.

Matter and Energy – Spectrometry is based on interactions between matter and energy. A sample stimulated with a specific kind of energy will respond in a way that is characteristic of the sample. Depending on the method, a sample responds to an energy input by absorbing energy, releasing energy or perhaps even by undergoing a permanent physical change. If a sample gives no response in a particular instrument, there is information in that result as well.

Biomedical Spectroscopy – This is a great example of the multidisciplinary nature of spectroscopy. Magnetic resonance spectroscopy (a subset of MRI) is often used to diagnose and study chemical changes in the brain which can cause anything from depression to physical tumours, as well as analyse the metabolic structure of muscle. This works by mapping a spectrum of wavelengths in the brain that correspond to the known spectrum, and carefully analysing patterns and aberrations in those patterns.

Ultraviolet (UV) Spectrometers – Ultraviolet (UV) spectroscopy works on a principle similar to that of colorimetry, except it uses ultraviolet light. UV spectroscopy is also called electronic spectroscopy, because the results depend on the electrons in the chemical bonds of the sample compound. Researchers use UV spectrometers to study chemical bonding and to determine the concentrations of substances (nucleic acids for example) that do not interact with visible light.

Atomic Spectrometers – Atomic spectrometers are used to find the elemental composition of samples and to determine the concentrations of each element. There are two basic types of atomic spectrometers: emission and absorbance. In either case a flame burns the sample, breaking it down into atoms or ions of the elements present in the sample. An emission instrument detects the wavelengths of light released by the ionized atoms. In an absorbance instrument, light of specified wavelengths passes through the energized atoms to a detector. The wavelengths of the emissions or absorbances are characteristic of the elements present.

Modern Spectrometry

The study of spectrometry dates back to the 1600s, when Isaac Newton first discovered that focusing a light through glass split it into the different colours of the rainbow, also known as the spectrum of visible light. The spectrum itself is an obviously visible phenomenon; it’s makes up the colours of the rainbow and creates the sheen we will see on the surface of a puddle, but it took centuries of piecemeal research to develop the study of this phenomenon into a coherent field that could be used to draw usable conclusions.

Simply put, as natural light filters from space from celestial bodies such as the sun, it goes through various reactions in our atmosphere. Each chemical element reacts slightly differently in this process, some visibly, those on the 390-700mm wavelength which detectable to the human eye and some invisibly.

Reference:   atascientific.com ,  sciencing.com , dictionary.com , wikipedia .

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