# College Physics 2013

## Educators

### Problem 1

Relative motion on an airport walkway A person is walking on a moving walkway in the airport. Her speed with respect to the walkway is 2 $\mathrm{m} / \mathrm{s}$ . The speed of the walkway is 1 $\mathrm{m} / \mathrm{s}$ with respect to the floor. What is her speed with respect to a person walking on the floor in the opposite direction at the speed of 2 $\mathrm{m} / \mathrm{s} ?$

Zulfiqar A.

### Problem 2

Running on a treadmill Explain how you can run on a treadmill at 3 $\mathrm{m} / \mathrm{s}$ and remain at the same location.

Zulfiqar A.

### Problem 3

Describe the important parts of the Michelson-Morley experimental setup and explain how this setup could help them determine whether Earth moves with respect to ether. Explain how the setup relates to the previous problem.

Check back soon!

### Problem 4

Describe what Michelson and Morley would have observed when they rotated their spectrometer if Earth were moving through ether compared to what they would have observed if Earth were not moving through ether.

Check back soon!

### Problem 5

Person on a bus A person is sitting on a bus that stops suddenly, causing her head to tilt forward. (a) Explain the acceleration of her head from the point of view of an observer on the ground. (b) Explain the acceleration of her head from the point of view of another person on the bus. (c) Which observer is in an inertial reference frame?

Zulfiqar A.

### Problem 6

Turning on a rotating turntable A matchbox is placed on a rotating turntable. The turntable starts turning faster and faster. At some instant the matchbox flies off the turning table. (a) Draw a force diagram for the box when still on the rotating turntable. (b) Draw a force diagram for the box just before it flies off. (c) Explain why the box flies off only when the turntable reaches a certain speed. In what reference frame are you when providing this explanation? (d) How would a bug sitting on the turntable explain the same situation?

Check back soon!

### Problem 7

Use your knowledge of electromagnetic waves to give an example illustrating that if the speed of light were different in different inertial reference frames, two inertial frame observers would see the same phenomenon differently. [Hint: Think about radio waves.]

Check back soon!

### Problem 8

A particle called $\Sigma^{+}$ lives for $0.80 \times 10^{-10} \mathrm{s}$ in its proper reference frame before transforming into two other particles. How long does the $\Sigma^{+}$ seem to live according to a laboratory observer when the particle moves past the observer at a speed of $2.4 \times 10^{8} \mathrm{m} / \mathrm{s}$ ?

Zulfiqar A.

### Problem 9

The $\Sigma^{+}$ particle discussed in the previous problem appears to a laboratory observer to live for $1.0 \times 10^{-10}$ s. How fast is it moving relative to the observer?

Zulfiqar A.

### Problem 10

A person on Earth observes 10 flashes of the light on a passing spaceship in 22 s, whereas the same 10 flashes seem to take 12 s to an observer on the ship. What can you determine using this information?

Zulfiqar A.

### Problem 11

A spaceship moves away from Earth at a speed of 0.990$c$ . The pilot looks back and measures the time interval for one rotation of Earth on its axis. What time interval does the pilot measure? What assumptions did you make?

Zulfiqar A.

### Problem 12

Extending life? A free neutron lives about 1000 s before transforming into an electron and a proton. If a neutron leaves the Sun at a speed of $0.999c$, (a) how long does it live according to an Earth observer? (b) Will such a neutron reach Pluto ( $5.9 \times 10^{12} \mathrm{m}$ from the Sun) before transforming? Explain your answers.

Zulfiqar A.

### Problem 13

A $\Sigma^{+}$ particle lives $0.80 \times 10^{-10} \mathrm{s}$ in its proper reference frame. If it is traveling at 0.90$c$ through a bubble chamber, how far will it move before it disintegrates?

Zulfiqar A.

### Problem 14

Extending the life of a muon A muon that lives $2.2 \times 10^{-6} \mathrm{s}$ in its proper reference frame is created $10,000$ $\mathrm{m}$ above Earth's surface. At what speed must it move to reach Earth's surface at the instant it disintegrates?

Zulfiqar A.

### Problem 15

Effect of light speed on the time interval for a track race Suppose the speed of light were 15 $\mathrm{m} / \mathrm{s}$ . You run a $100-\mathrm{m}$ dace in 10 $\mathrm{s}$ according to the timer's clock. How long did the race last according to your watch?

Zulfiqar A.

### Problem 16

Explain why an object moving past you would seem shorter in the direction of motion than when at rest
with respect to you. Draw a sketch to illustrate your reasoning.

Check back soon!

### Problem 17

Explain why the length of an object that is oriented perpendicular to the direction of motion would be the same for all observers. Draw a sketch to illustrate your reasoning.

Check back soon!

### Problem 18

You sit in a spaceship moving past the Earth at 0.97 c. Your arm, held straight out in front of you, measures 50 $\mathrm{cm} .$ How long is it when measured by an observer on Earth?

Zulfiqar A.

### Problem 19

Length of a javelin A javelin hurled by Wonder Woman moves past an Earth observer at 0.90$c .$ Its proper length is 2.7 $\mathrm{m} .$ What is its length according to the Earth observer?

Zulfiqar A.

### Problem 20

At what speed must a meter stick move past an observer so that it appears to be 0.50 $\mathrm{m}$ long?

Check back soon!

### Problem 21

Changing the shape of a billboard A billboard is 10 $\mathrm{m}$ high and 15 $\mathrm{m}$ long according to a person standing in front of it. At what speed must a person in a fast car drive by parallel to the billboard's surface so that the billboard appears to be square?

Zulfiqar A.

### Problem 22

A classmate says that time dilation and length contraction can be remembered in a simple way if you think of a person eating a foot-long “sub” sandwich on a train (the sandwich is oriented parallel to the train’s motion). The person on the train finishes the sandwich in 20 min. You, standing on the platform, observe the person eating a shorter sandwich but for a longer time interval. Do you agree with this example? Explain your answer.

Zulfiqar A.

### Problem 23

Give examples of cases in which two observers record the motion of the same object to have different speeds, to have different directions, and to have different velocities. Provide reasonable values for the relevant velocities in your examples. Sketch each example and explain how each observer arrives at the value of the measured speed.

Check back soon!

### Problem 24

Now repeat Problem 23, only this time instead of a moving object, use a light flash. Describe what speeds of light different observers should measure according to the second postulate of special relativity.

Check back soon!

### Problem 25

Life in a slow-light-speed universe Imagine that you live in a universe where the speed of light is 50 $\mathrm{m} / \mathrm{s}$ . You sit on a train moving west at speed 20 $\mathrm{m} / \mathrm{s}$ relative to the track. Your friend moves on a train in the opposite direction at speed 15 $\mathrm{m} / \mathrm{s}$ What is the speed of his train with respect to yours?

Zulfiqar A.

### Problem 26

More slow-light-speed universe In the scenario described in Problem 25, you and your friend listen to music on the same radio station. What is the speed of the radio waves that your antenna is registering compared to the speed of the waves that your friend’s antenna registers if the station is 100 miles to the west of you?

Zulfiqar A.

### Problem 27

You are on a spaceship traveling at $0.80c$ with respect to a nearby star sending a laser beam to a spaceship following you, which is moving at $0.50c$ in the same direction. (a) What is the speed of the laser beam registered by the second ship’s personnel according to the classical addition of the velocities? (b) What is the speed of the laser beam registered by the second ship’s personnel according to the relativistic addition of the velocities? (c) What is the speed of the second ship with respect to yours according to the classical addition of the velocities? (d) What is the speed of the second ship with respect to yours according to the relativistic addition of the velocities?

Check back soon!

### Problem 28

Your friend says that it is easy to travel faster than the speed of light; you just need to find the right observer. Give physics-based reasons for why your friend would have such an idea. Then explain whether you agree or disagree with him.

Check back soon!

### Problem 29

Your friend argues that Einstein’s special theory of relativity says that nothing can move faster than the speed of light. (a) Give physics-based reasons for why your friend would have such an idea. (b) What examples of physical phenomena do you know of that contradict this statement? (c) Restate his idea so it is accurate in terms of physics.

Zulfiqar A.

### Problem 30

An electron is moving at a speed of $0.90c$. Compare its momentum as calculated using a non relativistic equation and using a relativistic equation.

Zulfiqar A.

### Problem 31

Explain why a relativistic expression is needed for fast-moving particles. Why can’t we use a classical expression?

Zulfiqar A.

### Problem 32

If you were to bring an electron from speed zero to $0.95c$ in 10 min, what force would need to be exerted on the electron? What object could possibly exert such a force?

Zulfiqar A.

### Problem 33

If a proton has a momentum of $3.00 \times 10^{-19} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s},$ what is its speed?

Zulfiqar A.

### Problem 34

Determine the ratio of an electron's total energy to rest energy when moving at the following speeds: (a) 300 $\mathrm{m} / \mathrm{s}$ , (b) $3.0 \times 10^{8} \mathrm{m} / \mathrm{s},$ (c) $3.0 \times 10^{7} \mathrm{m} / \mathrm{s},$ (d) $1.0 \times 10^{8} \mathrm{m} / \mathrm{s}$ (e) $2.0 \times 10^{8} \mathrm{m} / \mathrm{s},$ and ( $\mathrm{f} ) 2.9 \times 10^{8} \mathrm{m} / \mathrm{s} .$

Zulfiqar A.

### Problem 35

Solar wind To escape the gravitational pull of the Sun, a proton in the solar wind must have a speed of at least $6.2 \times 10^{5} \mathrm{m} / \mathrm{s}$ . Determine the rest energy, the kinetic energy, and the total energy of the proton.

Zulfiqar A.

### Problem 36

At what speed must an object move so that its total energy is 1.0$\%$ greater than its rest energy? 10$\%$ greater? Twice its rest energy?

Zulfiqar A.

### Problem 37

Space travel $A 50$ -kg space traveler starts at rest and accelerates at 5$g$ for 30 days. Determine the person's total energy after 30 days. What assumptions did you make?

Zulfiqar A.

### Problem 38

A person’s total energy is twice his rest energy when he moves at a certain speed. By what factor must his speed now increase to cause another doubling of his total energy?

Zulfiqar A.

### Problem 39

A proton’s energy after passing through the accelerator at Fermilab is 500 times its rest energy. Determine the proton’s speed.

Zulfiqar A.

### Problem 40

A rocket of mass $m$ starts at rest and accelerates to a speed of 0.90$c$ . Determine the change in energy needed for this change in speed.

Zulfiqar A.

### Problem 41

Determine the total energy, the rest energy, and the kinetic energy of a person with $60-\mathrm{kg}$ mass moving at speed 0.95$c .$

Zulfiqar A.

### Problem 42

An electron is accelerated from rest across $50,000 \mathrm{V}$ in a machine used to produce $\mathrm{X}$ -rays. Determine the electron's speed after crossing that potential difference.

Zulfiqar A.

### Problem 43

A particle originally moving at a speed 0.90$c$ experiences a 5.0$\%$ increase in speed. By what percent does its kinetic energy increase?

Zulfiqar A.

### Problem 44

An electron is accelerated from rest across a potential difference of $9.0 \times 10^{9} \mathrm{V}$ . Determine the electron's speed (a) using the nonrelativistic kinetic energy equation and (b) using
the relativistic kinetic energy equation. Which is the correct answer?

Zulfiqar A.

Zulfiqar A.

### Problem 76

Which answer below is closest to the power of light and other forms of radiation emitted by 3 $\mathrm{C} 273 ?$
(a) $\approx 10^{8} \mathrm{J} / \mathrm{s} \quad(\mathrm{b})=10^{18} \mathrm{J} / \mathrm{s}$
(c) $\approx 10^{25} \mathrm{Js} \quad(\mathrm{d}) \approx 10^{32} \mathrm{J} / \mathrm{s}$
(e) $\approx 10^{40} \mathrm{J} / \mathrm{s}$

Zulfiqar A.

### Problem 77

Which answer below is closest to the mass of 3 $\mathrm{C} 273$ that is converted to light and other forms of radiation each second?
By comparison, the mass of Earth is $6 \times 10^{24} \mathrm{kg}$ .
(a) $\approx 10^{11} \mathrm{kg} / \mathrm{s} \quad$ (b) $\approx 10^{15} \mathrm{kg} / \mathrm{s}$
(c) $\approx 10^{19} \mathrm{kg} / \mathrm{s} \quad(\mathrm{d}) \approx 10^{23} \mathrm{kg} / \mathrm{s}$
$(e) \approx 10^{29} \mathrm{kg} / \mathrm{s}$

Zulfiqar A.

### Problem 78

What is the speed of light emitted by 3 $\mathrm{C} 273$ as detected by an observer on 3 $\mathrm{C} 273 ?$
(a) 1.15$c \quad$ (b) $c$
(c) 0.85$c \quad$ (d) None of these is correct.

Zulfiqar A.
If 3 $\mathrm{C} 273$ is moving away from Earth at $0.16 c,$ what speed below is closest to the light speed we on Earth detect coming from 3 $\mathrm{C} 273 ?$
(a) 1.15$c \quad$ (b) $c$
(c) 0.85$c \quad$ (d) None of these is correct.