# Test Prep

### Multiple Choice

#### 10.1 Postulates of Special Relativity

What was the purpose of the Michelson–Morley experiment?

- To determine the exact speed of light
- To analyze the electromagnetic spectrum
- To establish that Earth is the true frame of reference
- To learn how the ether affected the propagation of light

- $1.86\times {10}^{5}\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $3.00\times {10}^{8}\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $6.71\times {10}^{8}\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $1.50\times {10}^{11}\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$

- $1.80\times {10}^{7}\phantom{\rule{thinmathspace}{0ex}}\text{km}$
- $1.80\times {10}^{13}\phantom{\rule{thinmathspace}{0ex}}\text{km}$
- $5.00\times {10}^{6}\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $5.00\times {10}^{8}\phantom{\rule{thinmathspace}{0ex}}\text{m}$

- Events may appear simultaneous in all frames of reference.
- Events may not appear simultaneous in all frames of reference.
- The speed of light is not the same in all frames of reference.
- The laws of physics may be different in different inertial frames of reference.

In 2003, Earth and Mars were aligned so that Earth was between Mars and the sun. Earth and Mars were 5.6×10^{7} km from each other, which was the closest they had been in 50,000 years. People looking up saw Mars as a very bright red light on the horizon. If Mars was 2.06×10^{8} km from the sun, how long did the reflected light people saw take to travel from the sun to Earth?

- 14 min and 33 s
- 12 min and 15 s
- 11 min and 27 s
- 3 min and 7 s

#### 10.2 Consequences of Special Relativity

What does this expression represent: $\frac{1}{\sqrt{1-\frac{{u}^{2}}{{c}^{2}}}}$

- time dilation
- relativistic factor
- relativistic energy
- length contraction

What is the rest energy, E_{0}, of an object with a mass of 1.00 g ?

- 3.00×10
^{5}J - 3.00×10
^{11}J - 9.00×10
^{13}J - 9.00×10
^{16}J

The fuel rods in a nuclear reactor must be replaced from time to time because so much of the radioactive material has reacted that they can no longer produce energy. How would the mass of the spent fuel rods compare to their mass when they were new? Explain your answer.

- The mass of the spent fuel rods would decrease.
- The mass of the spent fuel rods would increase.
- The mass of the spent fuel rods would remain the same.
- The mass of the spent fuel rods would become close to zero.

### Short Answer

#### 10.1 Postulates of Special Relativity

- The speed of light remains the same in all inertial frames of reference.
- The speed of light depends on the speed of the source emitting the light.
- The speed of light changes with change in medium through which it travels.
- The speed of light does not change with change in medium through which it travels.

What is the postulate having to do with reference frames on which the theory of special relativity is based?

- The frame of reference chosen is arbitrary as long as it is inertial.
- The frame of reference is chosen to have constant nonzero acceleration.
- The frame of reference is chosen in such a way that the object under observation is at rest.
- The frame of reference is chosen in such a way that the object under observation is moving with a constant speed.

If you look out the window of a moving car at houses going past, you sense that you are moving. What have you chosen as your frame of reference?

- the car
- the sun
- a house

Why did Michelson and Morley orient light beams at right angles to each other?

- To observe the particle nature of light
- To observe the effect of the passing ether on the speed of light
- To obtain a diffraction pattern by combination of light
- To obtain a constant path difference for interference of light

#### 10.2 Consequences of Special Relativity

What is the relationship between the binding energy and the mass defect of an atomic nucleus?

- The binding energy is the energy equivalent of the mass defect, as given by E0 = mc.
- The binding energy is the energy equivalent of the mass defect, as given by E0 = mc
^{2}. - The binding energy is the energy equivalent of the mass defect, as given by ${E}_{0}=\frac{m}{c}$
- The binding energy is the energy equivalent of the mass defect, as given by ${E}_{0}=\frac{m}{{c}^{2}}.$

True or false—It is possible to just use the relationships *F* = *ma* and *E* = *Fd* to show that both sides of the equation E_{0} = mc^{2} have the same units.

- True
- False

- The law of conservation of energy is not valid in relativistic mechanics.
- The law of conservation of energy has to be modified because of time dilation.
- The law of conservation of energy has to be modified because of length contraction.
- The law of conservation of energy has to be modified because of mass-energy equivalence.

The sun loses about 4 × 10^{9} kg of mass every second. Explain in terms of special relativity why this is happening.

- The sun loses mass because of its high temperature.
- The sun loses mass because it is continuously releasing energy.
- The Sun loses mass because the diameter of the sun is contracted.
- The sun loses mass because the speed of the sun is very high and close to the speed of light.

### Extended Response

#### 10.1 Postulates of Special Relativity

- The older concept is that speeds are subtractive. For example, if a person throws a ball while running, the speed of the ball relative to the ground is the speed at which the person was running minus the speed of the throw. A relativistic example is when light is emitted from car headlights, it moves faster than the speed of light emitted from a stationary source. The car's speed does not affect the speed of light.
- The older concept is that speeds are additive. For example, if a person throws a ball while running, the speed of the ball relative to the ground is the speed at which the person was running plus the speed of the throw. A relativistic example is when light is emitted from car headlights, it moves no faster than the speed of light emitted from a stationary source. The car's speed does not affect the speed of light.
- The older concept is that speeds are multiplicative. For example, if a person throws a ball while running, the speed of the ball relative to the ground is the speed at which the person was running multiplied by the speed of the throw. A relativistic example is when light is emitted from car headlights, it moves no faster than the speed of light emitted from a stationary source. The car's speed does not affect the speed of light.
- The older concept is that speeds are frame independent. For example, if a person throws a ball while running, the speed of the ball relative to the ground has nothing to do with the speed at which the person was running. A relativistic example is when light is emitted from car headlights, it moves no faster than the speed of light emitted from a stationary source. The car's speed does not affect the speed of light.

A rowboat is drifting downstream. One person swims 20 m toward the shore and back, and another, leaving at the same time, swims upstream 20 m and back to the boat. The swimmer who swam toward the shore gets back first. Explain how this outcome is similar to the outcome expected in the Michelson–Morley experiment.

- The rowboat represents Earth, the swimmers are beams of light, and the water is acting as the ether. Light going against the current of the ether would get back later because, by then, Earth would have moved on.
- The rowboat represents the beam of light, the swimmers are the ether, and water is acting as Earth. Light going against the current of the ether would get back later because, by then, Earth would have moved on.
- The rowboat represents the ether, the swimmers are ray of light, and the water is acting as the earth. Light going against the current of the ether would get back later because, by then, Earth would have moved on.
- The rowboat represents the Earth, the swimmers are the ether, and the water is acting as the rays of light. Light going against the current of the ether would get back later because, by then, Earth would have moved on.

#### 10.2 Consequences of Special Relativity

A helium-4 nucleus is made up of two neutrons and two protons. The binding energy of helium-4 is 4.53×10^{-12} J. What is the difference in the mass of this helium nucleus and the sum of the masses of two neutrons and two protons? Which weighs more, the nucleus or its constituents?

- 1.51×10
^{-20}kg; the constituents weigh more - 5.03×10
^{-29}kg; the constituents weigh more - 1.51×10
^{-29}kg; the nucleus weighs more - 5.03×10
^{-29}kg; the nucleus weighs more

Use the equation for length contraction to explain the relationship between the length of an object perceived by a stationary observer who sees the object as moving, and the proper length of the object as measured in the frame of reference where it is at rest.

- As the speed
*v*of an object moving with respect to a stationary observer approaches*c*, the length perceived by the observer approaches zero. For other speeds, the length perceived is always less than the proper length. - As the speed
*v*of an object moving with respect to a stationary observer approaches*c*, the length perceived by the observer approaches zero. For other speeds, the length perceived is always greater than the proper length. - As the speed
*v*of an object moving with respect to a stationary observer approaches*c*, the length perceived by the observer approaches infinity. For other speeds, the length perceived is always less than the proper length. - As the speed
*v*of an object moving with respect to a stationary observer approaches*c*, the length perceived by the observer approaches infinity. For other speeds, the length perceived is always greater than the proper length.