Chapter 35 HW

PART A Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Assume that all the spaceships have equal length when at rest and that you watch the other spaceship as its clock ticks off one second. Rank the figures based on the length that you would measure for the other spaceship (in its direction of motion), from shortest to longest. PART B The four figures below are the same as those in Part A. This time, rank the figures based on your length as measured by the passenger in the other spaceship, from shortest to longest. PART C We can summarize the results of Parts A and B as follows: When another spaceship is moving by you (at constant velocity), you will measure the spaceship to be shorter than its rest length, while passengers on that ship will measure your length to be shorter. Imagine that you and the passengers on the other ship are arguing (by radio) about who really is the one that has become shorter. To settle the argument, you agree to meet up on Mars and put the two spaceships next to each other to see which one is really shorter. What will you find when you meet up on Mars?

A- Shortest Length 1. 0.85 c 2. 0.8 c 3. 0.75 c 4. 0.7 c Longest length B- Same as A C- Both spaceships are the same length.

PART A Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Imagine that you watch the other spaceship as its clock ticks off one second. Rank the figures according to how much time you would say passes (on your own ship) while the other ship's clock ticks off one second, from the shortest to the longest amount of time. PART B The four figures below are the same as those in Part A. This time, imagine that the passengers on the other spaceship are watching your clock as its ticks off one second. Rank the figures according to how much time the passengers (on the other ship) would say passes (on their ship) while they watch your clock tick off one second, from the shortest to the longest amount of time. PART C Consider again the spaceships from Parts A and B. Suppose that, at rest, both you and a passenger on the other spaceship have the same heart rate of 60 beats per minute. How will you and the passenger on the other spaceship observe each other's heart rates as you pass by in your spaceships?

A- Shortest time 1. 0.7 c 2. 0.75 c 3. 0.8 c 4. 0.85 c Longest time B- Same as Part A C- You would observe that the passenger in the other spaceship has a slower heart rate than you do, and she would observe that you have a slower heart rate than hers.

PART A How does the time measured in the spaceship's frame of reference change as the speed of the spaceship increases? PART B How does the time measured in Earth's frame of reference change as the speed of the spaceship increases? PART C How does the distance that light travels in Earth's frame of reference change as the speed of the spaceship increases?

A- The time measured in the spaceship's frame of reference does not change. B- The time measured in Earth's frame of reference increases. C- The distance that light travels in Earth's frame of reference increases.

PART A According to Jackie, __________. PART B What does Jackie say about the lights as they illuminate you? PART C Consider the following five statements: 1. The green light and red light both flash at the same time. 2. The green light reaches Jackie before the red light reaches her. 3. The green light and red light reach you at the same time. 4. Jackie is the one who is moving. 5. The green light and red light travel at the same speed. Which of these statements do both you and Jackie agree are true?

A- the green light illuminates her before the red light because she sees the green light flash first B- The green light illuminates you at the same time as the red light because although the green light flashes first, you are traveling away from it. C- Statements 2, 3, and 5 are true.

What is the same in Einstein's first postulate?

All laws of nature in all uniformly moving frames of reference

How does the correspondence principle relate to special relativity?

At everyday low velocities, relativistic equations approach the Newtonian equations.

What classical idea about space and time did Einstein reject?

Einstein rejected the idea that space and time are independent.

How do measurements of time differ for events in a frame of reference that moves at 50% of the speed of light relative to us? At 99.5% of the speed of light relative to us?

For 0.50c, time dilates to 1.15 times the proper time. For 0.995c, time dilates to 10 times the proper time.

Time is required for light to travel along a path from one point to another. If this path is seen to be longer because of motion, what happens to the time it takes for light to travel this longer path?

It takes longer.

Imagine that you are located on Earth while a spaceship travels from Earth to the star Vega at constant velocity of 0.8c. The following items describe quantities that, according to Einstein's special theory of relativity, would be either larger (or longer), smaller (or shorter), or the same as their rest values. (Note that by "rest value," we mean the value you would find if both you and the spaceship were at rest on Earth.) Match each item to the correct category.

Larger/longer than rest value: -one second on your clock as seen by spaceship passengers - one second on a spaceship clock as seen by you - mass of the spaceship as measures by you - your mass as measured by spaceship passengers Smaller/shorter than rest value: - distance from Earth to Vega as measured by spaceship passengers - length (in the direction of motion) of the spaceship as measured by you Same as rest value: - speed of the spaceship's headlight beam as measured by you

What is the maximum value of v1v2/c2 in an extreme situation? What is the smallest value?

Maximum 1, minimum 0

When a flashing light source approaches you, does the speed of light or the frequency of light - or both - increase?

Only frequency increases

Inside the moving compartment of Figure 35.4, light travels a certain distance to the front end and a certain distance to the back end of the compartment. How do these distances compare as seen in the frame of reference of the moving rocket?

The distances travelled by light are the same.

What two main obstacles prevent us from traveling today throughout the galaxy at relativistic speeds?

The large quantity of energy needed and radiation shielding

What would be the momentum of an object if it were moving at the speed of light?

The momentum would be infinite.

What is constant in Einstein's second postulate?

The speed of light in a vacuum

Do the relativity equations for time, length, and momentum hold true for everyday speeds? Explain.

They hold true but the differences they predict are hard to measure.

How long would the meterstick in the preceding question appear to be if it were traveling with its length perpendicular to its direction of motion?

1 m

If you walk at 1 km/h down the aisle toward the front of a train that moves at 60 km/h, what is your speed relative to the ground?

61 km/h