Chapter S2 Activities
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?
Both spaceships are the same length.
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 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 measured by you -your mass as measured by spaceship passengers Smaller/Shorter: -distance from Earth to Vega as measured by spaceship passengers -length (in the direction of motion) of the spaceship as measured by you Same Rest Value: -speed of the spaceship's headlight beam as measured by you
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.
Shortest to Longest: -0.7c -0.75c -0.8c -0.85c
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.
Shortest to Longest: -0.7c -0.75c -0.8c -0.85c
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.
Shortest to Longest: -0.85c -0.8c -0.75c -0.7c
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.
Shortest to Longest: -0.85c -0.8c -0.75c -0.7c
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?
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.
Match the words in the left-hand column to the appropriate blank in the sentences in the right-hand column. Use each word only once.
1. Astronauts are weightless in the International Space Station because they are in a (free-float frame). 2. The observation that you will measure the length of an object moving relative to you as being shorter than the same object at rest is an example of (length contraction). 3. The (general theory of relativity) applies even to cases in which gravity or accelerations are present. 4. When the Space Shuttle and Space Station are docked to each other, astronauts in these two spacecraft will make the same measurements about space and time because they are in the same (reference frame). 5. An observer on the Moon would observe astronauts on a spaceship passing by at 0.9c to age more slowly due to (time dilation). 6. A situation that at first does not seem to make sense is a (paradox). 7. The (special theory of relativity) tells us that objects in motion have greater mass than they do when at rest.
