## Unit 7

1. The twin paradox is often used to describe special relativity. Fill in the following data table to demonstrate your understanding.

 Trial Space Twins speed Earth twins time Space twins time 1 0 1 1 2 10 1.01 1 3 50 1.15 1 4 80 1.67 1 5 90 2.29 1 6 96 3.57 1 7 98 5.03 1 8 99 7.09 1 9 99.5 10.01 1

2. A person traveling at 0.90 c measures the following information in his frame of reference.

a. 3 years goes by.

b. He holds a 1.0 meter stick in the direction of motion.

c. He and his space ship have a mass of 550 kg.

Consider yourself at rest with respect to the person traveling at 0.90 c. Determine your measurements for each of the above measurements.

3. Fermi National Accelerator Laboratory accelerates protons to 99.996% c. Determine the mass of a proton (1.67 X 10-27 kg at rest) when traveling at that velocity.

4. If a bunch of protons (1 X 1012 of them) were traveling at the speed indicated above, how much momentum would they have?

5. A muon is a commonly created particle in our atmosphere (and at Fermilab). It has an average lifetime of 2.2 X 10-6 seconds when it is at rest.

a. How far should it be able to travel if its lifetime is not relativistically shifted and it traveled at 99.996% c?

If it's lifetime was not relativistically shifted it would be the same as it was at rest whic was 2.2x10-6s.

b. Determine how long its average lifetime should be traveling at 99.996% c according to us (at rest)?

It's average lifetime to us will be the same as if it were at rest which is 2.2x10-6s.

c. How far should it travel at this speed with a relativistically shifted lifetime?

d. Does that explain how muons are created 10.4 km above us at the top of our atmosphere, and yet make it down to the surface of the earth to be detected regularly? Explain.

No, it does not. However, there is most likely an irregularity where the average lifetime of a muon is not the actual lifetime of a muon and instead the lifetime is much greater which causes the particle to be able to travel much further and at almost the speed of light, that little bit of time can move a long way.

6. If you were traveling near the speed of light, which of the following would you notice (if any)?

a. Your pulse would slow down.

b. Your pulse would speed up.

7. The nearest galaxy is about 2 million light years in distance away from the earth. How many light years away would it be if we could rocket to it traveling at:

a. 0.5 c

b. 0.7 c

c. 0.99 c

d.0.9999 c

Glenbrook South Physics Team - Tom Henderson, John Lewis, Neil Schmidgall, Dave Smith, Suzanne Webb & Brian Wegley
4000 West Lake Ave
Glenview, IL 60025 - 1200
(847)729-2000
Page Maintained by: Brian Wegley

Last Updated: October 8, 1997