20. one point, from Lectures 20 and 22, picture and calculations.

Problems 20 and 21 are on the numerical effects of relativity. Be sure you understand all of these effects, including that they are reciprocal for the two observers!

In Prob. 20, you and I have relative velocity v=(4/5)c. Use the appropriate spacetime triangle and the formulas for length contraction, time dilation (clock slowdown), and mass increase to get the answers. Show all of your work!

(a) .2 The Gamma Triangle. Use a triangle (draw it to scale and label it) to get gamma. (.2)

(b) .2 How Fast? What is our actual relative speed in m/s? (c=3× 10^8m/s) (.2)

(c) .2 I Measure Your Meterstick You are carrying a meterstick (100 centimeters in one meter). How many centimeters long do I measure it to be? (.2)

(d) .2 I Measure Your Time Passage. While one minute passes on my clock, how much time do I measure passing on your clock? (.2)

(e) .2 I Measure Your Mass. Your rest mass is 60 kg on your own scale. What do I measure your mass to be? (.2)

21. one point, from Lectures 20 and 22, pictures and calculations.

In Prob. 21, parts (a) through (d), you and I have relative velocity such that gamma=13/5. Use the appropriate spacetime triangle and the formulas for length contraction, time dilation (clock slowdown), and mass increase to get the answers. Show all of your work.

(a) .1 The Gamma Triangle. Use a triangle (draw it to scale and label it) to get v/c. (.1)

(b) .2 You Measure my Bike. I am riding a bike which is 1.3 meters long at rest. How long do you measure it to be? (.2)

(c) .2 You Measure My Time Passage. It takes you 6.5 hours by your own clock to do this homework. How much time do you measure passing on my clock while you are doing your homework? (.2)

(d) .2 You Measure My Mass. Doing all this homework made me lose mass down to 50 kg on my own scale. How much mass do you measure me to have? (.2)

(e) .3 The Gamma Factor for Time Passage. Draw a series of pictures (.3), carefully labeled, of the tick-tock light clock from lecture, the video, or the book to describe how a factor of gamma fewer seconds pass on a moving clock than on a clock at rest.