## Optional Make-up Homework

Due Tuesday, December 3, 1996

NOTE: Your lowest scoring homework (or one you missed) will be dropped in computing your grade. This assignment can be used to fill in if you missed, or scored very low in, more than one homework assignment. The credit for this assignment will replace your next lowest score (the lowest one having been dropped). If you are reasonably happy with your unpledged homework scores, except possibly one, you do not need to do this assignment.

1 (a) Both momentum and kinetic energy are in some sense measures of the amount of motion of a body. How do they differ?

(b) Can a body change in momentum without changing in kinetic energy?

(c) Can a body change in kinetic energy without changing in momentum?

(d) Suppose two lumps of clay of equal mass traveling in opposite directions at the same speed collide head-on and stick to each other. Is momentum conserved? Is kinetic energy conserved?

(e) As a stone drops off a cliff, both its potential energy and its kinetic energy continuously change. How are these changes related to each other?

2. Review the Web notes on time dilation, a worked example, then consider the situation in which the astronaut zips past the two clocks at 0.8c (instead of at 0.6c, the speed in the example).

(a) How far apart does she see the clocks to be?

(b) What does her clock read as she passes the second ground clock?

(c) What does the second ground clock read as she passes it?

(d) What would she observe the first ground clock to read if she looked at it through a telescope as she passed the second ground clock?

(e) If she continuously observes the first ground clock as she recedes from it, how fast does it appear to her to be registering time?

(f) If she continuously observes the second ground clock as she is approaching it, how fast does it appear to her to be registering time?