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## 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 0.8*c* (instead of at 0.6*c*, 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?