4. Relativity (10 points)
(5 pts) (a) You and a friend agree to participate in a simulated trip to Mars, in which
you live in a perfectly sealed spacecraft simulator (on Earth) for three years. There is
plenty of food, water and oxygen in the simulator. You exercise to stay healthy, so you each
consume about 2500 (nutritional) calories per day. 1 nutritional calorie is about 4.2 kJ. The
simulator is kept at room temperature. Does the simulator (with you in it, of course) gain
mass, lose mass, or remain the same mass over the course of the trip? If it does change in
mass, calculate the change quantitatively, and explain how mass was gained or lost through
a completely sealed simulator.
(b) (5 points) Bert goes to Planet Claire, 20 light years away, going 5 km/sec less than the
speed of light. Ernie stays on Earth. How much time has elapsed on Ernie's clock when
Bert stops at Planet Claire? How much time has elapsed on Bert's clock? (Ignore the efieste
of acceleration and deceleration.) What story does each tell?