You wake up one morning to find yourself in a strange room with opaque walls, an

Question

You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. Clearly you’ve been abducted in your sleep! You’re immediately aware that the local gravity feels different from what you’re accustomed to, so it’s clear you’re not at rest on the surface of the Earth. You decide to do some experiments to find out more about your strange situation. Fortunately there seems to be some measuring equipment in the room - a meter stick, a stopwatch, and a scale, plus a few random objects you can try dropping. Your own body mass is 75 kg.

(a) You pick up an object and drop it from rest, starting at a height of 1.11 meters above the floor, and it hits the floor 0.38 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale, what weight will it register for your body?

(b) One possibility is that you are on the surface of an alien planet with gravity different from Earth’s. What would be the value of g (the acceleration due to gravity) for this planet?

(c) Another possibility is that you are in a spaceship, far from any planet, and that the “gravity” you experience is of the artificial sort, due to rocket engines located under the “floor” of your room. What would be the acceleration of the rocket in this case?

(d) Yet a third possibility is that you are in a rocket that has just lifted off from the Earth’s surface and is traveling upward with a constant acceleration, so that the gravity you feel is due to a combination of Earth’s gravity and the acceleration of the rocket. In this case, what is the acceleration of the rocket?

(e) Finally, a window magically appears on the floor, and you can see that what has really happened is this: you are in fact in a rocket which has just launched from the surface of an alien planet. Using your instruments you determine that the rocket has an upward acceleration of 6.0 m/s2. In this case, what is the value of g for this planet?

Explanation / Answer

a)

H = 1/2 * g*t^2

g = 2*H/t^2

g = 2*1.11/0.38^2 = 15.37 m/s2

W = mg = 75*15.37 = 1153 N

b)

g = 2*1.11/0.38^2 = 15.37 m/s2

c)

g = 2*1.11/0.38^2 = 15.37 m/s2

d)

g = 15.37-9.8 = 5.57 m/s2

e)

g = 15.37-6 = 9.37 m/s2

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