Question

An astronaut lifts off in a rocket from the surface of the moon, where g= 1.6m/s^2. What vertical acceleration should his rocket have so that his apparent weight is equal to his true weight on earth? Draw a free body diagram as well.

Answer 1

Let, vertical acceleration of rocket = a

free body diagram of astronaut will be:

now, by force balance on astronaut in vertical direction,

Fnet = m*g_e

here, g_e = surface gravity at earth = 9.8 m/s^2 (so that his apparent weight is equal to his true weight on earth)

Fnet = net force in vertical direction = Fm + Fp

Fm = gravitational force at surface of moon = m*g_m

Fp = psudo force on astronaut = m*a

m = mass of astronaut

g_m = surface gravity at moon = 1.6 m/s^2

So,

m*g_m + m*a = m*g_e

a = g_e - g_m

a = 9.8 - 1.6

a = 8.2 m/s^2 = vertical acceleration of rocket

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