Calculate the magnitude of its acceleration in a vertical takeoff from the Moon in meters per square second, assuming the acceleration due to gravity on the Moon is 1.67 m/s^2.

Question

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 12500 kg. The thrust of its engines is 29500 N.

Answer 1

For a body to take off from the surface of the Moon, the lifting force must

a) be able to completely compensate the gravitational pull from the Moon

a) be strong enough to provide the body an additional upward acceleration a

Therefore the rockets' engines must provide a lifting force (thrust) such that

F_AS=m(g_Moon + a)=12500 kg*(1.67 m/s²+a)=29500 N (1)

So, a=(29500N/1250kg)-1.67m/s²=0.69m/s²

Hope this is helpful.

Dr. Ariel B

Answer 2

Force due to gravity b = 12500*1.67=20875 N

Upward force = 2900

Net upward force = 8625 N

Acceleration = 8625/12500 m/s2 upwards