Question

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 10,000 kg. The thrust of its engines is 30,000 N. (a) Calculate its the magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.

Answer 1

Answer:

Part a)

a = 1.37 m/s/s

Part b)

since the force of gravity is more than the thrust force of rocket so it will not lift off the surface of Earth

Explanation:

Part a)

Net force on the Module due to thrust of engine is given as

$F = 30,000 N$

now net force while is ejected out of the surface of moon is given as

$F_{net} = F - F_g$

here we know that

$F_g = mg_{moon}$

where we have

$g_{moon} = \frac{g}{6}$

$F_{net} = 30,000 - (10000)(\frac{9.8}{6})$

$F_{net} = 13666.67 N$

now the acceleration of the module on the moon is

$a = \frac{F_{net}}{m}$

$a = \frac{13666.67}{10,000} = 1.37 m/s^2$

Part b)

Now on the surface of earth the force of gravity on the module is given as

$F_g = mg$

$F_g = 10,000 \times 9.8$

$F_g = 98000 N$

since the force of gravity is more than the thrust force of rocket so it will not lift off the surface of Earth