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

Answer 2

Acceleration is the rate of change of velocity. The acceleration of the module is 1.365 m/s².

Given to us

Mass of the Module = 10,000 kg

The thrust of the engine, Fₓ = 30,000 N

A.)

We know in order to lift the module the thrust produced by the engine must be greater than the gravitational pull by the module. therefore,

$F_{N} = F_x - W$

where W is the weight of the moon,

$F_{N} = F_x - (m\times g_{moon})$

Also, the acceleration on the moon is 1/6 of the acceleration on the earth,

$F_{N} = 30,000- (10,000\times \dfrac{9.81}{6})\\F_N = 13,650\ N$

We know that force is the product of mass and acceleration, therefore,

$F_N = m \times a\\\\13,650 = 10,000 \times a\\\\a = 1.365 m/s^2$

Hence, the acceleration of the module is 1.365 m/s².

B.)

If we need to lift the module on earth, we need a thrust that is greater than the weight of the module,

$Weight = mass \times acceleration\\W = 10,000 \times 9.81\\W = 98,100\ N$

As the weight of the module is greater than the thrust produced by engines. therefore, the module can not take off from the earth.

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