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.

Problem 14PE

Solution 14 PE

Step 1 of 4:

In this question, we need to find the magnitude of acceleration of rocket which is taking off from moon

In this second part , we need to analyse if the same rocket can take off from Earth, and if it does we are to calculate the acceleration of rocket

Data given

Mass of rocket

Thrust of engine

Gravitational force of Moon

Gravitational force of Earth

Step 2 of 4 :

Let us consider a free body diagram

We can acceleration of the module using

Here

To find acceleration we shall rearrange the relation

We get

In this question we have

Substituting values we get

Note :

Thus we have obtained force as