Question

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 1.00×104 kg. The thrust of its engines is 3.00×104 N. (a) Calculate the module’s 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.

a) (a) ( 2.00 , {m/s}^2 ), (b) No, due to Earth's stronger gravity
b) (a) ( 2.00 , {m/s}^2 ), (b) Yes, with an acceleration of ( 1.00 , {m/s}^2 )
c) (a) ( 3.00 , {m/s}^2 ), (b) No, due to Earth's stronger gravity
d) (a) ( 3.00 , {m/s}^2 ), (b) Yes, with an acceleration of ( 2.00 , {m/s}^2 )

Answer 1

The magnitude of acceleration during vertical takeoff from the Moon is 3 m/s². The module would not be able to lift off from Earth due to the stronger gravity. If it could, its magnitude of acceleration would be approximately 9.8 m/s². Therefore, the correct answer is c) (a) ( 3.00 , {m/s}^2 ), (b) No, due to Earth's stronger gravity.

Step-by-step explanation:

To calculate the magnitude of acceleration during vertical takeoff from the Moon, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. In this case, the force exerted by the engines is 30,000 N and the mass of the module is 10,000 kg. Therefore, the magnitude of acceleration is calculated as:

acceleration = force / mass
acceleration = 30,000 N / 10,000 kg = 3 m/s²

Therefore, the module's magnitude of acceleration during a vertical takeoff from the Moon is 3 m/s².

In order to determine if the module could lift off from Earth, we need to compare the gravitational forces acting on the module on the Moon and on Earth. The gravitational force is given by the equation:

force = mass × acceleration due to gravity

The acceleration due to gravity is larger on Earth compared to the Moon, so the force required to counteract the gravitational force is greater on Earth. Therefore, the module would not be able to lift off from Earth with the given engines. If it could, the magnitude of its acceleration would be the same as the acceleration due to gravity on Earth, which is approximately 9.8 m/s².