Question

An astronaut has a mass of 85 kg. The acceleration due to gravity at the surface of Earth is 9.8 m/s^2. The acceleration due to gravity at the surface of Earth's moon is 1.6 m/s^2. Calculate his weight on the Earth’s moon.

Answer 1

Answer: 136 Newtons (136N)

Step-by-step explanation:

Newton's Law of Gravitation states that the gravitational force is proportional to the masses of the two objects, and their separation distance between them. The proportionality constant is called Newtons constant denoted as capital 'G':

`F=GMm/r^2`

Now, due to Newton's 2nd Law of motion, we know that a net force acting on an object causes an acceleration. We can also say that the force is:

`F=ma`

Setting both of these equations equal to each other, we get:

`ma=GMm/r^2`

The smaller 'm' will cancel giving that the acceleration is:

`a=GM/r^2`

This is the equation which gives the gravitational field created from a source mass 'M'. To find the weight, find the product between the test mass and the gravitational field created by the source mass:

`Weight=mass*acceleration`

`W=ma`

`W=(85kg)(1.6m/s^2)`

`W=136N`

The units are Newtons due to weight being a force.