Question

The Sojourner Mars rover has a weight of 42.7 N on Mars where the acceleration due to gravity is 3.72 m/s2. What is Sojourner's mass on mars? What is Sojourner's mass on Earth? What is Sojourner's weight on Earth?

Answer 1

1) 11.5 kg

2) 11.5 kg

3) 112.7 N

Explanation:

1)

The relationship between the mass of an object and its weight is given by the relationship:

$W=mg$

where:

W is the weight

m is the mass of the object

g is the acceleration due to gravity (the strength of the gravitational field at the location of the object)

In this problem, the object is on Mars.

Its weight is:

W = 42.7 N

While the acceleration due to gravity is:

$g=3.72 m/s^2$

Therefore, we can re-arrange the equation to find the mass of the rover:

$m=\frac{W}{g}=\frac{42.7}{3.72}=11.5 kg$

2)

Here we want to find the mass of the rover on Earth.

We have to identify the main difference between mass and weight:

- The mass of an object is an intrinsec property of the object, and it describes the "amount of matter" contained in the object

- The weight of an object is the force of gravity acting on the object itself

From the definitions above, it is clear that:

- The mass of an object is independent from its location, therefore it does not change if the object moves to another planet

- The weight of an object depends on its location, as it depends on the value of $g$, the acceleration due to gravity

Therefore, the mass of the rover on the Earth is the same as the mass of the rover on Mars:

m = 11.5 kg

3)

The weight of an object, as stated before, is the force of gravity acting on the object, and it is given by

$W=mg$

where

m is the mass of the object

g is the acceleration  due to gravity

On the surface of the Earth, the value of the acceleration due to gravity is

$g=9.8 m/s^2$

While the mass of the rover is

m = 11.5 kg

Therefore, the weight of the rover on Earth is

$W=(11.5)(9.8)=112.7 N$