Question

If two 1000 kg trucks are sitting 20 meters apart, what happens to the gravitational force if the trucks are moved to 40 meters apart? What if, instead of moving the trucks, one of the trucks was 2000 kg instead? How would that affect the gravitational force?

Answer 1

If the trucks are moved to 40 meters apart, the gravitational force is 1/4 of the original.

If one of the trucks was 2000 kg, the gravitational force will be twice the original.

Step-by-step explanation:

The gravitational force can be calculated as

`F=G(m_1m_2)/(r^2)`

Where G is a constant, m1 and m2 are the masses of the trucks and r is the distance between the trucks. It means that the force is directly proportional to the mass of the trucks and inversely proportional to the square of the distance.

If the trucks of 1000 kg are 20 m apart, the gravitational force is

`F=G\frac{(1000\text{ kg\rparen\lparen1000 kg\rparen}}{(20m)^2}=2500G`

If the trucks are moved 40 meters apart, the gravitational force is

`F=G\frac{(1000\text{ kg\rparen\lparen1000 kg\rparen}}{(40\text{ m\rparen}^2}=625G`

So, when we compare these forces, we get:

`(625G)/(2500G)=(1)/(4)`

Therefore, if the trucks are moved to 40 meters apart, the gravitational force is 1/4 of the original.

In the same way, if one truck is 2000 kg, we get:

`F=G\frac{(1000\text{ kg\rparen\lparen2000 kg\rparen}}{(20\text{ m\rparen}^2}=5000G`

So, compared to the original

`(5000G)/(2500G)=2`

It means that if one of the trucks was 2000 kg, the gravitational force will be twice the original.

Therefore, the answers are

If the trucks are moved to 40 meters apart, the gravitational force is 1/4 of the original.

If one of the trucks was 2000 kg, the gravitational force will be twice the original.