Question

If a 50 KG object is at a location 25,600 km from Earth's Center, what is the gravitational force exerted by the objects on Earth? In what direction does that force act? Support your answer with evidence.

Answer 1

Answer: The force exerted by the object on Earth is 30.4 N, and the direction is towards the object.

Explanation:

The gravitational force between two objects of mass M1 and M2, that are at a distance R between them is written as:

F = G*(M1*M2)/R^2

Where G is the gravitational constant, such that:

G = 6.674*1^(-11) m^3/(kg*s^2)

We know that M1, the mass of the object, is 50kg

R is the distance, in this case, is 25,600km

But this needs to be written in meters, remembering that:

1km = 1000m

Then:

25,600km = (25,600*1000)m = 25,600,000 m

And M2 is the mass of Earth, which is:

M2 = 5.972*10^(24) kg

Replacing all of those in the force equation we get

F = (6.674*1^(-11) m^3/(kg*s^2))*(50kg*5.972*10^(24) kg)/( 25,600,000 m)^2

F = 30.4 N

We know that the gravitational force is attractive, then the direction in which this force acts is towards the 50kg object.

Now, remember the second Newton's law is:

F = M*a

Then the acceleration that the object causes on Earth is:

30.4N = ( 5.972*10^(24) kg)*a

a = 30.4N/( ( 5.972*10^(24) kg)) = 5.09*10^(-24) m/s

This acceleration is almost despreciable.