Question

Calculate the gravitational potential energy of the interacting pair of the Earth and a 4 kg block sitting on the surface of the Earth. You would need to supply the absolute value of this result to move the block to a location very far from the Earth (actually, you would need to use even more energy than this due to the gravitational potential energy associated with the Sun-block interacting pair).

Ugrav = J

Answer 1

`U=-2.4896* 10^(7) J`

Step-by-step explanation:

From the equation we know that the gravitational potential energy:

`U= -G(M.m)/(r)`.......................(1)

The negative potential indicates a bound state.

where:

M= mass of the earth

m= mass of the object

r= radial distance from the center of the earth

G= universal gracvitational constant=
`6.67* 10^(-11) N.m^(2).kg^(-2)`

Given:

m= 4kg

We, have

`M=5.972* 10^(24) kg`

∵The object is on the earth surface, we have the radius of the earth:

`r= 64000 km`

Putting the values in the eq. (1)

`U=-6.67* 10^(-11)* (5.972* 10^(24)* 4)/(64000* 1000)`

`U=-2.4896* 10^(7) J`