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

Answer:

$U=-2.4896\times 10^{7} J$

Explanation:

From the equation we know that the gravitational potential energy:

$U= -G\frac{M.m}{r}$.......................(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= $6.67\times 10^{-11} N.m^{2}.kg^{-2}$

Given:

m= 4kg

We, have

$M=5.972\times 10^{24} kg$

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

$r= 64000 km$

Putting the values in the eq. (1)

$U=-6.67\times 10^{-11}\times \frac{5.972\times 10^{24}\times 4}{64000\times 1000}$

$U=-2.4896\times 10^{7} J$

Answer 2

Answer:

- 2.425 x 10^5 J

Explanation:

The gravitational potential energy between earth and the bock is given by

$U=-G\frac{Mm}{r}$

Where, G is the universal gravitational constant = 6.67 x 10^-11 Nm^2/kg^2

M is the mass of earth = 5.8 x 10^24 kg

m is the mass of block = 4 kg

r be the radius of earth = 6380 km = 6380 x 10^3 m

by substituting the values in the above expression, we get

$U=-6.67\times10^{-11}\frac{5.8\times 10^{24}\times 4}{6380\times 10^{3}}$

U = - 2.425 x 10^5 J