Question

What is the gravitational potential energy of a two-particle system with masses 4.5 kg and 6.3 kg, if they are separated by 1.7 m? If you triple the separation between the particles, how much work is done (b) by the gravitational force between the particles and (c) by you?

Answer 1

Answer:

7.41 x 10^-10 J

Explanation:

m = 4.5 kg

M = 6.3 kg

d = 1.7 m

The formula for the gravitational potential energy is given by

$U = \frac{-GMm}{d}$

Where, G is the Universal gravitational constant

G = 6.67 x 10^-11 Nm^2/kg^2

$U = \frac{-6.67 \times 10^{-11}\times 6.3 \times 4.5}{1.7}$

U = - 1.112 x 10^-9 J

Now the separation is tripled, d' = 3 x d = 3 x 1.7 m = 5.1 m

Let the potential energy is U'

The formula for the gravitational potential energy is given by

$U' = \frac{-GMm}{d'}$

Where, G is the Universal gravitational constant

G = 6.67 x 10^-11 Nm^2/kg^2

$U' = \frac{-6.67 \times 10^{-11}\times 6.3 \times 4.5}{5.1}$

U' = - 3.71 x 10^-10 J

the work done is equal to the change in potential energy

W = U' - U

W = - 3.71 x 10^-10 + 1.112 x 10^-9

W = 7.41 x 10^-10 J