Question

The magnitude of the gravitational force between a particle of mass m1 and one of mass m2 is given by F(x) = G m1m2 / x2, where G is a constant and x is the distance between the particles. (Use any variable or symbol stated above as necessary.) (a) What is the corresponding potential energy function U(x)? Assume that U(x) → 0 as x → [infinity]. U(x) =

Answer 1

U = Gm₁m₂ / x

Step-by-step explanation:

F(x) = Gm₁m₂/x²

F(x) = -dU /dx

∫-dU =∫F(x)dx

U₁ -U₂ = ∫Gm₁m₂/x²dx

U₁ -U₂ = - Gm₁m₂/x

U₂ -U₁ = Gm₁m₂/x

When x = ∝ , U₁ =0

When x = x , U₂ =U

Putting these values, we have

U = Gm₁m₂ / x