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) =

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Physics

Isabel Schneider

26 February, 16:10

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) =

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Dana Morrison · Answer 1

U = Gm₁m₂ / x

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