PHY C8: Gravitational Potential Energy U and Gravitational Potential Φ

What is Gravitational Potential Energy (U)? (Definition)

The work done by an external force in bringing a mass from infinity to that point.

Why is the work required to bring the first particle from infinity zero?

Since there are no other masses exerting gravitational force on it.

What is the Gravitational Potential Energy (U) of a system of two point masses M and m separated by distance r?

U = -GMm/r.

Is Gravitational Potential Energy a scalar or vector quantity?

Scalar quantity.

What is the SI unit for Gravitational Potential Energy?

Joule (J).

Why is a negative sign indicated in the Gravitational Potential Energy formula? (Reason for Negative Sign)

Due to its definition: gravitational force is attractive, so external force does negative work to bring mass from infinity (where U=0) to a point in the field.

What is Gravitational Potential Energy (U) for small distances h above Earth's surface?

U ≈ mgh.

What is the Gravitational Potential Energy (U) at infinity (r = ∞)?

Defined to be zero (highest value).

How does Gravitational Potential Energy change from infinity towards mass M?

It decreases, becoming more negative.

What is the relationship between Force (F) and Potential Energy (U) for one-dimensional motion?

F = -dU/dr.

What does the negative sign in F = -dU/dr indicate?

The force points in the direction of decreasing potential energy.

What is the magnitude of the force (F) at distance r from M?

Equal to the numerical value of the gradient of the potential energy curve at r.

What is Gravitational Potential (Φ)? (Definition)

The work done per unit mass by an external force in bringing a small test mass from infinity to that point.

What is the formula for Gravitational Potential (Φ) at distance r from point mass M?

Φ = U/m = -GM/r.

Is Gravitational Potential a scalar or vector quantity?

Scalar quantity.

What is the SI unit for Gravitational Potential?

J kg⁻¹.

What is Gravitational Potential (Φ) at infinity (r = ∞)?

Defined to be zero (highest value).

How does Gravitational Potential change from infinity towards mass M?

It decreases, becoming more negative.

How is the Total Gravitational Potential found at a point due to two or more masses?

By adding the individual potentials algebraically.

What are Equipotential Lines/Surfaces?

Points at a fixed distance from a mass form an equipotential surface.

How do Equipotential Surfaces of equal interval behave as we move away from a spherical mass?

They are further apart, indicating a weaker field.

What is the relationship between Gravitational Field Strength (g) and Gravitational Potential (Φ)?

g = -dΦ/dr.

What does the negative sign in g = -dΦ/dr indicate?

The field strength points in the direction of decreasing potential.