13.4 A2 Level

Gravitational potential

7 flashcards to master this topic

Definition Flip

Define gravitational potential (ϕ) at a point in a gravitational field.

Answer Flip

Gravitational potential (ϕ) at a point is the work done per unit mass in bringing a small test mass from infinity to that point. It's a scalar quantity and is always negative.

Definition Flip

State the formula for gravitational potential (ϕ) due to a point mass M at a distance r.

Answer Flip

The gravitational potential (ϕ) is given by: ϕ = –GM / r, where G is the gravitational constant and r is the distance from the center of mass M. Note the negative sign; it indicates that work needs to be done *against* the gravitational field to increase potential.

Key Concept Flip

Explain why gravitational potential is always a negative value.

Answer Flip

Gravitational potential is negative because the gravitational force is attractive. Work is done *by* the field as a mass moves from infinity towards another mass. Since potential is defined as work done *against* the field, it is negative at all finite distances.

Key Concept Flip

How does gravitational potential change as you move further away from a point mass?

Answer Flip

As the distance (r) from a point mass increases, the gravitational potential (ϕ) becomes less negative (i.e., increases). At infinity, the gravitational potential is defined to be zero.

Definition Flip

State the formula for gravitational potential energy (EP) of two point masses, M and m, separated by a distance r.

Answer Flip

The gravitational potential energy (EP) is given by: EP = –GMm / r, where G is the gravitational constant. This represents the work done to separate the masses to infinity.

Key Concept Flip

Describe the relationship between gravitational potential energy and gravitational potential.

Answer Flip

Gravitational potential energy (EP) is the product of the gravitational potential (ϕ) at a point and the mass (m) placed at that point: EP = mϕ. Therefore, if you know the potential at a location, you can easily determine the potential energy of any mass placed there.

Calculation Flip

A 10kg mass is placed 5m away from a 1000kg mass. What is the gravitational potential energy of the 10kg mass?

Answer Flip

E_p = -GMm/r = -(6.67 x 10^-11)(1000)(10)/5 = -1.33 x 10^-7 J. Remember to use appropriate units.

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