7.2 - Gravitational Potential

Question 1

What is gravitational potential energy?

Answer 1

The energy an object possesses due to its position in a gravitational field.

Question 2

What is gravitational potential?

Answer 2

The work done per unit mass in bringing a test mass from infinity to a defined point.

Question 3

What does it mean when we are observing a mass from infinity?

Answer 3

Observed from infinity = don’t take into account the mass of the planet we are observing from.

Question 4

What is the gravitational potential symbol and units?

Answer 4

V, measured in K/kg

Question 5

Why is gravitational potential always a negative value?

Answer 5

It is defined as zero at infinity.
Since gravitational force is always attractive, work must be done on a mass to reach infinity.
(so V is increasing the further away from the centre of mass)

Question 6

Does gravitational potential increase or decrease when moving closer to a large body?

Answer 6

Decrease.

Question 7

What is the equation for gravitational potential?

Answer 7

V = GM/r
M = mass of body producing the g field
r = distance from the centre of the mass to the point mass

Question 8

Is gravitational potential a scalar or vector?

Answer 8

Scalar, the negative sign isn’t a direction

Question 9

What is the difference between gravitational field strength and gravitational potential?

Answer 9

g - the force per unit mass on an object in a gravitational field
V - the work done per unit mass in bringing s test mass from from infinity to a specific point in the g field.

Question 10

What is the equation that shows the relation of g, V and r?

Answer 10

g = - ΔV/Δr
g = grav field strength (N/kg)
ΔV = change in grav potential (K/kg)
Δr = distance from the centre of a point mass (m)

Question 11

What does the relationship of V against r look like graphically?

Answer 11

a -1/r reciprocal graph

Question 12

What are 4 key features of a V against r graph?

Answer 12

• value for V always negative
• -1/r
• the gradient at any point on graph is g at that point
• the graph has a shallow increase as r increases

Question 13

What does the graph of g against r look like?

Answer 13

A 1/r² relationship.

Question 14

What are 4 key features of a g against r graph?

Answer 14

• value of g always positive
• 1/r² = inverse square law relation
• Area under graph is ΔV
• graph has a steep decline as r increases

Question 15

What is the equation for work done in moving a mass?

Answer 15

ΔW = mΔV
ΔW = change in work done (J)
m = mass (kg)
ΔV = change in grav potential (J/kg)

Question 16

What is the change in work done equal to?

Answer 16

The change in gravitational potential energy

Question 17

What is an equation that represents the change in gravitational potential energy? (use force equation)

Answer 17

ΔGPE = GMm(1/r1 - 1/r2)
M = mass that is producing the grav field
m = mass effected by and moving in the grav field
r1 = first distance of m from centre of M (m)
r2 = second distance

Question 18

When is the equation ΔGPE = mgΔh relevant in this topic?

Answer 18

Only relevant for an object lifted in a uniform gravitational field (ie close the surface of Earth).
only works when g is CONSTANT

Question 19

What are equipotential lines?

Answer 19

Lines that are perpendicular to grav radial field and uniform fields.
Represented by dotted lines

Question 20

What do equipotential lines look like in a radial field? (eg around a planet)

Answer 20

Concentric circles that become further apart further away from the planet.

Question 21

What do equipotential lines look like in a uniform field?

Answer 21

Horizontal straight lines, parallel and equally spaced.

Question 22

Is work done when moving along an equipotential line or surface?

Answer 22

No, only between equipotential lines or surfaces