7.2 - Gravitational Potential Flashcards
What is gravitational potential energy?
The energy an object possesses due to its position in a gravitational field.
What is gravitational potential?
The work done per unit mass in bringing a test mass from infinity to a defined point.
What does it mean when we are observing a mass from infinity?
Observed from infinity = don’t take into account the mass of the planet we are observing from.
What is the gravitational potential symbol and units?
V, measured in J/kg
Why is gravitational potential always a negative value?
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)
Does gravitational potential increase or decrease when moving closer to a large body?
Decrease.
What is the equation for gravitational potential?
V = GM/r
M = mass of body producing the g field
r = distance from the centre of the mass to the point mass
Is gravitational potential a scalar or vector?
Scalar, the negative sign isn’t a direction
What is the difference between gravitational field strength and gravitational potential?
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.
What is the equation that shows the relation of g, V and r?
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)
What does the relationship of V against r look like graphically?
a -1/r reciprocal graph
What are 4 key features of a V against r graph?
- 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
What does the graph of g against r look like?
A 1/r² relationship.
What are 4 key features of a g against r graph?
- value of g always positive
- 1/r² = inverse square law relation
- Area under graph is ΔV
- graph has a steep decline as r increases
What is the equation for work done in moving a mass?
ΔW = mΔV
ΔW = change in work done (J)
m = mass (kg)
ΔV = change in grav potential (J/kg)
What is the change in work done equal to?
The change in gravitational potential energy
What is an equation that represents the change in gravitational potential energy? (use force equation)
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
When is the equation ΔGPE = mgΔh relevant in this topic?
Only relevant for an object lifted in a uniform gravitational field (ie close the surface of Earth).
only works when g is CONSTANT
What are equipotential lines?
Lines that are perpendicular to grav radial field and uniform fields.
Represented by dotted lines
What do equipotential lines look like in a radial field? (eg around a planet)
Concentric circles that become further apart further away from the planet.
What do equipotential lines look like in a uniform field?
Horizontal straight lines, parallel and equally spaced.
Is work done when moving along an equipotential line or surface?
No, only between equipotential lines or surfaces
