Learning Objectives. Book Reference : Pages 56-68 Book Reference : Pages 63-65. Gravitational Potential. To continue to explore the concept of Gravitational potential To examine gravitational potential near a spherical planet. Compare with contour lines on a map. Equipotentials 1.
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Book Reference : Pages 56-68
Book Reference : Pages 63-65
To continue to explore the concept of Gravitational potential
To examine gravitational potential near a spherical planet
Note in keeping with the inverse square law, the gravitational field becomes weaker further away from the planet
i.e. Equal increments in equipotential are spaced further apart
However, near the surface of a planet we consider the gravitational field to be uniform and we consider the equipotentials to be horizontal & parallel to the ground
A 1kg mass raised from the Earth’s surface by 1m gains 9.81J of G.P.E. It gains another 9.8J1 for the next metre etc
Ep = mgh
Can only be applied where h is small compared to the radius of the planet
Definition : gravitational field to be uniform and we consider the The potential gradient at a particular point in a gravitational field is the change in potential per metre
Near the Earth’s surface this is 9.81Jkg-1m-1 However, further away this reduces rapidly
In general for a change in potential V over a small distance r then
the potential gradient = V / r
V + V
For a small mass m being moved from a planet by gravitational field to be uniform and we consider the r against the gravitational force Fgrav then its gravitational potential is increased by:
V + V
For a gravitational field to be uniform and we consider the mass m, then the change in potential (remember W = mV)
V = W/m (substitute for W)
V = Fr/m (rearrange)
F = mV /r Which is equal & opposite to Fgrav
Fgrav = -mV /r
Remember gravitational field strength g = Fgrav/m
g = - V /r
g gravitational field to be uniform and we consider the is the negative of the potential gradient
Meaning that g acts in the opposite direction of the potential gradient.
The gradient is always at right angles to the equipotentials
When calculated the previous equation give us a value of -63MJkg-1This means that 63MJ of work must be done to remove each 1kg from the Earth’s surface to infinity.
Gravitational Field Strength
Distance from centre of planet with Radius R
Each square represents a 1N force acting for a distance of 2.5x106 m (and since W.D. = f x d each square represents 2.5MJ)