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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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 : 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 r against the gravitational force Fgrav then its gravitational potential is increased by:
V + V
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
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)
The area under the curve is the application of “work done = force x distance moved”....
You are advised to know how to draw g 1/r2 & V -1/r & hence be able to comment upon how g changes more sharply than V with increasing r