Gravitational Potential Energy (1 Viewer)

[Stopsign]

:wave: I need some help on some of these questions.

1.What is gravitational potential energy?
2.Explain why there's zero GPE at infinity and why there's a negative sign in the formula.
3.Is it true that escape velocity is reached when kinetic energy equals GPE? (Try it! There's cancelling out and it'll give you the formula!) Explain.

Thanks very much to all those who answer these questions.

 

[Tuna]

1. The amount of work done in Joules to move an object from a distance of 0 to X

2. Infinite is 0 because it corresponds to the curve similar to the hyperbola. As 'x' distance approached infinite 'y' approaches 0.

There is a negative sign so it is easier to know a definite point as you move back. If you move back from a zero it is negative.

 

[Ioup]

1) The amount of work in Joules required to move an object from an infinite distance to a point within a gravitational field.

2) Due to the inverse square nature of Newtons law of gravitational attraction GPE will only drop to zero at an infinite distance away from the point in the gravitational field. Therefore we choose infinite as our ground zero level much like the surface of the Earth is defined as zero when calculating the potential energy of an object at a certain height.
However, as the object is moved from infinity(Zero level) work is being done by the gravitational field since gravity is a force of attraction. Hence GPE is lost and there will be less GPE then there is at Zero level. So GPE will be a negative value.
GPE<o at the point in a gravitational field.
The missing energy implied by the negative symbol actually acts as a stability system. The missing energy is what binds together the Earth revolving around the sun as its this energy that the system trys to get back.

3)Rate of increase of GPE same as rate of decrease in kinetic energy when escaping gravitational field
final ek+finalEP=constant=initialEK+initial EP
Only at infinity will force between earth and object be 0.
Hence
0-Gmearth, mobject/infinity=1/2mvescsquared-Gmearth,mobject/r earth
divide by infinity
0=1/2mobject,vescsquared-Gmearth,mobject/r earth
Rearranging equation gives Vesc=square root(2Gm/r)

 

[Stopsign]

Thanks for the help guys.