Physics/Gravitational Potential Energy
I would really appreciate some help with a concept I just can't seem to wrap my heard around. I'm doing revision for my Physics exam next week and I'm really having trouble with the concept of Gravitational Potential Energy.
My understanding is GPE is the energy require for an object to resist the pull of gravity and remain in one place. Say a satellite was being launched from Earth at a specific velocity.
According to the formulas in the book, the total energy is the kinetic energy minus the gravitational potential energy but given that the satellite needs to both resist the pull of gravity and launch at a specific speed, shouldn't the KE and GPE add up?
If you launch the satellite at say 3x10^4 m/s, wouldn't subtracting the GPE reduce the speed?
The way I'm trying to imagine it is like with an object being dropped having it's PE gradually converted into KE, the center of the planet is the height the object is dropped from, and the speed it has at the surface of the planet is the speed a dropped object would have just before hitting the ground.
Am I getting this right? I'm just so confused.
Thanks a million in advance
GPE is energy an object possesses because of it being above a reference point. You said that "it is like with an object being dropped having it's PE gradually converted into KE". That is very true.
The location of the GPE reference point is arbitrary. It could be the center of the Earth. More often, the reference point is chosen to be the ground that something is going to fall down to. Or the bottom of an incline that something is going to slide to. A problem can be solved with the GPE reference point being chosen in various points. But the solution to the problem is easier with some points than with other points. The important thing about GPE is the change in GPE value as it moves through the various points an object finds itself. If the GPE is decreasing, the energy that is disapearing from the GPE value must be going somewhere. If the GPE is increasing, the energy being added to the GPE is coming from some source of energy.
Consider a 1 kg brick falling from a 100 m tall building. If it falls to the ground, it's generally convenient to set the reference point (where height = 0) at the ground. If we do it that way, before the brick falls, the initial GPE is
GPEi = m*g*h = 1 kg*9.8 m/s^2*100 m = 980 Joules
Velocity is zero before the fall begins, so the total energy = GPEi
As the brick falls I like to use the expression that the GPE is being cashed in to be converted to KE. If we assume that air resistance is insignificant then energy is conserved. So if you look at the condition as it passes the 50 m elevation, the sum of the remaining GPE and the amount of KE at that point equals the energy the brick started out with, GPEi.
GPEi = GPE + KE = m*g*h + (1/2)*m*v^2
GPEi = 1 kg*9.8 m/s^2*50 m + (1/2)*1 kg*v^2
The GPE at 50 m is 1/2 of GPEi so the other half of the brick's original energy has been converted to KE. So the energy equation is
980 J = 490 J + (1/2)*1 kg*v^2
You can solve that equation for v and know the brick's velocity as it goes past the 50 m height.
Immediately before the brick hits the ground, GPE is zero and all of the 980 Joule is in the form of kinetic energy. And you can find the velocity just before hitting the ground by solving this equation for v:
980 J = (1/2)*1 kg*v^2
You also said "GPE is the energy require for an object to resist the pull of gravity and remain in one place." I disagree with that. A book on a high shelf doesn't fall because the shelf provides an upward force that is equal and opposite the book's weight. If you move the book to a lower shelf, that lower shelf has to provide the same force equal and opposite the weight in order for the book to have zero net force acting on it -- which is the condition required for the book not to accelerate.
In your 3rd paragraph you asked, "shouldn't the KE and GPE add up?" If you mean that the way I think, yes, I agree. (Your book must have been talking about some particular situation if it said "the total energy is the kinetic energy minus the gravitational potential energy".) I think what you mean is that the values of KE and GPE at any point in a fall (like the brick) should be equal to the original total system energy. Such as just before a clumsy workman nudged that brick so it would fall off the scaffold.
You asked "If you launch the satellite at say 3x10^4 m/s, wouldn't subtracting the GPE reduce the speed?" Yes it would. If it launched with a short burn that resulted in a velocity of 3x10^4 m/s, it would slow down as it coasted higher because the energy in the KE category was being converted into the GPE category.
I hope this helps,