What Happens When You Subtract Potential Energy from Total Energy?

[Drew777]

What would it mean when you subtract potential energy of a higher elevation from the summation of energy(kinetic + potential of a lower elevation)?

 

[BruceW]

potential energy + kinetic energy = constant. Therefore the summation of energy of the lower position equals the summation of energy of the higher elevation.

So subtracting the potential energy of the higher position (from the summation of energy) gives the kinetic energy of the higher position.

 

[Drew777]

So is it possible to get a negative number as the kinetic energy of the higher elevation?

 

[rcgldr]

So is it possible to get a negative number as the kinetic energy of the higher elevation?

Kinetic energy can't be negative. A constant sum for gravitational potential energy and kinetic energy only occurs if there are no other forces involved. If some force other than gravity affects an object, then the work done by that force also affects the total energy.

 

[Drew777]

Kinetic energy can't be negative. A constant sum for gravitational potential energy and kinetic energy only occurs if there are no other forces involved. If some force other than gravity affects an object, then the work done by that force also affects the total energy.

I understand that. When I take the the potential energy of the higher point and subtract it from the summation of energy I get from (PEf +KEf) I get a negative number. What does this mean?

 

[Dr_Morbius]

It means you are doing the math wrong. You can't do that. What you're doing produces a meaningless number. You have to subtract the potential energy from the summation not from the kinetic energy.

 

[willem2]

I understand that. When I take the the potential energy of the higher point and subtract it from the kinetic energy I get a negative number. What does this mean?

kinetic energy can't be negative.
It means that a thrown object will fall back before it gets to this altitude.
If you throw something straight up, it will start to move down again when the kinetic energy is 0.

 

[Drew777]

kinetic energy can't be negative.
It means that a thrown object will fall back before it gets to this altitude.
If you throw something straight up, it will start to move down again when the kinetic energy is 0.

Sorry I wrote it down wrong. I went back to edit what I meant.

What I have is the potential energy of a low point that I will call PEf and I got the kinetic energy it took for the object to move down the incline(KEf). I added them together to get Ef.
Now I have to take this number Ef and subtract it from the higher point of potential energy, that I will call PE. I ended up with a negative number on all my trials but one. Why would this be?

 

[rcgldr]

Potential energy can be negative. In the case of GPE (gravitational potential energy) from a point source, GPE = -G M m / R relative to a reference point with a distance of infinity from the source point. Wiki article:

http://en.wikipedia.org/wiki/Potential_energy#General_formula

 

[BruceW]

What I have is the potential energy of a low point that I will call PEf and I got the kinetic energy it took for the object to move down the incline(KEf). I added them together to get Ef.
Now I have to take this number Ef and subtract it from the higher point of potential energy, that I will call PE. I ended up with a negative number on all my trials but one. Why would this be?

KEf + PEf = PE + KE
(rearranged): KEf + PEf - PE = KE

If you then get a negative number for KE, then maybe it is because you measured KEf and PEf at different points.
Also, if the object rolls down the incline, then it will have some rotational energy:
KEf + PEf + KE(rotational) = PE + KE
This might explain where the energy went. Also, if there was a lot of friction, then maybe the energy turned into heat.

 

[Drew777]

What was done is I slid a puck down an air table. I did this 7 times, each with a different weight. I calculated the potential energy of the high point and calculated the potential energy at the low point. The KEf I measured was using 1/2(m)(Vf^2). So the KEf is the kinetic energy from the high point (PEhp) to the lower point(PEf). To get Ef I added PEf + KEf.
Now I need to find Δ E. The equation for Δ E is Ef-PEhp.

Example
PEf + KEf=Ef
2,070,000 ergs + 623,000 ergs=2,690,000 ergs
Ef - PEhp=Δ E
2,690,000 ergs - 2,810,000 ergs= -107,000 ergs
All of my trials came out with a negative number except my last trial. It came out with a +20,000.
I am trying to understand where these numbers are coming from. Is -107,000 just the energy lost from the top to the bottom. If so then where did the positive number come from?
Thanks
Drew

 

[cepheid]

The KEf I measured was using 1/2(m)(Vf^2). So the KEf is the kinetic energy from the high point (PEhp) to the lower point(PEf).

Your phrasing doesn't make sense here. K_Ef is the kinetic energy that the object has when it is at the lowest point.

To get Ef I added PEf + KEf.
Now I need to find Δ E. The equation for Δ E is Ef-PEhp.

Example
PEf + KEf=Ef
2,070,000 ergs + 623,000 ergs=2,690,000 ergs
Ef - PEhp=Δ E
2,690,000 ergs - 2,810,000 ergs= -107,000 ergs
All of my trials came out with a negative number except my last trial. It came out with a +20,000.
I am trying to understand where these numbers are coming from. Is -107,000 just the energy lost from the top to the bottom. If so then where did the positive number come from?
Thanks
Drew

In the ideal (frictionless) case, since mechanical energy is conserved, ΔE should be 0 in all cases. (All potential energy lost during the descent is converted into kinetic energy). The fact that you get a negative ΔE means that mechanical energy is lost. This must be a combination of experimental error + the fact that the table is not entirely frictionless. It's probably mostly the latter, a consequence of which is that although total energy (as always) is conserved, mechanical energy (which means kinetic + potential) is not conserved. Some of the mechanical energy is converted into heat by friction. That's where the shortfall comes in: it's the work done by the frictional force.

I don't know why you get a positive ΔE in one instance. This could be an indication that the variation in your results is dominated by measurement error (contrary to what I assumed above, that friction was the dominant effect when it came to the deviation between expected and measured results).

We'd need more information about how you got your numbers in order to comment further.

 

[Dr_Morbius]

By the way, it is bad practice to edit a post you made. The edit you made to your post is now going to confuse readers because our replies no longer make sense. You can make edits for spelling and grammar but you need to do it immediately. Do not change the meaning of the post. If you made a mistake make another post with the correction.