Physics Question?

Question

It is really a question to an answer, here it is:

http://i97.photobucket.com/albums/l216/2RIP/ph.jpg

When Ep = -Ek , why is the kinetic energy being subtracted by 0 besides the fact that it will later in the question remove the negative sign. Are there any supporting evidence for doing this? Please explain.

I guess what i'm trying to ask is the purpose of the negative kinetic energy when it can just remain positive.

Answer 1

You can think of it this way: the change in the kinetic energy of the body is equal to the work done by all the forces acting on this body. They tell you that the work here is negative. That's why deltaEk = - deltaEp, or deltaEp = - deltaEk.

The change in kinetic energy is kinetic energy at the beginning minus kinetic energy at the end. Kinetic energy at the beginning was 0, kinetic energy at the end was (that expression they have there)

This is where the minus sign goes: deltaEp = -deltaEk, but they got a negative answer for deltaEk. So the minus sign got cancelled out by the other minus sign.

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The purpose is to show in your answer that you understand the physics behind the problem, not just the math. To show that you can be consistent when you are applying a physics law to a problem. When you have to deal with messy complicated systems you have to keep track of all those minus signs very carefully because the answer won't be so intuitively obvious. Oh crap, I do sound like annoying teacher... I'm too young!

Answer 2

Note that it is not Ep = -Ek

It is ∆ Ep = -∆ Ek

∆ denote the change in a quantity.

∆ Ep = -∆ Ek

In the above equation – sign shows a loss in that quantity.

Gain in potential energy = loss in kinetic energy

The same equation can be written as after multiplying by – sign as

- ∆ Ep = ∆ Ek

Now this equation shows that loss in potential energy is equal to gain in potential energy.

The same equation can be written as

∆ Ek- ∆ Ep = 0 or ∆ Ep- ∆ Ek =0

Noting that (-) sign refers to loss, the above two equations are read as

Gain in K.E plus loss in P.E is zero or

Gain P.E plus loss in K.E is zero.

Since the magnitudes of energy are equal if we consider one as gain then the other is loss.

In the given problem initially the speed is V and finally it becomes zero.

Change in K. energy is (Final – initial)

Final < initial and hence the change is negative showing that it is a loss.

This loss is gained as potential energy and hence change in P.E is positive or gain.