Question

Which of the following situations describes an object's kinetic energy being converted into gravitational potential energy?
A.
A ball rolls up an inclined ramp.

B.
A penny sits motionless atop a shelf.

C.
A kiwi is dropped from a second-story window.

D.
A water particle flows down a mountain stream.

(Please don't give direct answers)

Answer 1

Let's think about what gravitational potential and kinetic energy are.
Gravitational potential energy means that at some height h, there is energy stored that was given by the work needed to move it there. For example, let's say we put a book on top of a shelf. Work needed to be done on the book to give it energy which is now stored as potential energy at some height h. Mathematically, we can think of this as
\[PE=mgh=Wh\]Which states that the potential energy is the objects weight (mg) times the height at which it is placed!

Now let's think about kinetic energy.
When that book falls from the shelf, what happens to all that potential energy that we stored? The values of height are rapidly falling, so the PE falls as well! But we know that energy can't simply just "vanish," therefore is is being transferred to a different FORM of energy! Kinetic energy! We can express kinetic energy as the following: \[KE=\frac{ 1 }{ 2 }mv^2\] This means that the kinetic energy is the mass times the velocity of which it moves! (squared, of course). This is how we've obtained the Law of Conservation of Energy. Energy is never created nor destroyed, and thus, for this situation, can be expressed as:
\[KE_0+PE_0=KE_f+PE_f\]So the sum of kinetic and potential energy BEFORE is EQUAL to the sum of kinetic and potential energy AFTER!
If we look at our example with the book on the shelf, we see that initially it has NO kinetic energy. Why? It's not moving! But we already noted that is has potential energy! What about when it falls and right before it hits the ground? It has no potential energy anymore, because all the energy was stored into kinetic energy! Therefore, for this case: \[\large KE_0+PE_0=KE_f+PE_f \rightarrow 0+PE_0=KE_f+0\]This means that the potential energy before is equal to the kinetic energy after! Wow!

Answer 2

So, after now having this information, what do you think the answer is? If one is transferred into the other, how would you explain transferring kinetic into potential? Hint: It's the opposite of our example of the book falling from the shelf.

Answer 3

Thanks! Now I understand the different types of energy a bit better. (PE is just what it's name is.. And KE is when it's moving [Well, simply.] ) I think the answer is A (It makes the most sense to me since it would roll up then stop rolling.)

Answer 4

I'd say so too! :)