# Not sure if I'm understanding mechanical energy correctly?

A .5 kg ball is thrown vertically upward with an initial speed of 8 m/s. If the initial potential energy is taken as zero, find the following:
1. potential energy of the ball at a height of 2 m above the initial position
2. the initial kinetic energy of the ball
3. the total mechanical energy at the maximum height

PE= mgy
Potential Energy=(mass)(Gravity)(height)

KE(initial)+PE(initial)=KE(final)+PE(final)

1. So for the first one, this is how I solved for the potential energy:
PE=mgy
PE=(.5kg)(9.8m/s^2)(2m)
PE=9.8 J
I am pretty confident with how I solved this part of the problem.

2. The second question I had a little more trouble with.
I used:
KE(initial)+PE(initial)=KE(final)+PE(final), and plugged in what I knew:

KE(inital) + 0=0 + PE(final)

So since KE=PE I said that KE would also equal 9.8 J.

3. So if the ball had 9.8 J to begin with, and ended with 9.8 J, shouldn't this answer also be 9.8 J?

Thanks for the help.

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Doc Al
Mentor
1. So for the first one, this is how I solved for the potential energy:
PE=mgy
PE=(.5kg)(9.8m/s^2)(2m)
PE=9.8 J
I am pretty confident with how I solved this part of the problem.
Good!

2. The second question I had a little more trouble with.
I used:
KE(initial)+PE(initial)=KE(final)+PE(final), and plugged in what I knew:

KE(inital) + 0=0 + PE(final)

So since KE=PE I said that KE would also equal 9.8 J.
You need to calculate KE(initial) based on the speed that was given. (What's the definition of KE?)

Do not assume KE(final) is zero. No one said that 2 m was the maximum height of the ball.

So would I set up the equation to :

KEi= (1\2mv^2) + PEf ?

If so, what do I use for PEf so that I can solve the equation?

Doc Al
Mentor
So would I set up the equation to :

KEi= (1\2mv^2) + PEf ?

If so, what do I use for PEf so that I can solve the equation?
For question 2 all you need is the definition of KE. (All they ask for is the initial KE.)

When solving question 3, then you'll need to use conservation of mechanical energy. Hint: It's a trick question. You shouldn't have to do any further calculations beyond what you already did.

For question 2 all you need is the definition of KE. (All they ask for is the initial KE.)

When solving question 3, then you'll need to use conservation of mechanical energy. Hint: It's a trick question. You shouldn't have to do any further calculations beyond what you already did.
So, shouldn't the answer to the third one be 16?

Because:

PEi + KEi = PEf + KEf
0 + 16 = PEf + KEf

So it doesn't really matter what PEf and KEf are because they equal 16 combined, by the conservation of mechanical energy law?

Doc Al
Mentor
Exactly!

Thank you for the help! :)