Is potential energy the same in free fall as circular motion?

Question

I'll use values to try and get my question across. If a 1 kg block is being dropped straight down, will it have the same potential energy as a block attached to a 1m string being dropped from 90 degrees assuming it stops at 0 degrees? Assuming I did the calculations properly (1 x 9.81 x 1) the potential energy should be 9.81 for free fall. Would this be the case in the other situation?

Edit: As Cirric said, the real question is "would they strike with equal force?"

Edit2: I have just been told that height can be shown as L(1-cos[theta]) where L is the length of the string. This would lead me to beleive that the potential energy should be the same since cos[90] (or cos[pi/2]) is zero. Is this correct?

Answer 1

potential energy = mass x gravity x height
regardless

Answer 2

I don't think the string mass object will drop at 9.8 meters per second squared, like the free falling object does.

It is going to slow in acceleration as it approaches the bottom (0 degrees). At that point it will be going almost horizontal to the force of gravity, instead of parallel with it.
I don't know what the acceleration times mass would be, but it has to be less PE than the free fall, intuitively.

Answer 3

Hi. Your real question seems to be would each case strike a surface with equal force. My guess is yes.