# Confused about kenetic and potential energy problem

In this problem a mass m is dropped from a height h onto a flat surface. when it bounces it has the same speed before the collision. There is a constant force of air resistance f acting on the mass as it goes through this motion. (answer in terms of f, m, h, v, and g. )

the first asks how fast is the mass going as it collides.
Wnc=Ef-Ei (Ef=Uf (zero) + 1/2mv^2) (Ei=Ui (mgh) + 1/2mv^2 (initial v=0))
fhcos180=1/2mv^2-mgh
mgh-fh=1/2mv^2
(2h(mg-f))/m=v^2
got that one.

The second asks how high the mass goes after the collision.
fhcos180=mgh-1/2mv^2 (the final and initial switch because now the mass is moving upwards and the "final" in this equasion is when the ball reaches the peak.)
1/2mv^2=mgh+fh
mv^2=h2(mg+f)
h=(mv^2)/(2(mg+f))
v^2=(2h(mg-f))/m so...
h(after bounce)=(h(original)(mg-f))/(mg+f)
got that one too.

Now the final part of the problem asks after many bounces the ball stops. the displacement is -h, but it traveled much farther back and forth. what was that distance?

So far all i have is i know that for the ball to come to rest, the velocity and the height must equal zero. (also, Ef and Ei must equal zero.)

I don't have a clue as to what to do here, so could someone give me a push in the right direction? not the whole solution, please.

edit: advanced my solution to the second part

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## Answers and Replies

Andrew Mason
Science Advisor
Homework Helper
Try analysing the energy involved. The ball stops when the energy lost to friction equals the initial potential energy of the ball.

AM

wow i must have been tired last night.
Wnc=-Ei (had that)
-fd=-mgh (had that)
d=mgh/f

... is that it? if it is i'm going to kick myself.

Andrew Mason
Science Advisor
Homework Helper
mattysimins said:
wow i must have been tired last night.
Wnc=-Ei (had that)
-fd=-mgh (had that)
d=mgh/f

... is that it? if it is i'm going to kick myself.
Well, you still have to figure out how many bounces that takes.

AM

Nah, i should have typed it neater.
"After many bounces the ball stops (just a statement). The displacement is -h, but over the ball traveled a considerably larger distance. What was that distance?"

ruffneck2
A 10kg box is pulled 10m up an inclineed plane by a force of 100n parallel to the incline. The coefficient of friction is .1 (a) What is the work done by force? (b)what is the block potential energy? (c)what is the increase in block kinetic energy? (d)What is the work done against friction? (e)What is the final velocity?