In this problem a mass(adsbygoogle = window.adsbygoogle || []).push({}); mis dropped from a heighthonto a flat surface. when it bounces it has the same speed before the collision. There is a constant force of air resistancefacting on the mass as it goes through this motion. (answer in terms off, 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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# Homework Help: Confused about kenetic and potential energy problem

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