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In this problem a mass

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

*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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