mattysimins
Nov18-04, 09:24 PM
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
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