- #1
roam
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Homework Statement
http://img403.imageshack.us/img403/1751/problem1r.jpg [Broken]
Homework Equations
[itex]v_f = \frac{m v_1 + M v_2}{m+M}[/itex]
The Attempt at a Solution
Let "A" be the configuration immediately before the collision and "B" the configuration immediately after the collision, and "C" the very final state.
I have used the above equation and solved for the velocity when the bullet enters the system (immidiently after the collision):
[itex]v_B = \frac{m v_{1A}}{m+M}[/itex]
The expression for the total kinetic energy of the system right after the collision is
[itex]K_B = 1/2 (m + M) v_B^2[/itex]
Substituting vB we get
[itex]K_B = \frac{m^2v_{1A}^2}{2(m+M)}[/itex]
We then apply the conservation of mechanical energy principal to the system to get:
[itex]K_B+U_B = K_C + U_C[/itex]
[itex]\frac{m^2v_{1A}^2}{2(m+M)} + 0 = 0+ (m+M) gh[/itex]
[itex]v_{1A} = \left( \frac{M+m}{m} \right) \sqrt{2gh}[/itex]
This is very close to the answer, but how can I bring μk (coefficient of friction) into my equation? The potential energy is given by mgh, so how do I write it in terms of μk and d?
Any help is appreciated.
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