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conservation of energy physics question?
A factory worker accidentally releases a crate of mass m that was being held at rest at the top of a ramp with length d which is inclined at angle θ to the horizontal. The coefficient of kinetic friction between the crate and the ramp, and between the crate and the horizontal factory floor, is μk. (use g where applicable). (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)
how i thought to get the answer:
total energy at the top of the ramp = U (potential energy) = mgh
and total energy at the bottom of the ramp =
K (kinetic energy) - work done by friction = 1/2 * m * v^2 - mu * m * g * d * cos(theta)
so conservation of energy says energy at the top must equal energy at the bottom thus:
mgh = 1/2 mv^2 - mu *mgdcos(theta)
solving for v i get:
sqrt(2*g*d*(sin(theta) + mu * cos(theta)))
by the way i subbed d*sin(theta) for h, as im not allowed to use h
where did i go wrong???
its asking for the velocity of the box at the bottom of the ramp btw
1 Answer
- 7 years ago
I am not a PH.D fisicist but I think I see your problem.
Work is defined by W=Fd where d is the distance the object traveled under the influence of F(in this case b/c W is lost to friction it is -W).
W=KE(f)-KE(i) and KE(i)=mgdsin(theta).
KE(f)= -W+KE(i)
and I think you are good to go from there.
P.S. My English is really bad. And Let me know if I made a mistake. Thanks.