A particle can slide along a track with elevated ends and a flat central part. The flat part has length L=40 cm. The curved portions of the track are frictionless, but for the flat part the coefficient of kinetic friction is µk = 0.20. The particle is released from rest at point A, which is at height h = L/2. How far from the left edge of the flat part does the particle finally stop?
The answer is 20 cm but I don't know how to get this answer! Please Help!
2006-10-27 07:53:03 · 3 answers · asked by afchica101 1 in Science & Mathematics ➔ Physics
Friction energy expended sliding out on the flat track FE = Fs = friction force acting over s distance sliding.
Energy the particle has at the bottom of its slide down the curved part is KE = PE = mgh = W(L/2).
Conservations of energy states KE = PE = W(L/2) = kWs; so that s = (L/2)/k = 20/.2 = 100 cm. But L = 40 cm; so there is excess energy when it reaches the rise at the other end. Calculate the excess, that will have to be dissipated as it rolls back down again. Repeat the process until no more energy is left.
2006-10-27 08:18:03 · answer #1 · answered by oldprof 7 · 0⤊ 0⤋
I have to assume that point A is to the left of the left edge of the flat part. You really didn't say, and it's critical to the answer!
First, find the velocity at the bottom of the curved part: This will be the same as if it were falling straight down, since all the potential energy is converted to kinetic: v = sqrt(2gy) = sqrt(2*9.8*0.2) = 1.98 m/s.
The normal force on the flat surface is mg. So, the frictional force is mu*mg. Acceleration = F/m = mu*mg/m = mu*g = 0.2*9.8 = 1.96 m/s^2.
To find how far it goes on the flat, use x = (v^2)/(2a) = (1.98^2)/(2*1.96) = 1.000 meter.
Sounds to me like it will still have .7078 m/s velocity when it gets to the end of the flat. This will get it up the other curved part to a height of 2.55 cm. Maybe this is why the track has 2 curved ends?!!
2006-10-27 08:31:52 · answer #2 · answered by Steve 7 · 0⤊ 0⤋
Convert the potential energy at the beginning to kinetic energy as it hits the edge of the track then work out how much work needs to be done by friction to kill the kinetic energy.
It moves twice through the flat part before finally coming to rest half-way through the third pass.
2006-10-27 08:14:20 · answer #3 · answered by Anonymous · 0⤊ 0⤋