A frictionless ramp is constructed so that it is at a 30 degree angle to the hor

Question

A frictionless ramp is constructed so that it is at a 30 degree angle to the horizontal. It is 3.2 meters long and 1.6 meters high. A 3.0 kg block is released at the top of the ramp and slides down onto a frictionless horizontal surface where it hits and sticks to another block that has a mass of 7.0 kg. After the blocks travel some distance, the blocks come to a rough patch that has a coefficient of friction of 0.25 between the blocks and the rough surface. How far along the rough patch do the blocks go before stopping?

Explanation / Answer

acceleration = g sin x = g*1.6/3.2 = 4.9m/s2 so final velocity = sqrt(2*4.9*3.2) = 5.6m/s let after sticking with 7kg block velocity be v conserving momentum 3*5.6 = 10*v so v = 1.68m/s force acting on friction surface = 0.25*10*9.8 = 10a so a = 2.45 m/s2 so distance it will travel = v^2/2a = 1.68^2/2*2.45 = 0.576 m

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