A 4.5 kg block is given an initial speed of 14 m/s up an incline plane of angle

Question

A 4.5 kg block is given an initial speed of 14 m/s up an incline plane of angle of 45. When the block has moved 8.0 m along the plane, the speed of the block has decreased to 5.2 m/s. a) Find the coefficient of kinetic friction between the block and plane. b) Calculate the maximum distance the block moves up the plane.

Explanation / Answer

As in any mechanics problem, you have to do a sum of force for every body. Then, Sum of forces on block b Tb - mb g = mb a Sum of forces on block c Tc - mc g = mc a Sum of forces on block a Tb - Tc -Fr = ma a In the case of constant velocity a=0 and thus Tb = mb g Tc = mc g Fr = Tb - Tc = (mb-mc) g and uk = Fr / (ma g) = (mb - mc)/ma where Tb and Tc are the tensions in the string at the respective points. In this case mb > mc. Since the system is symmetric then it doesn't matter which is mb and which is mc as long as mb > mc. To calculate the acceleration, simply go back to the original set of equations above Tb - mb g = mb a Tc - mc g = mc a Tb - Tc - uk ma g = ma a Now you have a system of three equations with three unknowns (Tb, Tc, and a). Go ahead and solve for a.

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