A marble block of mass m 1 = 554.5 kg and a granite block of mass m 2 = 139.5 kg

Question

A marble block of mass m1 = 554.5 kg and a granite block of mass m2 = 139.5 kg are connected to each other by a rope that runs over a pulley as shown in the figure. Both blocks are located on inclined planes with angles ? = 38.6 and ? = 58.0. The rope glides over the pulley without friction, but the coefficient of friction between block 1 and the inclined plane is ?1 = 0.13, and that between block 2 and the inclined plane is ?2 = 0.31. (For simplicity, assume that the coefficients of static and kinetic friction are the same in each case.) What is the acceleration of the marble block? Note that the positive x-directionis indicated in the figure.

A marble block of mass m1 = 554.5 kg and a granite block of mass m2 = 139.5 kg are connected to each other by a rope that runs over a pulley as shown in the figure. Both blocks are located on inclined planes with angles ? = 38.6½ and ? = 58.0½. The rope glides over the pulley without friction, but the coefficient of friction between block 1 and the inclined plane is ?1 = 0.13, and that between block 2 and the inclined plane is ?2 = 0.31. (For simplicity, assume that the coefficients of static and kinetic friction are the same in each case.) What is the acceleration of the marble block? Note that the positive x-directionis indicated in the figure

Explanation / Answer

In this problem, there are four forces that affect the acceleration of the blocks. These forces are the components of the weights that the parallel to the inclined planes and the friction forces.

For the marble block:
Force parallel = 554.5 * 9.8 * sin 38.6 = 3390.22 N
Ff = 0.13 * 554.5 * 9.8 * cos 38.6 = 552.09 N

For the granite block:
Force parallel = 139.5 * 9.8 * sin 58 = 1159.37 N
Ff = 0.31 * 139.5 * 9.8 * cos 58 = 224.58 N

Since the force parallel of the marble block is greater than the force parallel of the granite block, the marble block will be moving down its inclined plane as the granite block moves up its inclined plane. The force that is causing the block

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