Two masses are connected by a string which passes over an ideal pulley as shown

Question

Two masses are connected by a string which passes over an ideal pulley as shown below. Block A has a mass of 3.00 kg and can slide along the inclined plane with a coefficient of kinetic friction mu k = 0.35. The plane is inclined 30.0degree to the horizontal. Find the mass of block B needed in order to cause block A to slide up the ramp with constant velocity. *Show appropriate free-body diagrams (sketch forces directly on the figure below) and write the corresponding equations as a starting point.

Explanation / Answer

For block A, the gravitational force pointing down the plane is

3g sin 30° = 1.5g.

The normal force perpendicular to the plane is 3g cos 30°, so the frictional force is

3g*cos 30° = 0.91g. .................( = 0.91)

To overcome this,

F = mg = (1.5 + 0.91)g

m = 2.41 kg.

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