3. A person gives a 5.57 kg block a push, causing it to slide up a ramp that is inclined 8.64 with respect to the horizontal. T

Question

1.    A person gives a 5.57 kg block a push, causing it to slide up a ramp that is inclined

           8.64° with respect to the horizontal. The coefficient of kinetic friction for the ramp is

           0.744.  While the block is sliding, it is accelerating (i.e., it has a nonzero acceleration).

           Find the acceleration.

Answer 1

The key to this problem is to know the forces that lead to motion act along the plane.

Since the block slides up the plane, there must be an upward pushing force in addition to the component of gravity down the slope as well as the frictional force (proportional to the normal force which is balanced).

Once the pushing force is removed, only the frictional force and the force of gravity act on the block.

Since the motion is upward both the frictional and downward force act downward, and the force equation is

F = ma = - mg sinθ - μmgcosθ

a =-g sinθ - μgcosθ = -9.8 sin(8.64°) - (0.744)9.8cos(8.64°) = -1.47 - 7.21 = - 8.68m/s²