Assume that the block on the table (Figure 1) has twice the inertia of the hangi

Question

Assume that the block on the table (Figure 1) has twice the inertia of the hanging block. You give the block on the table a push to the right so that it starts to move. If the magnitude of the force exerted by the table on the block is half the magnitude of the gravitational force exerted on the hanging block, what is the acceleration of the hanging block after you have stopped pushing the block on the table? Express your answer to two significant figures and include the appropriate units. Enter positive value if the is upward and negative value if the acceleration is downward. What would this handing-block acceleration be if you had pushed the block on the table to the left instead? Consider only a short time interval after you stop pushing. Express your answer to two significant figures and include the appropriate units. Enter positive value if the acceleration is upward and negative value if the acceleration is downward.

Explanation / Answer

a) According to the question,

Let us suppose the mass of hanging block be 'm' and acceleration be 'a'

for the block on table, frictional force, F = 0.5 x m x g

Using Newton's second equation of motion

Acceleration, a = net force/total mass

a = (mg - 0.5 mg)/(2 m + m )

a = 0.167 x g

a = 0.167 x 9.8

a = 1.633 m/s2

Hence, the acceleration of the hanging block is found to be 1.633 m/s2

b) Now, if the block is pushed to the left,

Acceleration, a = net force/total mass

a = (mg + 0.5 mg)/(2 m + m )

a = 0.5 x g

a = 0.5 x 9.8

a = 4.9 m/s2

Hence, the acceleration of the hanging block is found to be 4.9 m/s2

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