4 kg block is sliding down a vertical wall while being pushed by an external for

Question

4 kg block is sliding down a vertical wall while being pushed by an external force as shown in the figure.

a. What is the magnitude of the acceleration of the block (in m/s2) if the coefficient of kinetic friction between the wall and the block is k = 0.2 and the magnitude of the external force is 20 N?

b. What coefficient of kinetic friction would be required for the block to move down the wall at constant speed if the magnitude of the external force is 30 N?

c. What magnitude of the external force (in N) would be required for the block to move down the wall at constant speed if the coefficient of kinetic friction between the wall and the block is k = 0.2?

Explanation / Answer

a. What is the magnitude of the acceleration:

The magnitude of the normal force N = F sin(30 deg) = 20*sin(30 deg) = 10N

hence the acceleration = (mg-mu*N-F cos(30 deg))/m = (4*9.8-0.2*10-20*cos(30 deg))/4 = 4.969 m/s^2.

b. constant speed means no acceleration.

if mu is the coefficient of friction then the required force = (mg-mu*N-F cos(30 deg)) = 0

mg - mu*F*sin(30 deg) - F cos(30 deg) = 0

4*9.8 - mu * 30 *sin(30 deg) - 30*cos(30 deg) = 0

mu = 0.88

c. The equation of force will be:

mg - mu*F*sin(30 deg) - F cos(30 deg) = 0

F = 4*9.8/(0.2*sin(30 deg) + cos(30 deg)) = 40.578 N

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