A block with mass 20.0 kg rests on a ramp that is inclined at 53 Degree above th

Question

A block with mass 20.0 kg rests on a ramp that is inclined at 53 Degree above the horizontal. A light rope passes over a light frictionless pulley and connects the 20.0 kg block to a 6.0 kg block that hangs vertically in the air. When the system is released from What is the magnitude of the acceleration of the 20.0 kg block as it slides down the ramp? While the blocks are moving, what is the tension in the rope? What is the magnitude of the friction force that the ramp exerts on the 20.0 kg block? What is the coefficient of kinetic friction between the block and the surface of the ramp?

Explanation / Answer

a).

Consider the two blocks and the rope as a system

Let acceleration of the system is 'a'.

S = u*t + 0.5*a*t^2
=> 0.26 = 0 + 0.5*a*0.5^2
=> a = 2.08 m/s^2

b).

For the 6 kg block,
F = m*a
=> T - mg = m*a
=> T - 6*9.8 = 6*2.08
=> T = 71.28 N

c).
Friction force will act upwards on the 20 kg block.

Let the friction force be F1.

For the 20 kg block,
F = m*a
=> mg*sin53 - T - F1 = m*a
=> 20*9.8*sin53 - 71.28 - F1 = 20*2.08
=> F1 = 43.6 N

d).
F1 = u*N
=> F1 = u*mg*cos53
=> 43.6 = u*20*9.8*cos53
=> u = 0.369

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