Two masses are attached by a massless. non-stretching cord strung over a massles

Question

Two masses are attached by a massless. non-stretching cord strung over a massless, bcrionless pulley, as shown below. One mass hangs freely (m_1) and is 1.00 kg, while the other (m_2) is on an incline and is 0.500 kg. The length of the incline is 2.50 m, and one end is 1.00 m higher than the other. There is friction between m_2 and the incline. When released from rest, m_1 accelerates downward at 3.50 m/s^2. c) what is the magnitude of the friction force acting on the block on the slope? d) Calculate the coefficient of friction between the block and the slope.

Explanation / Answer

writing equations of motions to m1 and m2

for m1

m1g-T = m1a

T = m1(g-a) = 1*(9.81-3.5) = 6.31 N

for m2

-m2*g*sin(theta)-fk+T = m2*a

-0.5*9.81*(1/2.5) - fk + 6.31 = 0.5*3.5

kinetic frictional force fk = (-0.5*3.5)+(6.31)-(0.5*9.81*1/2.5) = 2.598 N

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d) fk =mu_k*N

mu_k = fk/N = 6.098/(m2*g*cos(theta))

theta = sin^(-1)(1/2.5) = 23.6 degrees

then mu_k = 2.598/(0.5*9.81*cos(23.6))

coefficient of friction is mu_k = 0.578

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