A pulley is massless and frictionless. The masses 3 kg, 2 kg, and 7 kg are suspe

Question

A pulley is massless and frictionless. The masses 3 kg, 2 kg, and 7 kg are suspended as in the figure. What is the tension T_1 in the string between the two blocks on the left-hand side of the pulley? The acceleration of gravity is force acting on the block on the incline. Answer in units of N. Calculate the coefficients of friction. In the figure below the left-hand cable has a tension T_1 and makes an angle of 46^degree with the horizontal. The right-hand cable has a tension T_3 and makes an angle of theta_3 with the horizontal. A 91.1 N weight is on the left and a 85 N weight is on the right. The cable connecting the two weight is horizontal. Find the tension T_1. Answer in units of N. Find the tension T_2. Answer in units of N. Find the angle theta_3. Answer in units of degree.

Explanation / Answer

a)Under equilibrium, the horizontal forces:

T1 cos46 = T3 cos(theta)

For the vertical forces:

T1 sin46 = 91.1

T1 = 91.1/sin46 = 126.64 N

T1 = 126.64 N

b)T1 cos46 = T3 cos(theta)

126.64 x cos46 = 87.97

T3 cos(theta) = 87.97 (i)

T3 sin(theta) = 85 N (ii)

(ii)/(i)

tan(theta) = 85/87.97 => theta = 44

T3 = 87.97/cos44 = 122.3 N

T2 = T3 cos(theta)

T2 = 122.3 x cos44 = 87.97 N

b)T2 = 87.97 N

c)theta = 44 deg

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