A block of mass m1 = 38 kg on a horizontal surface is connected to a mass m2 = 2

Question

A block of mass m1 = 38 kg on a horizontal surface is connected to a mass m2 = 21.8 kg that hangs vertically as shown in the figure below. The two blocks are connected by a string of negligible mass passing over a frictionless pulley. The coefficient of kinetic friction between m1 and the horizontal surface is 0.28. (a) What is the magnitude of the acceleration of the hanging mass? m/s2 (b) Determine the magnitude of the tension in the cord above the hanging mass. Consider Newton's Second Law for each mass. N

Explanation / Answer

a) on m1:

in vertical, N - m1g = 0

N = m1g

friction force = uN = 0.28m1g

In horizontal:

T - 0.28m1g = m1a ..........(i)

on m2:

m2g - T = m2a .....(ii)

adding (i) and (ii)

m2g - 0.28m1g = (m1 + m2)a

21.8x9.8 - 0.28x38x9.8 = (21.8 + 38)a

a = 1.83 m/s^2

b) m2g - T = m2a

T = m2 ( g - a) = 21.8 ( 9.8 - 1.83)

T = 173.77 N

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