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 = 22.2 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 0.27. (Assume gravity acts toward the +y direction and the +x-axis is parallel to the surface and to the right.)

(a) What is the acceleration of the hanging mass? (Indicate the direction with the sign of your answer.) m/s2

(b) Determine the tension in the cord. (Indicate the direction with the sign of your answer.) N

Explanation / Answer

mg - T = ma

(22.2 * 9.8) - T = 22.2 * a

T = 217.56 - 22.2 a -------------------(1)

In the horizontal T - mu m g = ma

T - (0.27)(38)(9.8) = (38)a

T - 100.55 = 38 a --------------------(2)

217.56 - 22.2 a - 100.55 = 38 a

117.01 = 60.2 a

a = 1.94 m/s2

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T = 217.56 - 22.2 (1.94)

T = 174.49 N

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