Problem 18.50 The compound disk pulley consists of a hub and attached outer rim

Question

Problem 18.50 The compound disk pulley consists of a hub and attached outer rim Figure 1 Figure 1 of 1 100 mm 30 mm previous l 7 of 15 next Part A If it has a mass of 5 kg and a radius of gyration kG 45 mm determine the speed of block A after A descends 0.4 m from rest. Blocks A and Beach have a mass of 2 kg Neglect the mass of the cords. Express your answer to three significant figures and include the appropriate units. 1.92 m vA Submit My Answers Give Up incorrect; Try Again; 5 attempts remaining Provide Feedback Continue

Explanation / Answer

Here ,

let the angular speed of the pulley is w

speed of B = w * 0.030

speed of A = w * 0.100

when block A descends 0.40 m

height raised by B = 0.40 * 30/100 = 0.12 m

Using conservation of energy

0.50 * (5 * 0.045^2) * w^2 + 0.50 * 2 * ( w * 0.030 )^2 + 0.50 * 2 * (0.100 * w)^2 = 2 * 9.8 * 0.40 - 2 * 9.8 * 0.12

solving for w

w = 18.54 rad/s

speed of block A = 18.54 * 0.100 = 1.85 m/s

the speed of block A is 1.85 m/s

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