The pinion A of the hoist motor drives gear B. which is fixed to the hoisting dr

Question

The pinion A of the hoist motor drives gear B. which is fixed to the hoisting drum C. The block D is lifted from rest and reaches an upward velocity of 2 ft sec after traveling a vertical distance of 12 inches at constant acceleration. As block D passes this position, determine (a) the magnitude of acceleration of point E on the drum which is in contact with the cable that hoists block D, and (b) the angular velocity and angular acceleration of the pinion A . The dimensions shown in the graph are: rA = 4.8in; rS = 9in; rC = 12in.

Explanation / Answer

as the block is moving upwards , drum c is rotating anticlockwise
v= 2 ft/sec
rc = 12 in = 1 ft
hence = v/rc = 2 rad/sec

= angular acceleration = 0

so acceleratio of E = aE = 2 * rc = 2^2 * 1 = 4 ft/sec^2

this acceleration is downwards

b) now * rb = a * ra

so a = 3.75 rad/sec ,which angular velo of point a

angular accelaration = 0 as the whole system is moving at constant speed

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