Question

A bucket crane consists of a uniform boom of mass M - 201 kg and length L- 59.09 ft that pivots at a point on the bed of a fixed truck. The truck supports an elevated bucket with a worker inside at the other end of the boom, as shown in the figure. The bucket and the worker together can bc modclcd as a point mass of wcight 195 Ib locatcd at the end point of the boom. Supposc that when thc boom makes an angle of 66.3" with the horizontal truck bed, the bucket crane suddenly loses power, causing the buckct and boom to rotate frecly toward the ground. Find the magnitude of the angular acceleration lal of the system just after the crane loses power. Take the rotation axis to be at the point where the boom pivots on the truck bed. Use g 9.81 m/s2 for the acceleration due to gravity. For unit conversions, assume that 1 m - 3.28 ft and 1 lb -4.45 N. Express your answer to at least two decimal places

Answer 1

Solution,

Length, L = 59.09 ft = 18.01 m

w = 195 lb = 867.40 N

Mg = 201 x 9.8 = 1971.81 N

(mg cos66.3 x L/2) + (w cos66.3 x L) = (mL^2/3 + wL^2/9.8) a

13416.22 = 50441.31 a

Angular acceleration, a = 0.266 rad/sec^2

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