Question

A bucket crane consists of a uniform boom of mass ?=201 kg and length ?=59.91 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 be modeled as a point mass of weight 197 lb located at the end point of the boom. One end of a long straight boom of mass capital m and length capital l is connected to a pivot point on a truck bed. The end of the boom opposite to the truck bed is elevated such that the boom makes an angle theta with the truck bed. The boom supports a bucket and worker of combined mass lowercase m at its far end point. Suppose that when the boom makes an angle of 65.3∘ with the horizontal truck bed, the bucket crane suddenly loses power, causing the bucket and boom to rotate freely toward the ground. Find the magnitude of the angular acceleration ||?⃗ || 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 ?=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

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