Open-Response Homework Problem 16.4 A new construction crane has the following s

Question

Open-Response Homework Problem 16.4 A new construction crane has the following specifications: The hook has mass 1000kg the maximum capacity of the hook is 400kg. the constant lifting speed of the hook is 1.5?, and the hook must achieve this speed in 2 seconds at a constant acceleration, beginning at rest. (a)[7 pt(s) What is the maximum average power the crane motor must deliver to get up to cruising speed? (b)[5 pt(s) What constant power must the motor supply as the hook rises, after attaining its cruising speed upward?

Explanation / Answer

a)

distance travelled in 2 sec = 0.5 * (1.5/2)*2^2

distance travelled = 1.5 m

Here , as time taken is 2 sec

then , work done by motor = 0.5 *(1000 + 400) * 1.5 ^2 + 1400 * 9.8*1.5

Work done = 22155 J

Power of motor = work done/time

Power of motor = 22155/2

Power of motor = 11077.5 W

the maximum power of motor is 11077.5 W

b)

when moving with constant velocity

F = mg

then

Power = F.v

Power = 1400*9.8*1.5

Power = 20580 W

the constant power of motor is 20580 W

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