7. A crane cable that is capable of withstanding 22,000 N is attached by a hook

Question

7. A crane cable that is capable of withstanding 22,000 N is attached by a hook to a 2,000 kg block that is resting on the ground. The cable initially starts lilting the block at the maximum acceleration that the cable can withstand for 4 sec. It then continues to raise the Wan at constant velocity for further 2 sec. At this time the block slips off the hook at the end of the cable. Full 30 points will be awarded for the correct answer to the following question: What is the maximum height that the black reaches above ground? If the full credit cannot be awarded, then partial credit will be awarded for the correct answers to the following questions (2 points per question): What is the magnitude of the force of gravity acting on the block? What is the magnitude of the total force acting on the block? What is the direction of the total force acting on the block? What is the acceleration of the block in the first 4 seconds? How far will the block travel in the first 4 seconds? What velocity will the block achieve in the first 4 seconds? How far will the block travel in the last 2 seconds at the velocity found in vi}? What is the total distance traveled by the block?

Explanation / Answer

for full credit

during the 4 sec

Fnet = m*a

T - m*g = m*a = m*v/t

22000 - (2000*9.8) = (2000*v)/4

v = 4.8 m/s

a = v/t = 4.8/4 = 1.2 m/s^2

distance travelled y1 = u*t + 0.5*a*t^2

y1 = 0.5*1.2*4*4 = 9.6 m

distance travelled with constant speeed for 2 sec

y2 = v*t2 = 4.8*2 = 9.6 m

when the cable breaks the block has 48 m/s in upwards direction and is moving under gravity

y3 = v^2/2g = (4.8*4.8)/(2*9.8) = 1.175

total distance from ground Y = y1+y2+y3 = 9.6+9.6 + 1.175 = 20.375m

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