A certain crane can provide a maximum lifting force of 25 000 N. It hoists a 2000-kg load starting at ground level by applying the maximum force for a 2-second interval; then, it applies just sufficient force to keep the load moving upward at constant speed. Approximately how long does it take to raise the load from ground level to a height of 30 m?
A)2 s
B)5 s
C)7 s
D)9 s
E)10 s

Question

Quizplus · Accepted Answer

First, we need to find the force required to lift the load against gravity:
F(gravity) = mg
F(gravity) = (2000 kg)(9.81 m/s²)
F(gravity) = 19 620 N

Next, we can find the additional force (F) required to keep the load moving upward at constant speed:
F = 25 000 N - 19 620 N
F = 5380 N

Now we can use the equation of motion for constant acceleration to find the time it takes to raise the load to a height of 30 m:

Δy = v₁t + 1/2at², where Δy = 30 m, v₁ = 0 m/s, a = F/m = 5380 N / 2000 kg = 2.69 m/s²

30 m = 1/2(2.69 m/s²)t²
t² = 22.26 s²
t = 4.72 s (rounded to two significant figures)

Therefore, approximately 7 seconds would be needed to lift the load from ground level to a height of 30 m, taking into account the 2-second initial interval of maximum force.

A Certain Crane Can Provide a Maximum Lifting Force of 25