A worker in a warehouse uses a rope passing through some pulleys to lift a heavy crate. The worker exerts a force five times less than the weight of the crate but has to move the rope four times as far as the crate moves. This situation...

A) can happen because the extra distance traveled makes up for the smaller force applied

B) can happen because there is friction in the pulleys so the work done by the worker will not equal the work done on the crate

C) cannot happen because a crate that heavy would lift the worker, rather than the worker lifting the crate

D) cannot happen because the work done by the worker is less than the work done on the crate

I thought the answer was B, but my teacher said that wasn't right. Is it A? I don't think it would be impossible, but I might be wrong.

work done by man: 4h*1/5w=work

work done on crate: h*w=work
w&h = 1

man = 4*.2 = 0.8
crate = 1*1 = 1

So is it D?

Exactly, you figured it out. The man would have to pull farther (more parts in the tackle), like maybe eight times as far at 1/5 the weight

The correct answer is D) cannot happen because the work done by the worker is less than the work done on the crate.

In a system of pulleys, the force exerted by the worker is shared among the multiple segments of rope, but the total work done by the worker should be equal to the work done on the crate. The work done is calculated by multiplying the force applied by the distance moved.

According to the given information, the worker exerts a force five times less than the weight of the crate. Let's denote the weight of the crate as W. So, the force applied by the worker is 1/5th of W, or W/5.

It is also mentioned that the worker has to move the rope four times as far as the crate moves. Let's denote the distance moved by the crate as d. Therefore, the distance moved by the worker is 4d.

The work done by the worker is calculated as follows:
Work done by the worker = Force applied by the worker × Distance moved by the worker
= (W/5) × (4d)
= 4/5 * Wd

On the other hand, the work done on the crate is calculated as follows:
Work done on the crate = Force acting on the crate × Distance moved by the crate
= W × d

Since the work done by the worker (4/5 * Wd) is less than the work done on the crate (Wd), this situation cannot happen.

Therefore, option D is the correct answer.

To determine the correct answer, let's analyze the situation using the principles of work and mechanical advantage.

In this scenario, the worker exerts a force five times less than the weight of the crate but moves the rope four times as far as the crate moves. This is a clear indication that the worker is using a system of pulleys to gain a mechanical advantage.

Mechanical advantage is defined as the ratio of the output force to the input force, or the ratio of the distance over which the output force is exerted to the distance over which the input force is exerted. In this case, the mechanical advantage can be calculated as the ratio of the distance moved by the worker to the distance moved by the crate.

Let's represent the force exerted by the worker as Fw, the weight of the crate as Wc, the distance moved by the worker as Dw, and the distance moved by the crate as Dc.

According to the given information, Fw = (1/5) * Wc, and Dw = 4 * Dc.

Using the formula for mechanical advantage (MA = output force / input force = distance output / distance input), we can calculate the mechanical advantage gained by the worker:

MA = Dw / Dc = 4 * Dc / Dc = 4.

This means that the worker is gaining a mechanical advantage of 4. This allows the worker to lift the crate with less force, but over a greater distance.

Now, let's consider the answer choices:

A) "Can happen because the extra distance traveled makes up for the smaller force applied": This choice accurately reflects the situation. The additional distance traveled by the worker compensates for the smaller force applied and allows the worker to lift the crate.

B) "Can happen because there is friction in the pulleys, so the work done by the worker will not equal the work done on the crate": This statement is not necessarily true. Friction in the pulleys may reduce the efficiency of the system, but it does not affect the principle that the worker can gain a mechanical advantage.

C) "Cannot happen because a crate that heavy would lift the worker, rather than the worker lifting the crate": This choice is incorrect. The presence of a mechanical advantage enables the worker to lift the heavy crate without being lifted themselves.

D) "Cannot happen because the work done by the worker is less than the work done on the crate": This choice is also incorrect. The work done by the worker may be less, but the mechanical advantage gained allows them to displace the crate over a greater distance, compensating for the smaller force exerted.

Based on this analysis, the correct answer is A) "Can happen because the extra distance traveled makes up for the smaller force applied." Therefore, your initial understanding was correct.