A pulley system is used to lift a piano 2.6 m. If a force of 2510 is applied to the rope as the rope is pulled in 14 m, what is the efficiency of the machine? Assume the mass of the piano is 750 kg.

I know the equation is eff = Wout / Win
I'm just confused on what I'm supposed to plug-in.

I figured it out!

PEg = g x m x h
W = F x h

PEg/W

I figured it out!

PEg = gmh
W = Fh
PEg/W

To calculate the efficiency of the machine, you need to determine the work output and work input.

1. Determine the work output:
Work output (Wout) is the work done on the piano, which is equal to the force applied multiplied by the distance the piano is lifted.

Wout = force × distance

Given:
Force applied = 2510 N
Distance lifted = 2.6 m

Wout = 2510 N × 2.6 m

2. Determine the work input:
Work input (Win) is the work done by the person pulling the rope, which is equal to the force applied multiplied by the distance the person pulls the rope.

Win = force × distance

Given:
Force applied = 2510 N
Distance the rope is pulled = 14 m

Win = 2510 N × 14 m

3. Calculate the efficiency:
Efficiency (eff) is the ratio of work output to work input.

eff = Wout / Win

Substitute the values for Wout and Win:

eff = (2510 N × 2.6 m) / (2510 N × 14 m)

Simplifying the equation, we get:

eff = (2.6 m) / (14 m).

Therefore, the efficiency of the machine is (2.6 m) / (14 m), which simplifies to 0.186 or 18.6%.

To calculate the efficiency of the machine, you need to determine the work output (Wout) and work input (Win) of the pulley system.

First, let's calculate the work output. The work output is equal to the force applied multiplied by the distance the load is lifted:

Wout = Force * Distance

In this case, the force applied is 2510 N (given in the question) and the distance the load is lifted is 2.6 m (also given in the question). So, plugging in these values:

Wout = 2510 N * 2.6 m

Next, let's calculate the work input. The work input is equal to the force applied multiplied by the distance over which the force is applied:

Win = Force * Distance

We are given that the force is 2510 N and the distance over which the force is applied is 14 m. Plugging in these values:

Win = 2510 N * 14 m

Now that you have calculated both the work output (Wout) and work input (Win), you can find the efficiency by dividing the work output by the work input:

efficiency = Wout / Win

So, plug in the values you calculated for Wout and Win into this equation to find the efficiency of the machine.