# Simple Machines

I totally do not understand how to do this. I missed this day in class and the teacher hasn't had time to explain it to me. Could someone help?

The efficiency of a pulley system is 73%. The pulleys are used to raise a mass of 58 kg to a height of 3.0 m. WHat force is exerted on the string of the pulley systen if the string is pulled for 18.0 m in order to raise the mass of the required height?

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ShawnD
Originally posted by pvpanther05
The efficiency of a pulley system is 73%. The pulleys are used to raise a mass of 58 kg to a height of 3.0 m. WHat force is exerted on the string of the pulley systen if the string is pulled for 18.0 m in order to raise the mass of the required height?
The way pullies work is by doing an equivalent amount of work by decreasing the amount of force needed and increasing the distance the force is applied over.
work = work
$$F_1d_1 = F_2d_2$$

Efficiency is always what you get out divided by what you put in. I'll use a little "e" to express efficiency.
e = out/in
e*in = out

Now just fill in values

$$eF_1d_1 = F_2d_2$$

$$(0.73)F_1(18.0) = (58)(9.8)(3)$$

$$F_1 = 129.77$$

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