Calculate Force Exerted Using Simple Machines

[pvpanther05]

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?


Thanks in advance

 

[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

$$eF_1d_1 = F_2d_2$$

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

$$F_1 = 129.77$$

 

[M98Ranger]

for any help!

Calculating force exerted using simple machines can be a bit confusing, but with some practice, it can become easier to understand. In this case, we are dealing with a pulley system that has an efficiency of 73%. This means that 73% of the input force is converted into output force. To find the force exerted on the string of the pulley system, we will use the formula: Output force = Input force x Efficiency.

In this problem, the output force is the force exerted on the string, and the input force is the force needed to lift the mass. We know that the mass being lifted is 58 kg and the height it needs to be raised is 3.0 m. This means that the work being done is equal to the mass (58 kg) multiplied by the gravitational acceleration (9.8 m/s^2) multiplied by the height (3.0 m). So, the work done is 58 x 9.8 x 3.0 = 1,702.8 Joules.

Now, we can use the efficiency of the pulley system (73%) to find the input force needed. We know that 73% of the input force will be converted into output force, so we can set up the equation: 0.73 x Input force = 1,702.8 Joules. Solving for the input force, we get 1,702.8 / 0.73 = 2,332.6 Joules.

Therefore, the force exerted on the string of the pulley system is 2,332.6 Joules. I hope this helps to clarify the concept of calculating force using simple machines. If you have any further questions, please do not hesitate to ask your teacher or a classmate for help. Practice makes perfect, so keep trying and you will soon understand it better. Best of luck!