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How to calculate work input in a pulley

Updated July 19, 2017

Every natural event has an equation to determine its outcome. When two objects come together to produce work, the energy generated by one object may need to be multiplied to affect the other. Pulley systems multiply force. Work creates force, and though force may be multiplied by the use of pulleys, the amount of work input remains the same. To calculate work input in a single pulley or a system of pulleys, you must learn the equations that determine the outcome of these laws of relativity, and how gravity, energy, and force affect our physical world.

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  1. Set up a single pulley system where the pulley is secured to the overhead support and the cord is run over the top. Create a loop at one end of the cord where the scale can be inserted into the opening and then pulled, once a mass is attached to the other end. Write down the law of work input and work output. In a pulley system without friction, work input equals work output: Work (in) = Work (out).

  2. Attach a known mass to the other end of the cord. It will be necessary to determine force when you want to calculate the work input in a pulley or a system of pulleys. Work is determined by multiplying force by distance travelled: Work (W) = Force (F)X Distance (d) W=Fd. Write this equation down to use when you want to calculate work input in a pulley or a system of pulleys.

  3. Lift the mass by pulling on the cord using the newton spring scale. Using a measuring stick to measure the height the mass is lifted and the distance the cord is pulled, you can determine the work input in a pulley or a system of pulleys. Using a known mass will let you determine the work input/work output of any pulley system if you put all these measurements together. Therefore, the final equation to calculate the work input in a pulley is determined as follows: Record the measurement of weight lifted (w) in milligrams. Measure how high the Mass was lifted for an (h) measurement. Use the scale reading to determine the force exerted (f). Measure the distance that the cord was pulled (d). On the notepad you will create notations for each of these measurements to calculate the work input in a pulley or a system of pulleys.

  4. Calculate the work input in a pulley by using the previous readings in the correct mathematical equation: Work (W) equals force (f) multiplied by distance (d), or W=fd. The work done by the pulley is the equation of weight (w) multiplied by height travelled (h). Using these physics equations you can calculate the work input/work output of any pulley system.

  5. Tip

    Pulling down on the spring scale using these methods will alter the results. The weight of the scale and the force of the weight while being pulled down will return a different result because the scale is not reading its own weight during the test.


    Friction alters the results of the equations above. Friction must be determined before the actual work in/work out can be determined. Fd equals Wh + work versus friction.

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Things You'll Need

  • Pulley
  • Cord (rope)
  • Spring scale (Newtonian)
  • Measuring stick

About the Author

Francis Walsh has been working as a freelance writer since 2003. He has contributed to websites such as Shave, Autogeek and Torque & Chromeas, as well as provided content for private clients. Walsh has worked as a performance part-packer and classic car show promoter, now serving as crew chief for Nitrousfitz Racing.

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