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Understanding Mechanical Advantage and Efficiency in a Pulley System

A stage hand operates a pulley system to close 5500 N curtains over a distance of 2 m, applying 225 N of force with 55 m of rope. This case demonstrates how to calculate the mechanical advantage (MA), ideal mechanical advantage (IMA), and efficiency of the system. We determine the forces, apply the relevant formulas, and analyze our results. The mechanical advantage is found to be 24.4, the ideal mechanical advantage is 27.5, and the system’s efficiency is calculated at 88.7%, confirming that the system functions effectively within expected parameters.

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Understanding Mechanical Advantage and Efficiency in a Pulley System

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  1. 10.2 Notes Machines

  2. Example Problem 1 • A stage hand uses a pulley system to close the 5500 N curtains a distance of 2 m. She uses 225 N of force as she pulls in 55 m of rope. • A. What is the mechanical advantage of using this pulley system? • B. What is the ideal mechanical advantage? • C. Determine the efficiency of the system.

  3. Problem solving steps: • Determine what Fr, Fe, dr, and de are. • Find the right formula • Plug in numbers • Check your answers – does it make sense?

  4. For MA • Fr = • Fe = • de = • dr =

  5. Fr = 5500 N • Fe = 225 N • Divide Fr by Fe and you’ll get 24.4 • This pulley system makes your job 24.4 times easier

  6. For IMA • de = 55 m • dr = 2 m • Divide de by dr and you get 27.5 • In a perfect world – no friction or wasted energy, this pulley system makes your job 27.5 times easier

  7. For efficiency, • Since we have solved for MA and IMA, use the efficiency formula MA/IMA x 100 • 24.4/27.5 x 100 = 88.7% efficient

  8. Do your answers make sense? • MA should be greater than 1. Is it? • IMA should be great than both 1 and the MA. Is it? • Efficiency should be less than 100%. Is it?

  9. Oh Yeah!!!

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