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Q & A: Ideality of Mechanical Advantage?

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Most recent answer: 05/11/2015
Q:
What is the difference between IMA and AMA and how are the calculations different?
- Amy (age 12)
ON Canada
A:

(For other readers, IMA means "ideal mechanical advantage", AMA means "actual mechanical advantage", as discussed here: https://en.wikipedia.org/wiki/Mechanical_advantage)

Energy losses give the difference. In the physicist's model world, a system can work ideally and energy is conserved. You can build machines, as simple as some pulleys, and the amount of work you put will be what you get. What such a machine would be good for is to reduce the force that you apply, so that your strength is enough to, say, lift a 1000 kg elevator. But you will be pulling the rope more to compensate for this. Ideal mechanical advantage is the ratio of forces that you would have to apply without the machine to that with the machine, equivalently output force/input force.

In the engineer's world, nothing can be ideal. There will be losses mainly due to friction, but also other things such as additional weight of the pulleys, deformation of the material, elasticity of the strings or compressibility of any bulk material. All of these may cause additional energy concerns and change the forces that you need to apply. Actual mechanical advantage is found similarly as IMA, but also accounts for these additional effects. In an ideal system, you can estimate the mechanical advantage by calculating the required force, but without knowing the system of concern, it is not possible to give a generic recipe. I do not think an analytical expression will always be available, either. In practice you could set up a physical experiment and measure the forces/torques or attempt to find an approximate solution via a computer.

Tunc


(published on 05/11/2015)

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