If someone pulls an object once with long rope and another time with short rope on smooth surface and if work and displacement be same, explain which one the guy applied more force? (Do not consider friction.)

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I was reading my book because I have test tomorrow and I saw this question. Can anyone explain and answer this?

If someone pulls an object once with long rope and another time with short rope and if Work and Displacement be same, explain which one the guy applied more force? (Do not consider friction.)

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>if work and displacement be same, explain which one the guy applied more force?

This line is all you need

Work = Force * Displacement

If Work and Displacement are the same in both cases then Force *must* be identical

For a practical situation with a non-zero mass rope with some slight stretch to it the longer rope will require more work to be done because some energy is lost into the rope but since you’re ignoring friction you can also ignore non-ideal ropes and are just left with W=FxD
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