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.)

Question

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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Answer 1

If the rope attaches to the object is lower than the person’s hands, that is if the ropes are not pulling parallel to the surface, greater force would be required on the short rope to achieve the same work and displacement. The force component parallel to the surface would be the same but the force component perpendicular to the surface would be greater for the short rope, so total force would be greater for the short rope. You would be pulling up more to achieve the same lateral force.