Is the Work Done in Rolling a Stone Less Than Lifting It?

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The discussion centers on whether rolling a stone requires less work than lifting it, particularly when rolling on a smooth incline. It is established that the work done against gravity remains the same in both scenarios. However, the work involved in accelerating the stone differs, as lifting requires upward acceleration without rolling. Despite these differences, it is concluded that if the stone starts and ends at rest, the total work done in both cases should be identical, as any initial acceleration differences are compensated by deceleration at the end. Thus, the overall work done is effectively the same.
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Is less work done in rolling the stone than lifting it? I think so that as gravity is conservative field therefore work done should be equal. But rolling could mean rotational kinetic energy so please clarify this?
 
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Can you elaborate? Are you rolling the stone across a smooth, flat surface, up a hill, or somewhere else?
 
Drakkith said:
Can you elaborate? Are you rolling the stone across a smooth, flat surface, up a hill, or somewhere else?
It is being rolled on smooth incline.
 
Well, the work done against gravity is the same in both cases. However the work done in accelerating the boulder will probably be different. When lifting it, you just have to accelerate it upwards and there's no rolling.
 
Drakkith said:
However the work done in accelerating the boulder will probably be different. When lifting it, you just have to accelerate it upwards and there's no rolling.
Assuming that the stone begins and ends at rest, any difference in acceleration at the beginning will be made up for at the end, when the deceleration helps it to finish rolling to the top.. So the work should be identical even considering differences in acceleration.
 
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