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

[oreo]

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?

 

[Drakkith]

Can you elaborate? Are you rolling the stone across a smooth, flat surface, up a hill, or somewhere else?

 

[oreo]

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.

 

[Drakkith]

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.

 

[FactChecker]

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.