Negative and positive work - Question

[SigmaScheme]

I accelerate a mass upward by 2G (2×force of gravity) over some change in height Δh$_{1}$, then I apply only $\frac{1}{2}$G over some other change in height Δh$_{2}$.

If, over Δh$_{2}$, the mass still moving upward (but accelerating downwards), am I doing positive work over Δh$_{2}$ even though the mass is accelerating in the opposite direction to the force I am applying?THANKS!

 

[Ken G]

No-- the work depends on the sign of the force (and so the acceleration), times the sign of the displacement. So switching the sign of one or the other (but not both) will change the sign of the work.

 

[SigmaScheme]

OK, thanks, So what about MY work alone due to the force I am applying, rather than the work due to the net force.

MY force and x ARE in the same direction (although the mass is slowing down). Splitting the question into components, am I alone doing positive work regardless of net work - even though the mass is slowing down?

 

[A.T.]

am I alone doing positive work regardless of net work - even though the mass is slowing down?

Yes, you are still doing positive work on the object. The Earth is doing negative work. And the net work done on it is negative.

 

[PJC01]

Yes, you are still doing positive work over Δh_{2} even though the mass is accelerating in the opposite direction to the force you are applying. This is because work is defined as the product of force and displacement, and in this case, the force and displacement are in the same direction. The fact that the mass is accelerating in the opposite direction does not change the fact that you are still exerting a force and causing a displacement. However, the magnitude of the work done may be less than the work done over Δh_{1} due to the decrease in applied force.