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.