How can net force point in the direction of *negative* work?

[Kalibasa]

Homework Statement

It was just a basic work problem:

The two ropes seen in the figure below are used to lower a 245 kg piano 6.0 m from a second-story window to the ground. How much work is done by each of the three forces? (T1 = 1910 N andT2 = 1140 N)

There was a diagram with the angles labeled, and I got the right answers:
w: 14406 J
T1: -9925 J
T2: -4837 J

Homework Equations

W= Fcos(theta)d

Fnet_y= T1_y + T2_y - w

The Attempt at a Solution

Actually I got the problem right- T1 and T2 perform negative work and w performs positive work. But when I tried calculating the net force I found that it pointed upwards. This seems contradictory, since the piano has a displacement downwards. How can you have a net force opposite the displacement?

I guessed that if the net force pointed downwards too the weight would be exceeding the tension forces and the ropes would snap; in other words, you have to have a net force upwards so that the tension forces are strong enough to keep the piano in place. Is that right? But then I don't know where the displacement is coming from. Would you say that the piano is in dynamic equilibrium and that it's only moving because you're increasing the length of the ropes?

I'm confused...

 

[kuruman]

Imagine throwing a ball straight up in the air. Neglect friction. While the ball is going up, the displacement is up but the net force (gravity) is down and opposite to the displacement. Note that the speed of the ball decreases as it moves up.

Same thing with the piano. As the piano is lowered its downward speed decreases because the net force (and therefore the acceleration) are opposite to the velocity.

 

[kerimek]

It is correct that the net force in this scenario would point upwards. This is because the piano is being lowered from a higher point to a lower point, meaning it is moving in the opposite direction of the force of gravity. In this case, the net force is the combination of the tension forces (T1 and T2) and the weight of the piano (w). Since the piano is moving downwards, the net force must point upwards in order to balance out the gravitational force pulling it downwards. This does not mean that the tension forces are not strong enough to keep the piano in place. In fact, the tension forces are strong enough to not only keep the piano in place, but also to lower it to the ground. The displacement is coming from the fact that the ropes are being lengthened, as you mentioned. This is how the piano is moving downwards, even though the net force is pointing upwards. Overall, the net force in this scenario is pointing in the direction of negative work because the displacement is in the opposite direction of the net force.