# How much work does a crane and gravity do on a large box?

1. Nov 30, 2015

### Warlic

1. The problem statement, all variables and given/known data

2. Relevant equations
E(p)=mgh
W = Fs

3. The attempt at a solution

The book says the crane does mgh amount of work, while gravity does -mgh.
What I dont understand is, for the box to be lifted up, doesn't string tension force have to be bigger than gravity - or else it would remain in place and not accelerate upwards? If so, formula for work is W=Fs, the distance s is same for both forces, but string tension force is bigger, so doesnt crane do more absolute work on the box that gravity?

2. Nov 30, 2015

### SteamKing

Staff Emeritus
Who says that the box is accelerating upwards? You can lift things perfectly well at constant velocity.

You're making the mistake by assuming that if acceleration = 0, then velocity = 0. If something has zero acceleration, it could be stationary or moving at constant velocity. You can't tell which situation applies unless you are given more information. In this case, the crane is 'slowly lifting' the box, which implies that velocity is not zero.

3. Dec 1, 2015

### Warlic

Thank you, now I feel stupid.

4. Dec 1, 2015

### haruspex

You shouldn't. You are quite right that the tension had to exceed mg at some point, but perhaps only by the tiniest amount, and for the briefest period. Once the box is in motion, the tension can drop back to equal mgh until the box is at the desired height. It might just take a while.

By the way, as I understand it, the book should not insist the crane did mgh of work on the box. It did mgh of work, but the net work done on an object is its increase in KE. If you throw a ball up with enough speed to reach height h then you do mgh work on the ball, then the ball does that same work against gravity (i.e. it does that work on the ball-Earth system). But if the crane lifts the mass slowly and steadily to a height h, you could equally say the crane did mgh work against gravity and none on the box.

5. Dec 17, 2016

### Manimech

Why crane booms are made up of rectangular cross sections instead of circular section?

6. Dec 17, 2016

### haruspex

Probably because they are easier to make.
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