# B Work calculated for a force not producing displacement?

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1. Aug 26, 2016

### donaldparida

If a force acting on an object displaces the object, then why do we calculate the work done by all the forces acting on the body (those which did not cause the body to move as well as the force which caused the body to move) instead of the work done only by the force responsible for the displacement. For example when we lift an object up it, the force applied by us is causing the body to move up but we calculate both the work done by the applied force and the force of gravity even though the force of gravity is not responsible for moving the object up.

2. Aug 26, 2016

### Staff: Mentor

In applying the work-energy principle, you want the net work done on the body, which includes the work done by all forces acting on the body. In the case of lifting up an object at uniform speed, the work done by all forces is zero, thus the kinetic energy does not change.

3. Aug 26, 2016

### donaldparida

Is it correct that the displacement is caused by one force only and that work done by all force is calculated for work energy theorem?

4. Aug 26, 2016

### Staff: Mentor

This idea of forces responsible for displacement doesn't make sense. In your example, for instance, the force of gravity is very much responsible for moving the object, it accelerates it downwards compared to where it would have been without gravity. What about situations where the object has some high initial velocity, then none of the forces can be said to be responsible for the motion.

This concept of a responsible force is not part of Newtonian physics, and I don't see how it could be made usable.

5. Aug 26, 2016

### Merlin3189

I would think not.
If two people were pushing an object, its motion would be the result of both forces (and maybe others.)
In your example of lifting, the movement of the object depends both on the force I use to lift it and the force of gravity. If gravity were not there and I used the same force, the object would get a much greater vertical acceleration.
Objects are (generally) not intelligent enough to know which force is responsible for their displacement. They just have mass, and mass responds to all forces applied. Although we usually sum forces to find a resultant, you could actually calculate the acceleration that would be caused by each force alone, then simply sum all the accelerations.

Although gravity does not move the object UP, it does cause a vertical acceleration, which must be added to the upward acceleration caused by your upward force if you chose to ignore the force of gravity.
For work, you could say (I think!) the object has positive work done by you in lifting an object has negative work done on it by gravity. Its change in KE is the net sum (ie. the difference.) The negative work lost to gravity is accounted for as gravitational PE, which can be returned when the object is lowered again. Then gravity does positive work on the object and adds to any work you do by applying downward force. If you, instead, lower it gently by applying upward force as you lower it, then you now do negative work and leave less net work to increase the objects KE (which is why you do it.) Unlike gravity, you don't keep it on trust as PE, but rather squander it as heat! (But it would have ended up as heat when the falling object hit the floor very fast if you had not lowered it gently.)
I'm not sure we often do. Sometimes we do, sometimes we don't. It depends what we are interested in. If I lift a heavy object, I'm probably interested only in the work I do. But to calculate that I may need to know about all the forces acting on the body. If gravity were less, then I'd need to apply less force myself and do less work.
Or I could apply the same force or do the same work and get the object moving faster. (I have to be careful here, because if I apply the same force and it moves faster, I'd have to apply it for a shorter time, otherwise I'd end up doing more work than with the strong gravity!)

Just be clear what you want to know and why. Then you 'll know which forces to be interested in.

6. Aug 26, 2016

### Staff: Mentor

To add to Dale's explanation, be careful about saying that forces "cause" displacement. A net force is required for an acceleration. So when you lift that object, you initially have to exert slightly more force than gravity it order to start it moving. But once it's moving it will just keep moving, as long as the net force stays at zero. Of course you have to keep pushing, otherwise gravity will take over and start the object accelerating downward.

In the work-energy theorem (at least one standard version of it) you set the work done by all forces equal to the change in kinetic energy.