Concerning work and force

[Class1P]

Hi, I mainly wanted to clarify 2 things with all your smartypantses

Work = Force x Distance

Is it always displacement or is it displacement sometimes and distance others? Like say you have a particle in an E field experiencing a force and it makes some roundabout way of getting to the oppositely charged plate. In that case the work done is W=F*displacement

On the other hand if you have a box you are pushing across a cement parking lot, the box experiences friction. You go from one side to the other but make some curly-Qs in the middle to get there. Would the work done by you pushing the box be F*distance?

So what I am asking is whether work done is dependent on whether your force is in the direction of motion?



Question #2: It's the NET force right? if you drop an object into water and it sinks, the work done by gravity is (mg - Fb) so would the work done by gravity be (mg-Fb)* hight?

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[milski]

It's a long topic, let's start with the abbreviated and we can clarify more on what's missing.

There are two types of forces (from perspective of work): conservative and non-conservative. Work done by conservative forces is dependent only on the position change. In other words, in that case W=Fxd where d is the displacement. These are forces which generally don't depend on the velocity of the object - like gravity, electrical or magnetic forces. Non-conservative forces depend on the velocity of the object - in some cases both as direction and size. Typical example here is the friction force which is always pointed in direction opposite to the velocity of the object. In this case the work done is W=Fxd where d is the total distance traveled by the object.

What do you mean by your second question? In general when talking about work you either talk about "work done on an object by a force" or "total work done on an object."

In your example you could talk about work done on the object by the gravity - that would be -m*g*h, or work done on the object by the buoyant force - that would be Fb*h. You can also talk about total work on the object which will be (Fb-mg)*h in this case.

The total work needs a bit of extra attention. Saying that it is (Fb-mg)*h is correct only before the object hits the floor of the ocean. Once that happens the normal from the bottom will do some work on it too and that needs to be taken into account. A simpler way to calculate the total work is to know that Wt=ΔKE where KE is the kinetic energy.

That leads to an example which confuses a lot of people. Take a brick from the ground and put it on a table. What is the total work done on the brick?

The answer is ΔKE=0 since the brick was at rest and is still at rest. It might seem a bit counterintuitive but if you look at the details it makes sense. The force that lifted the brick did a work W. In the same time gravity was doing exactly the same work but with an opposite sign, so it did work -W. The total work is W+(-W)=0.

 

[Class1P]

Ahh thank you. That clears things up quite a bit. I forgot to consider that one is a conservative force. It has been a long time since I took physics.

As for question 2, I wasn't thinking of it as work done on or work done by. I forgot they were separate things and that the net work would be separate entirely.

Thanks again, milski.