Question regarding Work

[IlyaR]

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I'm a bit confused as to why a magnetic field doesn't do any work on a charged particle moving through it. I understand that it is perpendicular to the movement, and W=FDcosTheta, but the particle is still being displaced in another axis. Am I wrong in this?


Is this because the force eventually makes the particle arrive at the same point in its path (circular)?

What if the particle is not allowed to make a full circle. Ex: Projectile path of a particle in a magnetic field which causes a force analogous to gravity. If the particle hits "Ground", wouldn't there be work done by the magnetic field?

Thanks!

Just realized, Work= dK.E.
Still a bit confused though

 

[milski]

The magnetic force is always perpendicular to the direction of movement - if that direction changes, the force changes as well and the result is that the magnetic forced does no work on the particle.

The path is really irrelevant - you can apply other forces on the particle and make it follow arbitrary trajectory. The magnetic force is still not going to do any work, since at any point along the trajectory it will be perpendicular to the direction of movement.

In the case where the particle is not following a circle, the work is actually done by the forces which make it deviate from its path. In your case, when the particle hits "ground," the work will be done by the "normal" of the ground acting on the particle.

 

[IlyaR]

Thanks, one more question if you don't mind:

If a forklift lifts a box, it is doing work equal to mgh on the box, right?
However, if it just moves the box, at the same height, 10 meters to any side, is it still doing work? I remember an EK question that stated that it does not, and was a bit confused as to why. It's applying a force and moving it a distance D, no?

Is it also because Theta is 0? It just seems very unintuitive to me

 

[milski]

In the ideal case, when there is no friction, the forklift does some amount of work to accelerate from stopped position and then the same amount of work is done to stop it. As a result the word done on the object is zero.

The trick here is to pay careful attention to the forces. If the forklift has accelerated and is moving at a constant speed, the only force applied from it to the object is the normal (the object resting on the fork) which is perpendicular to the direction of movement.

Obviously, friction changes all this and the forklift does some work in the non-ideal case.

Think about pushing something heavy on a very smooth surface - once you get it going, you barely need any effort to keep it moving. Or try running with some really heavy backpack, you'll notice that it's only starting/stopping/turning that are hard.

 

[IlyaR]

Ok, so I'm not crazy then. But in the ideal case, how could it possibly even accelerate? Sorry that I'm asking question after question, it's just frustrating me.

The way that I thought of this problem was that the forklift accelerates , thus applying a force F to the box, and moves it a distance of D, so W=FD. If Fk is equal to the the MA of the forklift, then it would be moving at a constant velocity, but it still would exert a F on the box, no?

Thanks again!

 

[milski]

When moving horizontally, any force F>0 will cause acceleration. The only way to have constant speed horizontal motion is for the force to be zero. At the end, you'll have to apply the opposite force, -F, and you'll end up with some negative work and total of zero.

To reiterate: if the fork is moving the object at constant speed horizontally, the only force from the forklift on the object is vertical (keeping it from falling on the ground) and since that is perpendicular to the motion, it does no work.

The difference between moving vertically and horizontally comes from the fact that you have another vertical force acting on the object, gravity. That changes what the forklift needs to do to achieve constant speed motion in each direction - apply a certain force, mg, for the vertical case and no force for the horizontal case.

 

[IlyaR]

Thanks you very much, that makes a lot more sense. Hypothetically, if the forklift was accelerating, the entire distance, THEN there would be work done right?

 

[milski]

Yes, that would be correct. And the object will have more energy at the end, if that was the case.