00:01
All right, so let's say we have some rails and we have a bar that is hung across the rails and attached to a string that is connected to a pulley which has a hanging mass down here.
00:14
And we're told that a section of these rails has a resistance r, the bar has a mass little m, and then there is a magnetic field pointing upwards like this.
00:28
And lastly, the length of this whole apparatus is l.
00:32
So we want to find the speed of the bar as a function of time.
00:37
So if we write out newton's second law, the mass times the acceleration is going to be the tension in that cable, which is, i hope we can see, is just m times g.
00:48
All right, so plus the magnetic force.
00:53
And if we look at what direction that has to be in, so the current has to be going this direction in order to counteract the increase in flux.
01:01
And so that means the magnetic force is going to be to the right, so we can write this as capital mg minus b times i times l.
01:11
And then the current, of course, is the emf divided by the resistance.
01:16
The emf is going to be b times l times v over r.
01:21
So what we'll have is ma equals capital mg minus bl squared times v over r...