What Is the Least Current to Prevent a Cylinder from Rolling Down an Incline?

[Saffire]

Problem -- need direction

Hey all, I just need a lil prodding in the right direction, I'm not totally sure where to start on this problem.

Figure 29.38 shows a wooden cylinder with mass m = .25 kg and length L = .7 m, with N = 20 turns of wire wrapped around it longitudinally, so that the plane of the wire coil contains the axis of the cylinder. What is the least current 'i' through the coil that will prevent the cylinder from rolling down a plane inclined at an angle theta to the horizontal, in the presence of a vertical, uniform magnetic field of 0.75 T, if the plane of the windings is parallel to the inclined plane?

Don't have a picture, but Fig 29.38 has a wooden cylinder on a slope, with the attributes as above.

I'm trying to balance the equation out, but I'm getting nowhere as I'm neglecting length L and N turns. I figure net force/torque should be 0, but I can't get anywhere from that.

Thanks.

 

[Daaf]

I am no expert at this since it's been 8 months since I last had magnetism, but I'll try to help.
The sum of the forces must be 0. First, we need the part of the gravity that makes the cilinder roll, being cosinus(90-theta). This must equal the lorentz force. The magnetic field is uniform, and produces a force of which, again, only the portion pointing up the slope counts.
The rest of the gravital force and lorentz force will push onto the slope and produce a normal force in return. Not sure if you americans call it thesame.
So the Lorentz force has a formula (dont forget the cosinus), you know the gravital force (dont forget the cosinus), make the equation and do the math! I believe L and N both have an effect on the lorentz force but I might be wrong.

Good luck!

 

[M98Ranger]

Hey there,

It sounds like you're on the right track by trying to balance the equation and considering the net force/torque. One approach you could take is to first calculate the gravitational force acting on the cylinder (mg) and then determine the minimum magnetic force needed to counteract that force and prevent the cylinder from rolling down the slope. From there, you can use the equation F = BIL to solve for the minimum current (i) needed, where B is the magnetic field strength, I is the current, and L is the length of the wire.

Another approach could be to calculate the torque on the cylinder due to the magnetic force (τ = BILsinθ) and set it equal to the torque due to the gravitational force (τ = mgrsinθ), and solve for the minimum current from there.

I hope this helps guide you in the right direction. Don't hesitate to reach out if you need further clarification or assistance. Good luck!