U Shaped Conductor w/ Rod & Magnetic Field

[ninjadrummer8]

Homework Statement

This is one of those problems with a U-Shaped Conductor, but this time it is at an angle and the Earth's Magnetic Field is perpindicular to the plane of it. The rails are 10m apart and the conducting rod weights 10 kg. No friction on the ramps, and the only resistance is in the resistor at the bottom.

Question 1: What is the value of the resistance if the rod slides with constant speed 20m/s?

Question 2: What would happen to the rod if the resistance was a lot less than what I found?

Homework Equations

F=(B^2)(L^2)V / R
F=ma

The Attempt at a Solution

Answer 1:
B=5x10^-5 T
L=10m
V=20m/s
F=ma=10(9.8)=98 N
So I can just plug those in and solve for R, correct? Or am I not able to use these equations in this case?

Answer 2:
Lower R would mean Lower EMF, which would also mean lower velocity, is this correct? So I think the rod would fall slower?

 

[Chi Meson]

Homework Equations

F=(B^2)(L^2)V / R
F=ma

The second equation is misleading. The acceleration of the system is zero, isn't it? The more appropriate equation is for weight: "w=mg." After learning and understanding General Relativity, you can go back to assuming they are the same equation, but in classical physics it is better to make the distinction between an accelerated object, and an object in a gravitational field.

Anyway, you analysis has only one flaw. The entire force of gravity is NOT balancing the electromagnetically induced force. Only the component of the weight along the direction of the rails can balance with this (The component of the weight perpendicular to the rails is balanced by the normal forces of the rails).

Is an angle, theta, assumed or given for this problem?

 

[ninjadrummer8]

yes, you are right. I forgot to add that in my diagram. The angle between the rails and the ground is 50 degrees