You have a summer job working at a company developing systems to safely lower large loads down ramps. Your team is investigating a magnetic system by modeling it in the laboratory. The safety system is a horizontal conducting bar that can slide, under the effect of gravity, without friction on two parallel conducting rails running down the sides of the ramp. The magnetic field is uniform and vertical. This time, there is no power supply. Instead, the two rails are connected together at the bottom, and the magnetic field has a braking effect that causes the bar to slide down the ramp at a constant velocity instead of accelerating. Your task is to calculate the velocity of the bar as a function of the mass of the bar, the strength of the magnetic field, the angle of the ramp from the horizontal, the length of the bar which is the same as the distance between the tracks, and the resistance of the bar. Assume that all of the other conductors in the system have a much smaller resistance than the bar. a) If the force due to the changing flux exactly cancells out the net force due to the combination of gravity and normal force, then the bare will cease to accelerate and instead move at a constant velocity. Please solve for this velocity algebraically.
b) Write out the units for each of your variables and show (by cancellation and substitution) that the units for your veloctiy will be m/s on both left and right side of your equation.