# Determining Velocity from a Freely Falling Bar in a Magnetic Field

1. Nov 2, 2009

### guitarman

1. The problem statement, all variables and given/known data
A metal bar of length 1.3 m and mass 0.04 kg slides with negligible friction but with good electrical contact down between two vertical metal posts. After speeding up initially, the bar falls at a constant speed (zero acceleration). The falling bar and the vertical metal posts have posts have negligible electrical resistance, but the bottom rod is a resistor with resistance 26 ohms. Throughout the entire region there is a uniform magnetic field of magnitude 1.5 tesla coming straight out of the page.

Find the constant speed at which the bar falls.
v = ____ m/s

2. Relevant equations
Fgrav=mg
Fmag=I*(deltaL X B)
deltaV=I*R

3. The attempt at a solution
I know that Fgrav = 0.04* 9.8 = 0.392, and this must be equal and opposite to Fmag. The logic behind this is that the bar eventually falls at a constant speed, meaning there is no net force acting upon it. Therefore, I do
0.392 = I *(1.3 * 1.5)
I = 0.2
Using the current, I can find the change in voltage by 0.2 * 26 = 5.2 V.
This is where I am getting confused, is there any way to readily convert from volts to the velocity? I feel that I have all the necessary information, but could anyone let me know if I am wrong? Thanks!