Magnetic Launcher HW: Find Constant Current Flow

[Angie K.]

Homework Statement

A sort of 'projectile launcher' is shown in the figure above. A large current moves in a closed loop composed of fixed conducting rails, a power supply, and a very light, almost frictionless metal bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has length L = 15.5 cm, mass m = 1.44 g, and is placed in a field of 1.96 T, what constant current flow is needed in order for it to accelerate to 30 m/s in a distance of 1.0 m?

•Start by finding the magnetic force on the bar, which determines its acceleration via Newton's second law F = ma.
•The kinematic relation v2 = 2ax may be helpful (where v is the velocity attained by an object having acceleration a over a distance x.)

Homework Equations

F = I*B*L (current, magnetic field, length)

F = m*a

v^2 = 2ax where v is the velocity of object with an acceleration of a/x and x being the distnace

The Attempt at a Solution

F = I*B*L
43.2 = I*(1.96T)(15.5*10^-2cm)
I tried solving for I that way, which didn't work

I tried the velocity using the v^2 = 2ax equation that was given and I got 7.746

But I'm not quite sure what to do with this.

 

[mfb]

Where does the value 43.2 come from? You need the kinematics to find F.

I tried the velocity using the v^2 = 2ax equation that was given and I got 7.746

7.746 what? And how did you get it?