Rail Gun Problem: Force & Friction Analysis

[David112234]

Homework Statement

Homework Equations

F_f = Nu
F_B - IL x B

The Attempt at a Solution

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Using the hint
"The rod will begin to move when the force of friction is equal to the force due to the magnetic field."
I was able to get the answer
But I don't understand why it is that way. In order make the rod move, wouldn't the force from the magnetic field have to be greater than the friction force? if they are equal than the net force is zero and there can not be an acceleration since F(net) = ma

 

[TomHart]

Technically, you are right. If they are equal, there will be no acceleration. However, if the force increases beyond that by an infinitesimal amount, the rod will begin to move. That's why you set them equal.

 

[haruspex]

Technically, you are right. If they are equal, there will be no acceleration. However, if the force increases beyond that by an infinitesimal amount, the rod will begin to move. That's why you set them equal.

To add to that, in the real world there is always noise, such as vibrations, and exact equality is only a theoretical concept.
As soon as there is the slightest movement, kinetic friction applies, and that is nearly always less (certainly never more) than static friction.