Calculating Minimum Magnetic Field for Sliding Copper Rod on Two Rails

[tomrja]

Homework Statement

A copper rod of mass 0.6 kg rests on two rails 1.3 m apart and carries a current of 31 A from one rail to the other. The coefficient of static friction is 0.3. What is the magnitude of the least magnetic field that would cause the bar to slide?

Homework Equations

F= ILxB

F=ma

f=(Fn)(u) where f is the frictional force, Fn is the normal force, and u is mu.

The Attempt at a Solution

I set up a free body diagram and found the equation: F-(Fn)(u)=ma. In the y direction Fn=mg=(0.6)(9.8)= 5.88N. Then I plugged that into my first equation for the x direction and got F= 0.6a + 5.88. I know that F=ILB, so I plugged that in and solved for B: B= (.6a + 1.764)/40.3. Am I on the right track? If I am then where do I get the acceleration of the copper rod from? Thanks

 

[tiny-tim]

hi tomrja!

(have a mu: µ )

… What is the magnitude of the least magnetic field that would cause the bar to slide?
…
Am I on the right track? If I am then where do I get the acceleration of the copper rod from?

yes

and the acceleration is zero …

you only need just enough force to get the bar to start moving

 

[tomrja]

hi tomrja!

(have a mu: µ )


yes

and the acceleration is zero …

you only need just enough force to get the bar to start moving

Ahhh duh, guess I should have read the problem again haha. Thanks!

 

[gneill]

Just to stir the pot a bit, if the applied force is not horizontally directed it is possible to increase or decrease the normal component of the net force, thus altering the net frictional force. So you might consider finding the optimum angle to apply the force first.

 

[tiny-tim]

wow! i never thought of that!

yes, tomrja, you need to do that also