A conducting rod slides down between two frictionless vertical copper tracks

AI Thread Summary
A conducting rod slides down frictionless copper tracks at a constant speed of 4.5 m/s in a 0.56-T magnetic field. The rod has a length of 1.2 m and maintains electrical contact with the tracks, with a negligible resistance. The change in gravitational potential energy over 0.20 seconds was initially calculated incorrectly, with attempts yielding values of 0.485727 J and 0.20483 J. The confusion arose from not accounting for the electromagnetic force due to induction, which affects the rod's motion. Understanding the role of electromagnetic induction is crucial for accurately determining the potential energy change.
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Homework Statement



A conducting rod slides down between two frictionless vertical copper tracks at a constant speed of 4.5 m/s perpendicular to a 0.56-T magnetic field. The resistance of the rod and tracks is negligible. The rod maintains electrical contact with the tracks at all times and has a length of 1.2 m. A 0.82-Ω resistor is attached between the tops of the tracks. Find the change in the gravitational potential energy that occurs in a time of 0.20 s.

Homework Equations



s = ut+ (1/2) gt^2

U = mgh

The Attempt at a Solution



I found the mass of the rod to be 0.2528777 kg

Here's my attempt at the answer, but I went wrong somewhere (I'm positive the mass I found is correct):

From the kinematic relations
s = ut+ (1/2) gt^2
= 0 +(1/2)gt^2
= (0.5)(9.80 m/s2)(0.20 s)^2
= 0.196 m
The change in the gravitational potential energy is
U = mgh
=( 0.2528777 kg)(9.80 m/s2)(0.196 m)
= 0.485727 J

My second attempt:

When it comes to finding ∆h I assumed free-fall (used 'g') ... but the rod was falling at constant speed
so I tried ∆h = 0.9 m
=(0.2528777 kg)(0.9 m)
= 0.20483

Neither of these are correct, but I am confused as to where I went wrong.
 
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there will be force due to electromagnetic induction. F = BIL
 
Got it-- thank you!
 
welcome.
 
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