A conducting rod slides down between two frictionless vertical copper tracks

In summary, a conducting rod with a mass of 0.2528777 kg slides down between two 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 and the rod maintains electrical contact with the tracks at all times. A 0.82-Ω resistor is attached between the tops of the tracks. The change in gravitational potential energy that occurs in 0.20 s is calculated using the equations s = ut+ (1/2) gt^2 and U = mgh, resulting in a value of 0.485727 J. However, the assumption of free-fall is incorrect as there will be
  • #1
cclement524
8
0

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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  • #2
there will be force due to electromagnetic induction. F = BIL
 
  • #3
Got it-- thank you!
 
  • #4
welcome.
 
  • #5




Hello, thank you for your question. It seems like you have the right approach but there are a few errors in your calculations. First, let's clarify the situation. The conducting rod is sliding down between two vertical copper tracks, which means that the motion is not in free-fall. The rod is moving at a constant speed of 4.5 m/s, so we can use the equation s = ut to find the distance traveled in 0.20 s, which is 0.9 m. This is the distance the rod has moved in the gravitational field, so we can use this to find the change in gravitational potential energy.

The mass of the rod is correct at 0.2528777 kg. However, when calculating the change in gravitational potential energy, we need to use the change in height (∆h), not the distance traveled (s). This is given by the equation ∆h = s sinθ, where θ is the angle between the direction of motion and the direction of the gravitational field. In this case, θ is 90 degrees, so sinθ = 1. Therefore, ∆h = 0.9 m.

Now, we can calculate the change in gravitational potential energy using the equation U = mgh, where h is the change in height. Plugging in the values, we get:

U = (0.2528777 kg)(9.80 m/s^2)(0.9 m)
= 2.203 J

This is the change in gravitational potential energy that occurs in 0.20 s. I hope this helps clarify your understanding of the problem. Let me know if you have any further questions.
 

What is the purpose of conducting rod sliding down between two frictionless vertical copper tracks?

The purpose of this experiment is to demonstrate the principles of electromagnetic induction and the relationship between a moving conductor and a magnetic field.

What is the role of the copper tracks in this experiment?

The copper tracks provide a path for the conducting rod to slide down, and also act as conductors for the magnetic field to pass through.

Why are the vertical copper tracks frictionless?

The tracks are made frictionless to eliminate any external forces that may affect the movement of the conducting rod, allowing for a more accurate demonstration of electromagnetic induction.

What factors can affect the speed at which the conducting rod slides down the tracks?

The speed at which the conducting rod slides down the tracks can be affected by the length and angle of the tracks, the strength of the magnetic field, and the mass and material of the conducting rod.

How does the movement of the conducting rod create an electric current?

As the conducting rod moves through the magnetic field created by the copper tracks, it experiences a change in magnetic flux, which induces an electric current in the rod according to Faraday's law of induction.

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