Motional emf, Gaussian flux, and lenz's law help

[Turpulus]

Homework Statement

Two bars, each 30cm long, and each having a resistance of 2-ohms, are connected to a 1,500 volt battery. The bars are attached to each other with 3 insulating springs, each having a spring constant of 9N/m. The two bars are initially at rest, 4cm apart. The switch is closed, and then opened. Assume no friction anywhere in the system. 1. How far will the two bars be from each other with the switch is closed? 2. After the switch is open, what is the closest the two bars wil get to each other? 3. After the switch is open, what is the farthest the two bars will get from each other? 4. Describe the motion of the two bars at time, t, after the switch is open.

Homework Equations

v ir
Spring constant equations

The Attempt at a Solution

I know motional emf would cause the bars to move apart but they're not passing through a magnetic field. Are they generating a mag field? Are they acting as capacitors and building up repulsive charges? If so, how do you get the area of the bar if you are only given the length? Thanks!

 

[issacnewton]

Hi, is there a diagram given ? without the aid of a diagram its difficult to understand.
Always post the question AS IT APPEARS in your textbook or homework...

 

[Turpulus]

Here is the exact question with diagram:
Two bars, each 30cm long, and each having a resistance of 2.00 ohms, are connected to a 1500V battery. The bars are attached to each other with 3 insulating springs each having a spring constant of 9N/m. The two bars are initially at reast, 4cm apart. The switch is closed, and then opened. Assume there is no friction anywhere in the system. Note: One can define the equivalent srping constant for the system equal to 27N/m. 1. How far will the two bars be from each other with the switch closed? 2. After the switch is open, what is the closest the two bars will get to each other? 3. After the switch is open, what is the farthest the two bars will get from each other. 4. Describe the motion of the two bars at time, t, after the switch is open.


So I realize that the bars are connected in parallel, so the equivalent resistance is 1ohm. I'll post a diagram.

 

[Turpulus]

Here is the diagram. Thanks!

 

[asteriatic]

I would like to clarify a few things about the given scenario. First, motional emf is a phenomenon that occurs when a conductor moves through a magnetic field, inducing a voltage. In this scenario, there is no mention of a magnetic field, so it is unlikely that motional emf is a factor in the movement of the bars.

Second, Gaussian flux is a concept used in electromagnetism to calculate the electric field through a closed surface. Again, since there is no mention of a magnetic field or electric field in the scenario, it is not relevant to the problem.

Lastly, Lenz's law is a fundamental principle in electromagnetism that states that the direction of an induced current will be such that it opposes the change that caused it. In this scenario, it is not clear what is causing the change in the bars' position, so it is difficult to apply Lenz's law.

To answer the given questions, we can use basic principles of mechanics and electricity. When the switch is closed, the bars will experience a force due to the electric field created by the battery. This force will cause the bars to move away from each other, compressing the springs. The distance between the bars can be calculated using Hooke's law, where the force is equal to the spring constant multiplied by the displacement. In this case, the force is 1,500 volts divided by the resistance of 2 ohms, which is 750 N. Using this force and the spring constant of 9 N/m, we can calculate the displacement to be 750/9 = 83.3 cm.

After the switch is open, the bars will start to move towards each other due to the restoring force of the springs. The closest they will get to each other is when the springs are fully compressed, which is 4 cm.

The farthest the bars will get from each other is when the springs are fully extended, which can be calculated using the same method as above. The force in this case will be the weight of the bars (assuming they have uniform density) and the force due to the springs, which will be equal and opposite. The weight can be calculated using the mass of the bars and the acceleration due to gravity, and the displacement can be calculated using Hooke's law.

The motion of the bars at any given time after the switch is open will be a simple harmonic motion, with the bars oscillating back and forth between their