Speed & Distance of Sliding Bar on Rails - Get Help

[Sir_Pogo]

Can i get some help on this problem?
A conducting bar of length L = 25.6 cm and mass M = 35.0 g lies across a pair of conducting rails. The contact friction between the bar and the rails is negligible, but there is a resistor at one end with a value R = 45.0 Ohms. Initially the rod is given an initial speed of v0 = 41.0 meters per second. There is a uniform magnetic field perpendicular to the plane containing the rod and rails of magnitude B = 1.4 T.
What is the speed of the rod at time t = 23.297 s?
How far does the rod slide before coming to rest?
Thanks in advance.

 

[OlderDan]

https://www.physicsforums.com/showthread.php?t=94380

 

[Sir_Pogo]

the velocity induces an emf, the emf gives a current, and
the current gives a backward force F=ILB
How do i set it up to solve for the final velocity?I can't figure out how to do part two either because
setting v to zero, you cannot solve for t because ln (0)
is undefined.

 

[OlderDan]

the velocity induces an emf, the emf gives a current, and
the current gives a backward force F=ILB
How do i set it up to solve for the final velocity?


I can't figure out how to do part two either because
setting v to zero, you cannot solve for t because ln (0)
is undefined.

The movement of the bar changes the flux through the loop in a way that depends on the velocity. The emf and the current are related to the rate of change of the flux. The force is related to the current and the strength of the field. The rod decelerates in proportion to the force. Start writing the equations that describe these phenomena and see if you can come up with an equation for the acceleration of the rod.

 

[Sir_Pogo]

which equation is the one that deals with flux and velocity, i was trying to use these ones to solve:
F=ma=ILB
I=BLV/R

 

[OlderDan]

which equation is the one that deals with flux and velocity, i was trying to use these ones to solve:
F=ma=ILB
I=BLV/R

For a constant magnetic field perpendicular to a loop, flux through the loop is Φ = BA where A is the area enclosed by the loop. The induced emf is proportional to the rate of change of flux through the loop (Faraday's Law). In this problem there is a current loop whose area is changing as the rod moves. An emf is induced, so a current flows, and the current carrying rod experiences a force that is proportional to its velocity and the field strength.

Your equations come from application of these ideas to this problem. If you combine the equations you find that the force (and hence the acceleration) is proportional to the velocity. From there you need to do some calculus to solve the problem. What function (for the velocity) do you know that is proportional to its own derivative (acceleration)?