A 0.200-kg metal rod carrying a current of 10.0 A glides on two horizontal rails 0.500 m apart.

step 1 All righty, we've got a pretty interesting problem here today. You have this .2 kilogram metal r

A 0.200-kg metal rod carrying a current of 10.0 A glides on...

Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept involves the force experienced by a conductor when it carries an electric current and is placed in a magnetic field. The force is given by the equation F = I L B sin?, where I is the current, L is the length of the conductor within the magnetic field, B is the magnitude of the magnetic field, and ? is the angle between the conductor and the field direction. In cases where the conductor is perpendicular to the magnetic field, sin? becomes 1, simplifying the calculation. This phenomenon is a fundamental aspect of electromagnetism and underpins the operation of devices like electric motors and generators.

Dynamic Equilibrium

Dynamic equilibrium refers to a state where an object is moving at a constant velocity because the net external force acting on it is zero. In such situations, all the acting forces, such as the driving force (in this context, the magnetic force) and opposing forces (like friction), exactly cancel each other out. This concept, derived from Newton's first law of motion, is crucial for analyzing systems where constant speed or steady motion is maintained, ensuring that the forces involved are properly balanced.

Kinetic Friction

Kinetic friction is the resistive force that opposes the relative motion between two surfaces sliding against each other. It is calculated as F_friction = ?_k N, where ?_k is the coefficient of kinetic friction and N is the normal force, which for a horizontal surface is equal to the weight of the object. Understanding kinetic friction is essential in dynamics problems and helps in determining the net force acting on moving bodies, particularly in systems where friction plays a role in balancing other forces.

Transcript

00:01 All righty, we've got a pretty interesting problem here today.

00:03 You have this .2 kilogram metal rod.

00:05 I'll put that right here.

00:07 M equals 0 .270 kilograms.

00:11 We also know that we have a current.

00:13 There's a current that's going to cross this rod.

00:16 And that current i is equal to 10 .0 amps.

00:22 Now it glides across this rod glides across two horizontal rails.

00:26 You can imagine the setup.

00:27 If we were looking at it from above, you have these two rails here.

00:30 Rail on this side and then you have some cylinder that just lays right on top of these and it's charged and it slides across these or this rod rather that slides across these horizontal rails they're 0 .5 millimeters or 0 .5 meters apart 0 .5 meters and what else do we know the coefficient of kinetic friction between the rod and the rails is equal to 0 .10 we know that and we want to figure out what a vertical magnetic field is required to keep the rod moving at a constant velocity throughout the entire bit of the motion.

01:18 All right.

01:19 So how are we going to do that? well, let's go ahead and just jump right into newton's second law apply it in both directions and we should be done pretty quickly.

01:27 You guys know this law.

01:28 We've used it a ton if you want to write it out officially, it's like this and it's a vector equation that breaks down into far case two components.

01:45 Here's the thing though about these two components.

01:48 If you want this to be moving at a constant velocity, well we know no matter what for that to happen, it's got to have to be a zero acceleration.

01:57 You know no matter what the y direction is going to have zero, but in this case the x direction as well will have zero.

02:05 So we know that.

02:07 So we have to solve these two equations and we should be good to go for the x direction.

02:13 Let's go ahead...

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