Two blocks are free to slide along the frictionless, wooden...

Two blocks are free to slide along the frictionless, wooden track shown in Figure $\mathrm{P} 9.27$ . The block of mass $m_{1}=$ 5.00 $\mathrm{kg}$ is released from the position shown, at height $h=$ 5.00 $\mathrm{m}$ above the flat part of the track. Protruding from its front end is the north pole of a strong magnet, which repels the north pole of an identical magnet embedded in the back end of the block of mass $m_{2}=10.0 \mathrm{kg}$ , initially at rest. The two blocks never touch. Calculate the maximum height to which $m_{1}$ rises after the elastic collision.

Two blocks are free to slide along the frictionless, wooden track shown in Figure $\mathrm{P} 9.27$ . The block of mass $m_{1}=$ 5.00 $\mathrm{kg}$ is released from the position shown, at height $h=$ 5.00 $\mathrm{m}$ above the flat part of the track. Protruding from its front end is the north pole of a strong magnet, which repels the north pole of an identical magnet embedded in the back end of the block of mass $m_{2}=10.0 \mathrm{kg}$ , initially at rest. The two blocks never touch. Calculate the maximum
height to which $m_{1}$ rises after the elastic collision.

Key Concepts

Conservation of Linear Momentum

In isolated systems where no external forces act in the direction of motion, the total linear momentum remains constant during interactions. This concept is essential in collision problems as it enables the determination of post-collision velocities when two objects interact.

Elastic Collision

An elastic collision is one in which both kinetic energy and linear momentum are conserved. This concept is crucial when analyzing interactions where objects collide (or in this case, repel each other) without any loss of energy to deformation or heat, allowing the precise calculation of resulting motions.

Conservation of Mechanical Energy

This principle states that in the absence of non?conservative forces (like friction), the total mechanical energy (sum of potential and kinetic energies) of a system remains constant. It is key in analyzing motion on frictionless tracks where gravitational potential energy converts into kinetic energy and vice versa.

Transcript

00:01 Here we have a situation where there are two blocks on a frictionless track.

00:05 Block 1 is going down the ramp, has a magnet in it, and rappels off magnet 2.

00:11 Now the fact that they never touch actually doesn't mean anything, we still have an elastic collision.

00:17 Now mass 2 is more than likely going to move to the right, and mass 1 is going to go back up the ramp.

00:23 We have been asked to find the maximum height, where m1 will rise after the collision has occurred.

00:30 So to figure that out, we have to look at block one first and find its original maximum speed after it goes to the bottom of the ramp.

00:38 So to do that, we have to look at conservation of energy.

00:41 Now, remember that in conservation of mechanical energy, all energy at the beginning has to equal all energy at the end.

00:49 Now, in this case, we have two types, right? we have potential energy, mgh, and we have kinetic energy, one -half mv squared.

01:02 Now, initially, we don't have any kinetic energy.

01:08 And at the end, we don't have any gravitational potential energy.

01:17 So what we can do is remove those two things from those sides of the equation.

01:26 So potential energy is equal to the final kinetic energy because it goes down the ramp.

01:33 Now we know the masses here are the same.

01:37 So, g .h is equal to one half vf squared, and therefore, vf is equal to the square root of 2gh.

01:58 And plugging in those numbers, it's 2 times 9 .8, multiplied by the height, which is 5.

02:07 So the speed where it is kind of coming into contact with the other block comes out to be 9 .90 meters per second...

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