Two particles with masses m and 5m are moving toward each...

Two particles with masses m and 5m are moving toward each other along the x-axis with the same initial speeds vi. Particle m is traveling to the left, while particle 5m is traveling to the right. They undergo an elastic, glancing collision such that particle m is moving in the negative y-direction after the collision at a right angle from its initial direction. (a) Find the final speeds of the two particles in terms of vi. particle m: ____________ × vi particle 5m: ____________ × vi (b) What is the angle θ at which the particle 5m is scattered?

Transcript

00:01 So here in this question we are given two particles whose mass let's say mass of first particle m1 is equals to m and the mass of second particle is equals to 5m.

00:12 So here they are moving towards each other along the x -axis with the same initial velocity v1.

00:18 Particle m is traveling to the left while the particle 5m is traveling towards right.

00:23 So this is 5m and this is m.

00:30 So here in this question let we are considering that the final velocity of m1 be v1 and the final velocity of m2 be v2.

00:48 So as we know that mv will move in minus y direction m1 is moving towards minus y direction and it will have no velocity component in the x direction.

01:02 So here in the first part of the question we need to find out about that the we need to find out the speed of two particle.

01:11 So here we are applying the conservation of momentum in x direction.

01:24 So according to the conservation of momentum initial momentum which is represented by pix is equals to the final momentum that is equals to pfx.

01:34 So initial momentum here in this case become equals to mass multiplied by the velocity for mass for the first particle is 5mv minus mv because mass 1 is moving in the negative y direction this is in the positive y direction this from here is equals to 5mv of 2x solving this term we get the value that 4mv is equals to 5mv of 2x further simplifying this term we get the value of v2x that become equals to 4 divided by 5 multiplied by the v.

02:05 Now in the same way we are applying the conservation of momentum in y direction.

02:17 So from here what we can write it as that py of x is equals to pf of y.

02:23 So momentum initial momentum in y direction is 0 that become equals to and final momentum will be 5mv of 2 of y minus mv1 of y.

02:34 So we can say that v1 of y is equals to 5 of v2 of y.

02:39 Now this is done from here now we are applying the conservation of energy.

02:47 So according to the law of conservation of energy initial energy is equals to the final energy...

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