Next we will examine a glancing collision in two dimensions....

Next we will examine a glancing collision in two dimensions. Mass 1, traveling with a velocity of v?? in the x? direction, collides with mass 2, which is initially at rest. After the collision, the masses move with velocities v?? and v?? at angles ?? and ?? from the x axis as shown. Before Collision After Collision Assume that the collision is elastic, and assume that no net external force act on the system. Write down three equations comparing the system before and after the collision: one for the conservation of kinetic energy, and two for conservation of momentum (one for the x direction and one for the y direction).

Transcript

00:02 Okay, so we've got a collision happening here.

00:06 So we're taking our axes to be y upwards and x cross.

00:11 And we're going to draw the situation before and after.

00:14 So before, we've got m1 moving with speed v1 initial, which will denote v1i, and m2 at rest.

00:25 Then after we've got m1 making an angle of theta 1 with the horizontal moving in this direction at speed v1f, and similarly, for m2, moving at some angle, not necessarily the same, theta 2, with magnitude v2f.

00:52 And the question asks us to write down three equations comparing the system before and after the collision.

00:58 So we don't even have to solve the equations, but it sounds we've just got to write them down.

01:02 So the first one that we can talk about is the conservation of, of energy.

01:07 So we need to conserve kinetic energy.

01:10 So we've got that, the kinetic energy beforehand, m2 is at rest, so this contributes no kinetic energy.

01:21 And m1 is just going to be, it's the same as always, it's a half mv squared.

01:26 So in this case, this is a half m1 times v1 i squared.

01:31 This is kinetic energy before and it has to equal the kinetic energy after, which is now we've got two particles that are moving.

01:37 So we've got a half, the kinetic energy of m1, it's going to be m1 v1f squared, and of m2 is going to be a half m2 v2f squared.

01:52 So that's our equation number one, a kinetic energy equation.

01:56 Then we also have to conserve momentum, and we have to conserve it in both dimensions.

02:02 So we're first going to talk about the x direction momentum conservation...

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