Part A Railroad car A rolls at a certain speed and collides...

Part A Railroad car A rolls at a certain speed and collides inelastically with car B of the same mass. After the collision the cars stick together. How does their speed after the collision $v_{AP}$ compare with the initial speed of car A, $v_{A0}$?

Transcript

00:02 So in this question we are given that there are two cars as shown and one car has a car has mass m and the other car has mass 2 m and a car that has mass m let's say has kinetic energy ke1 and the car 2 has ke2 kinetic energy which is half the kinetic energy of the first car and let's also assume that they are moving with velocities v1 and v2.

00:28 And direction does not matter.

00:29 It could be this direction.

00:30 So we'll use this to first find out what is the relationship between v1 and v2.

00:37 And the second condition we are given is that if you add 7 meters per second to both the cars or the cars accelerate such that they increase their speed each by 7 meters per second, then their kinetic energy in the new case becomes equal.

00:50 So we'll first use this and then use the second information.

00:53 So using the first information we find out that ke1 is half mv1 square.

00:59 The kinetic energy of this car is based on these variables.

01:04 And the kinetic energy 2 is half 2m v2 square because the mass of the second car is 2 times m.

01:15 And this is equal to half of k e1.

01:17 So we can take k e1 from here and say it is half mv1 square.

01:23 The halves can get cancelled out.

01:24 The m can get cancelled out.

01:27 And that gives us that so this two also can be taken up on the other side.

01:34 4 v2 square is equal to v1 square or 2 v2 is equal to v1...

Question

Part A Railroad car A rolls at a certain speed and collides inelastically with car B of the same mass. After the collision the cars stick together. How does their speed after the collision $v_{AP}$ compare with the initial speed of car A, $v_{A0}$?

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