Momentum, Collisions and Explosions Audio Guided Solution MC13Q1

A 4.53 gram object is moving to the right with a speed of 19.2 cm per second and makes an elastic head-on collision with a 10.31 gram object that's initially at rest. This is an elastic collision, so our two objects are not going to stick together. They're going to move separately after the collision with their own individual V1 prime and V2 primes. Now what we're asked to do is to find the velocity of that second object, the 10.31 gram object, after the collision. In an elastic collision such as this one, you end up with two unknowns, the speed of the 4.53 gram object afterwards and the one of the 10.31 gram object afterwards. And so to solve for the two unknown values, you have to use another equation besides simply the momentum conservation equation, an equation that I would use as a kinetic energy conservation equation. I would use the simplified form of it, which states that V1 plus V1 prime equal V2 plus V2 prime. The general idea is you write two equations for your two unknowns and you get your system of two equations and you use it to solve for one of the unknowns. In this case, it's V2 prime that I'm looking for. So here's how I write momentum conservation. You should write this down as we talk. You go 4.53 times 19.2 plus 0, that's optional, equal 4.53 V1 prime plus 10.31 V2 prime. That's your momentum conservation equation. And then for your simplified form of the kinetic energy conservation, you go 19.2 plus V1 prime equal V2 prime, and that's it. There's your two equations, two unknowns. Now what I typically do is I take this V2 prime equal 19.2 plus V1 prime, I take that expression for V2 prime and I stick it in my momentum conservation equation in the place of V2 prime. That turns that momentum conservation equation into one equation with one unknown in it and you can solve for V1 prime. When you're done solving for V1 prime after several algebra steps, you'll have to be careful about that. You will have the velocity after the collision of that 4.53 gram object. Take it, stick it back into the other equation for kinetic energy conservation and solve for V2 prime. You just lay that baby right in there where it says V2 prime equal 19.2 plus V1 prime and you've got your V2 prime. That's your answer. Now there is something that will likely come up in your mind and that is what do I do with the units because these are nonstandard units. And as you go through the problem, what you should note is that the grams will be in every term of the equation and as such, when it's in every term, should you convert, you'd have to convert every term multiplying every term within the equation by the same factor and you might as well just keep it in grams because at any time you want, you can multiply or divide every term in that manner. Same thing can be said of the centimeters per second of velocity units. What is always important is that you keep track of units, that you know what unit you're doing your calculation is and then when you perform an operation, whether it be square or divide, multiply, that you're paying attention to the fact that by so multiplying, you get a different unit and it's the desired one. Well, good luck to you.