08 Solving Elastic Collision Problems In Class Activity PDF

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In-Class Activity: Solving Elastic Collision Problems In the following activity we will analyze a one-dimensional elastic collision. In an elastic collision momentum and kinetic energy are conserved. pT  pT and E k  E k . Generally in a one dimensional collision, where only momentum is conserved, there can be only one unknown. For a one dimensional elastic collision, we can solve for two unknowns. Example: Two physics students are bowling. There is one pin of mass 6 kg left in the ally. A 2 kg bowling ball has a head-on elastic collision with the pin at a speed of 4 m/s. Determine the velocity of each ball and the pin after the collision. The key words to this problem are “head-on elastic collision” this means it is a one-dimensional elastic collision problem. (1) Begin by writing down your knowns and unknowns using the proper symbols. In this example we will call the bowling ball mass one and the pin mass two. How many unknowns do we have? (answer card 1) (2) In this problem there are two things that are conserved. What are those two things? Write two equations one for each of the equations that are conserved. Try simplifying these equations as much as possible for this problem, without plugging in the numbers. (answer card 2) (3) Remember that we have two unknowns in this problem, but notice that we now have two equations. Recall from your math class how you can solve for two unknowns using two equations. How can you solve for two unknowns using two equations? In order to make things look simpler, at this point you can plug in all your knowns into your two equations. You do not need to include units in this particular problem. (answer card 3) (4) Simplify these equations as much as possible, then solve for v1 in the equation you got from momentum and substitute it into the equation you got from kinetic energy. Note: You are actually squaring vectors in this substitution. When we square a vector it becomes a scalar, so drop the vector symbols. (answer card 4) (5) You now should have one equation with one unknown ( v2 ). Solve for v2 . You will have to do some simplification to do this. There should be two solutions, one of them you can ignore. You should get v2 2m / s . If you did not get this number, before looking at the next answer card look back through your work and check for any errors. (answer card 5) (6) You must now find v 1 . Since you know v2 2m / s you can substitute one of your earlier equations to solve for v 1 . Choose the equation that has v 1 and v 2 in it that would give you v 1 with the least effort. (answer card 6) (7) Congratulations have solved your first head-on elastic collision problem. You may now shout for joy....