COLLISIONS OBJECT: To verify that momentum is conserved in collisions on an air track; to study inelastic collisions, demonstrating that kinetic energy is n_ot conserved; to study elastic collisions, demonstrating that kinetic energy is conserved. NOTE: This lab is somewhat \"fiddly" requiring some adjustment of things on your part. We make no apology for this since a lot of experimentation in physics requires skill and judgement and it's good for you to be exposed to this aspect of physics. However, and this is the good news, numerical processing will be done by a spreadsheet on one of the lab computers. Apart from the trial calculations to check, there will be almost no numerical processing by hand. Therefore, please spend your time in the lab getting the equipment to work well and afterwards, in discussing the systematic and other errors affecting your experiment. SUGGESTED READING: Halliday & Resnick FUNDAMENTALS OF PHYSICS, 12th Edition, Secs. 9.4-9.7 REQUIRED EQUIPMENT: 0 Smart Carts, Cart Weights and Track 0 Computer with Capstone software 0 Mass Balance THEORY: The linear momentum of a mass m, travelling at velocity v is defined simply as E = my. Note that both P and v are vector quantities. In one dimension we take each as being positive if pointing to the right, and negative if pointing to the left. The S1 unit for momentum is the kg.m/s. Now it will be (or was) shown in class that, if external forces are negligible in some interaction between bodies (such as in a collision), then, because of Newton's third law, the total momentum (vector sum) before the interaction must equal the total momentum (vector sum) after the collision. In this experiment, we will be dealing with gliders on an air track and the situation may be represented schematically below: a, EE 1 ' m1 1'1 + m2 1'2 m1v1 + m2 1'2 Total momentum before Total momentum after Velocities y] and y: are the velocities before the collision and E1' and 22' are the velocities aer the collision. (Notice that, to avoid confusion, we have shown all velocities to the right and therefore as positive quantities; if any of the velocity vectors are actually pointing in the other direction, the corresponding quantity will be negative.) Now usually, one will know the initial velocities 11 and 22; quantities 21' and 22' will then be unknown. Therefore with only one equation we will not have enough information to solve for the unknowns. What is happening? Well, we need to know the w of collision. The gliders aer all could stick together - we would call this an inelastic collision - or they could bounce apart. If they bounce apart perfectly, we call this an elastic collision. The whole situation can be summarized by the following equation: v} - v}: = -(v; - V2) (2) Quantity e is called the coeicient of restitution. For inelastic collisions, e = 0 and V1' = V2' = V (the masses stick together); for perfectly elastic collisions, e = 1. (Intermediate cases, with 0 Heavy -1.211 -49.98 -1.789 -52.42 -1.962 -51.95 Inelastic Light -> Heavy -0.891 -66.51 -3.132 -68.10 -3.621 -68.31 Heavy -> Light -1.239 -35.32 -2.001 -35.71 -1.617 -36.15 % Change in total % Change in total momentum kinetic energy Heavy -> Heavy -1.075 -5.810 -1.621 -2.196 -1.93 -3.113 Elastic Light -> Heavy -3.518 -7.810 -0.912 -3.831 +1.701 -1.672 Heavy -> Light +0.4961 +1.462 2.622 -5.100 -2.738 -5.549