Lab 7

Collisions Previously, we have explored the motion of single objects but often multiple objects interact with each other. When two objects collide, it is difficult to calculate the force between them as a function of time. However, we can use the concept of linear momentum to understand their motion. The linear momentum of an object of mass m moving with velocity ¥ is given by p =mi. @ Linear momentum is a vector quantity that points in the same direction as the velocity. If we consider the change in linear momentum of an object (assuming its mass is constant) with respect to time, we see that md = Foe ) So, the change in linear momentum per unit time is given by the net force on the object. Therefore, if the net force is zero the linear momentum remains constant. Now we consider the case of two objects colliding with each other. We will assume that during the collision the only force acting on the objects is a force between them. However, Newton’s third law states that the force on object 1 from object 2 must be equal in magnitude but opposite in direction to the force on object 2 from object 1. This means that the net force on the system must be zero. Therefore, in any collision with no outside forces the total momentum of the system must remain constant. This does not mean that the momentum of each object must remain constant but rather the total momentum of the system is constant. For example, the first object can slow down while the second object speeds up. In contrast to the linear momentum of the system, the kinetic energy of the system does not need to remain constant. As an example, consider two cars having a head-on collision and stopping. Before the collision, they were moving and therefore both had kinetic energy but after the collision they are stopped. So, kinetic energy must have been lost in the collision. A collision in which the kinetic energy decreases is called an inelastic collision. A collision in which the kinetic energy remains constant is called an elastic collision. While the kinetic energy can change during a collision, the total energy is conserved. The collision just changes the kinetic energy into some other form of energy. In this lab, we will be colliding carts on a track to observe the conservation of linear momentum. The carts can either undergo elastic or inelastic collisions. We will be measuring the linear momentum and energy before and after the collisions and therefore can determine whether a collision is elastic or inelastic. Goals of this lab: e Demonstrate linear momentum conservation for collisions. o Classify collisions as elastic or inelastic. ® Measure energy loss in inelastic collisions. 70

Lab equipment: Collisions Track The cart will travel along this 1.2 meter long track. Smart Cart This cart moves along the track. In this lab, you will be using a red and a blue cart with the built-in rotary position sensor. Mass Set This box contains a set of masses to put on the cart ranging from 1-200 g. 71