© 2004 Penn State University Physics 211R: Lab – Momentum Conservation Physics 211: Lab Momentum Conservation Reading Assignment: Chapter 9, Sections 4-10 http://www.carbuyingtips.com/disaster.htm Introduction: How do insurance companies reconstruct an accident, such as a car crash, to determine exactly what happened and who was at fault? They make use of one of the most fundamental ideas in physics: conservation. During the collision, they treat the two colliding cars as two isolated particles interacting only with each other. This allows them to apply one of the conservation laws that, to the best of our knowledge, are always true: Conservation of Momentum. Conservation laws lie at the foundation of physics. Conserved quantities are fundamental to the development of both classical and quantum mechanical models of systems. Conservation laws are not derived. Rather, they are empirical. That is, they result from experimental studies of the real world. In this lab, you will explore this basic idea in terms of the collisions between two carts. Christian Huygens defined the term momentum, p, to describe the motion of objects, as he realized that both mass and velocity affect the way in which objects behave. This vector quantity is easily defined: Momentum is conserved in a system only if the system is isolated from all external effects. In other words, conservation of momentum occurs when all objects that interact with each other are considered to be part of the system. For example, consider the collisions that take place on a pool table when playing billiards. If only one ball is considered to be “the system,” then the momentum of that ball is not conserved because the ball is being influenced by the other billiard balls. However, if all of the billiard balls together define “the system,” then the momentum lost by some of the balls is found to be gained by the others. Perfectly isolated systems rarely, if ever, occur. In the case of billiard ball collisions, the table itself is in contact with the balls and should be considered as part of “the system.” Some external effects are small, however, and can often be ignored. Consider a system of only two objects that are completely isolated from any outside influences. If momentum is conserved when they collide, then the momentum lost by one is the momentum gained by the other. This can be expressed mathematically as follows: p=mv∆p1=−∆p2p1f−p1i=−(p2f−p2i)© 2004 Penn State University Physics 211R: Lab – Momentum Conservation Rearranging results in the common form of the Conservation of Momentum Equation: Notice that the left side of this equation represents the total momentum of the two-object system before the interaction and the right side represents the total momentum of the two-object system after the interaction. Even though the momentum of each object changes, the total momentum of the system remains the same. Systems involving more than two objects are more complicated. However, the Conservation of Momentum Equation can easily be generalized: It is important to remember that momentum is a vector quantity. Addition of momentum vectors is accomplished in the same way as the addition of any other vector quantity. When the motion is in one dimension, direction can easily be incorporated into the above equation by simply using + or - signs. Motions involving two or three dimensions can be simplified by considering components because, if momentum is conserved overall, then it is also conserved in each dimension. For the purposes of this lab, only collisions in one dimension will be analyzed. One special case of conservation of momentum occurs when the masses are equal. Notice that if all of the particles in the system have equal mass, then the above equations become a description of Conservation of Velocity: This law states that the sum of the initial velocities is equal to the sum of the final velocities for all objects in the system. One of the activities in the lab is to verify this case. Newton later defined the term impulse, I, to describe the change in momentum of an object, as he realized that an object undergoing translational motion often changes speed, direction, and/or mass. This expression shows that, when the momentum of an object changes, it is not conserved. This realization often confuses students who have been taught that the Law of Conservation of Momentum has been verified experimentally many times. Its apparent failure here is due to a lack of clarity of the conditions that must be satisfied in order for momentum to be conserved. It is important to remember that momentum is conserved only if the system being considered is isolated from all external influences. p1i+p2i=p1f+p2fp1i+p2i+...+pni=p1f+p2f+...+pnfpinitialall∑= pfinalall∑m1v1i+m2v2i+...+mnvni=m1v1f+m2v2f+...+mnvnfv1i+v2i+...+vni=v1f+v2f+...+vnfI=∆p=pf−pi© 2004 Penn State University Physics 211R: Lab – Momentum Conservation Momentum Conservation Goals: • Determine the impulse exerted on an object by knowing its mass and measuring its change in velocity. • Verify the Law of Conservation of Momentum. • Determine the conditions necessary in order for Momentum to be conserved. • Analyze the data for evidence of frictional effects. Equipment List: Low Friction Track (2 meter) 2 collision carts with extra masses 2 motion sensors Data Studio™ Excel™ Lab Activity 1: Determine the Momentum of a Cart 1. Set up Data Studio™ to read the data collected from the motion detectors located at the ends of the 2-meter track. Sitting on the track should be two carts. Be aware that each motion detector will record the position of the closest cart. 2. Each cart has a mass of 500 grams. If desired, you may place one or two additional 500 gram mass blocks in your cart. Record the total mass of your cart. (You will need to enter this mass into your momentum