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HOLT PHYSICS CHAPTER 06 MOMENTUM AND COLLISIONS I. Momentum and Impulse Objectives: • Compare the momentum of different moving objects. • Compare the momentum of the same object moving with different velocities. • Identify examples of change in the momentum of an object. • Describe changes in momentum in terms of force and time. A. Linear Momentum 1. Momentum is defined as mass times velocity. 2. Momentum is represented by the symbol p, and is a vector quantity. 3. momentum = mass × velocity (p = mv) B. Impulse 1. The product of the force and the time over which the force acts on an object is called impulse. 2. The impulse-momentum theorem states that when a net force is applied to an object over a certain time interval, the force will cause a change in the object’s momentum. 3. F∆t = ∆p = mvf – mvi; force × time interval = change in momentum 4. Stopping times and distances depend on the impulse-momentum theorem. 5. Force is reduced when the time interval of an impact is increased. II. Conservation of Momentum Objectives: • Describe the interaction between two objects in terms of the change in momentum of each object. • Compare the total momentum of two objects before and after they interact. • State the law of conservation of momentum. • Predict the final velocities of objects after collisions, given the initial velocities, force, and time. A. The Law of Conservation of Momentum: 1. The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects. 2. total initial momentum = total final momentum: • m1v1,i + m2v2,i = m1v1,f + m2v2,f 3. Newton’s third law leads to conservation of momentum 4. During the collision, the force exerted on each bumper object causes a change in momentum for each object. 5. The total momentum is the same before and after the collision. III. Elastic and Inelastic Collisions Objectives: • Identify different types of collisions. • Determine the changes in kinetic energy during perfectly inelastic collisions. • Compare conservation of momentum and conserva-tion of kinetic energy in perfectly inelastic and elastic collisions. • Find the final velocity of an object in perfectly inelastic and elastic collisions. A. Perfectly Inelastic Collisions 1. Perfectly inelastic collision 2. A collision in which two objects stick together after colliding and move together as one mass is called a perfectly inelastic collision. 3. Conservation of momentum for a perfectly inelastic collision: • total initial momentum = total final momentum • m1v1,i + m2v2,i = (m1 + m2)vf B. Elastic collisions 1. A collision in which the total momentum and the total kinetic energy are conserved is called an elastic collision. 2. Momentum and Kinetic Energy Are Conserved in an Elastic Collision • m1v1,i + m2v2,i = m1v1,f + m2v2,f