One-Dimensional Collisions

One-Dimensional Collisions - PHYSICS 215 ONE-DIMENSIONAL...

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1 PHYSICS 215 ONE-DIMENSIONAL COLLISIONS Object: The object of this experiment is to study the conservation of momentum and change in kinetic energy in one-dimensional collisions. Apparatus: Air track Carts (1 small, 1 medium) Light beam timers (2) Meter stick Beam balance Masking tape 1. Introduction Historically and traditionally, classical mechanics begins with Newton’s laws of motion. We have already discussed the first law, called the law of inertia. The concept of force plays a dominate role in the second and third laws. Now we will begin our study with the concept of linear momentum and its conservation. There are a number of reasons for this choice: 1. Linear momentum and the conservation of linear momentum emerge in a simple way from elementary experiments. 2. Once the meaning and significance of momentum is clear, the concept of force and of Newton’s second and third laws easily follows. 3. The conservation of momentum principle provides us with information about collisions without our knowing in detail the forces acting between colliding particles. 4. Momentum plays a dominate role in modern physics—in relativity and quantum physics—while the concept of force is secondary in physics of the atom and nucleus. 2. Theory 2.1 Momentum and Impulse In physics, momentum has a precise definition. A slowly moving elephant has a lot of momentum, but so does a bullet shot from the muzzle of a gun. We therefore expect that momentum will depend on an objects mass and velocity. The linear momentum, p, of an object of mass m moving with velocity v is the product of its mass and velocity: ݌ Ԧ ൌ ݉ݒ Ԧ (1) SI Unit: kg meter per second (kg m/s) By looking at equation (1), we can see that doubling either the mass or the velocity doubles it momentum; doubling both quantities quadruples its momentum. Momentum is a vector quantity with the same direction as the objects velocity. Its components are given by ݌ ൌ ݉ݒ ݌ ൌ ݉ݒ ݌ ൌ ݉ݒ (2) where p x is the momentum of the object in the x-direction, p y its momentum in the y-direction, and p z its momentum in the z-direction. Changing the momentum of an object requires the application of a force. This is, in fact, how Newton originally stated his second law of motion. Starting from the more common version of the second law, we have ܨ Ԧ ௡௘௧ ൌ ݉ܽ Ԧ ൌ ݉ ∆ݒ Ԧ ∆ݐ ∆ሺ݉ݒ Ԧሻ ∆ݐ (3)
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