Chapter 6: Momentum & Collisions Section 1 – Momentum & Impulse

Momentum measures the amount of motion an object contains Momentum measures the amount of motion an object contains. It is a vector quantity. Momentum is the product of an object’s mass & velocity. Objects with zero velocity have zero momentum Momentum: p = mv The masses of the bike & cyclist are added together to find the total momentum.

An unbalanced force is needed to change the momentum of an object. Changes in momentum are NOT instantaneous. Impulse (J) is the change of momentum of an object. Impulse is the product of Force & Time. As the Impulse: J = F ∆t = ∆p

As the time needed to cause and impulse increases, the amount of force required decreases. The impulse (change of momentum) cause by the pitcher and the catcher is the same. Because the momentum changes for a longer period of time, the force applied by the pitcher is lower. Because the momentum changes for a very small time period, the force applied by the catcher is greater.

Two eggs of equal mass are dropped from the same height. Consider this: Two eggs of equal mass are dropped from the same height. Which egg is most likely to break, and why? Cushion… Concrete…

Impulse is very important to automobile manufacturers… Imagine what would have happened if the car were made of rigid metal that did not crumple as easily.

The Law of Conservation of Momentum states that the total momentum of objects interacting with each other (during a collision event) remains constant. When objects collide, momentum is transferred between them.

The Law of Conservation of Momentum So, the momentum must remain constant. We can express this with: The momentum before a collision equals the momentum after the collision. This relationship is true within isolated systems. The Law of Conservation of Momentum p1i + p2i = p1f + p2f m1v1i + m2v2i = m1v1f + m2v2f

Chapter 6: Momentum & Collisions Section 2 – Collisions

Collisions can be classified as either “elastic” or “inelastic:. Definition: collision – a brief event in which two objects impact each other. You witness and experience collisions every day and probably do not realize it. Some examples: A tackle on a football field. Playing ping-pong or tennis. Kicking a soccer ball. Collisions can be classified as either “elastic” or “inelastic:.

Energy is NOT conserved in a PIC. A perfectly inelastic collision causes two objects stick together after colliding. Energy is NOT conserved in a PIC. During a “PIC”, the objects act as one single body after the collision. v1i m2 m1 v2i SPLAT! m2 m1 vf m1 + m2

After a PIC, the objects will be moving at the same final velocity! The objects’ mass will be added together. Of course, we can apply the conservation of momentum to such collisions. In fact: It is very important to pay attention to the signs when using this formula! Momentum after a PIC: p1 + p2 = (m1 + m2)vf OR m1v1i + m2v2i = (m1 + m2)vf

The sound of the impact causes some kinetic energy to be lost. The KE of the two objects in a PIC is not conserved. Some of the KE is converted into other forms…sound energy, mechanical energy, and thermal energy. The sound of the impact causes some kinetic energy to be lost.

During an elastic collision, both KE and Momentum are conserved. Elastic collisions occur whenever objects “bounce” away from each other. This can happen when one object is stationary, or when both are moving.

Momentum after an Elastic Collision: p1,i + p2,i = p1,f + p2,f m1v1,i + m2v2,i = m1v1,f + m2v2,f

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