Momentum is defined as p = mv, where p is the symbol for momentum, m is the symbol for mass, and v is the symbol for velocity. Momentum is a vector quantity and points in the direction of the direction of the velocity. Momentum has units of kg m/s. A large mass moving at a high velocity has a large momentum.
Impulseis defined as J = Fav Δt, where J is the impulse and Favis the average force over an event (collision) over a time period Δt. The time interval is normally short, but that is not a real restriction. Impulse has the same units as momentum and, in normal usage, an impulse is given to an object producing a change in momentum. Thus, J = mΔv for an object involved in a collision type event.
Conservation of Momentum is a law regarding the total momentum of a system when external forces can be neglected. The most common use of this law is in describing features of collisions. The simplest of these events is a head on collision between two objects. In that situation, the total momentum of the colliding objects before the collision is equal to the total momentum after the collision. m1v1+m2v2= m1v1’ + m2v2’
Totally Elastic Collisionis a collision where kinetic energy is conserved. This is an ideal situation, because some kinetic energy is almost always lost in a collision.
Totally Inelastic Collision is a collision where the two (or more) colliding objects stick together after the collision. A significant amount of kinetic energy will be lost in this type collision.
Example Using Impulse and Momentum Concepts - Answer the Questions Below.
A 2 kg cart rolls across the floor, runs into the wall, and sticks. Before the collision, the cart has a velocity of 4 m/s in the x direction. The collision took place in 0.1 s. The bold quantities below are vectors and require a direction as part of the answer.
1. What was the cart’s momentum before the collision? ______________
2. What was the cart’s KE before the collision? ______________
3. What was the cart’s momentum after the collision? ________________
4. What was the change in the cart’s momentum? ________________
5. What was the impulse delivered to the car by the wall? ________________
6. What was the average force exerted on the car by the wall? _______________
7. What was the average force exerted on the wall by the car? _______________