Momentum, Impulses, and Collisions

A. Background Information 1.Momentum of an object is anything that has inertia and is moving a. It is based on an objects mass and velocity, only 2.Momentum is represented by a P 3.Formula for momentum: a.P = m x v b.P = kg x m/s

4. Momentum is a vector quantity a. Magnitude and Direction are required b. The direction of momentum is the same as the direction of velocity 5. Momentum Momentum

Example: An object has a velocity of 20 m/s. If momentum is 30 kg x m/s what is the mass?

B. Impulses and Change in Momentum 1.Impulse (J)- the product of the net force acting on a object in a period of time a. Impulse is also the change in momentum of an object. b. What is a net force? 2.Impulse is a vector quantity  the direction of the impulse is the same as the direction of the net force or the change in momentum

3. Formula’s for impulse  J = F net x t J = Δp 4. If the object is in equilibrium: a. There is no net force acting on the object b. there is no change in momentum, therefore no impulse

Example: A 5 kg object has an initial velocity of 8 m/s due east. An unbalanced force acts on the object for 3 seconds, causing its velocity to decrease to 2 m/s east. Calculate the magnitude and direction of the unbalanced force.

C. Conservation of Momentum 1.Conservation of momentum happens only in closed systems a. A closed system is a group of objects not acted on by an outside force

2. Inside a closed system, if a force is applied an equal and opposite reaction occurs

Equation: p before = p after 3. Law of Conservation of Momentum- the total momentum of objects in a closed system is constant

4. Two types of Collisions: Elastic- When 2 objects that collide with each other bounce off of each other after the collision m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f Inelastic- When 2 objects that collide stick together after the collision m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v 2f The opposite of an inelastic collision is recoil: (m 1 + m 2 )v 1i = m 1 v 1f + m 2 v 2f

A 1 kg cart A is initially at rest on a frictionless horizontal track. A 0.2kg cart B is moving to the right at 10 m/s on the same track. Cart B collides with cart A causing cart A to move to the right at 3 m/s. Calculate the velocity of cart B after the collision.

A 2kg cart moving due east at 6 m/s collides with a 3 kg cart moving due west. The carts stick together and come to rest after the collision. Calculate the initial speed of the 3kg cart.

At the circus, a 100 kg clown is fired 15 meters per second from a 500 kg cannon. What is the recoil speed of the cannon?