Momentum

A measure of how hard it is to stop a moving object. Related to both mass and velocity. Possessed by all moving objects.

Calculating Momentum For one particle p = mv For a system of multiple particles P =  p i =  m i v i Momentum is a vector!

Which has the most momentum?

Impulse (J) The product of an external force and time, which results in a change in momentum J = F t J =  p Units: Ns or kgm/s

Impulse (J) F(N) t (ms) area under curve

Law of Conservation of Momentum If the resultant external force on a system is zero, then the vector sum of the momenta of the objects will remain constant. pi = pfpi = pfpi = pfpi = pf

Collisions Collisions are governed by Newton's laws. Newton’s Third Law tells us that the force exerted by body A on body B in a collision is equal and opposite to the force exerted by body B on body A.

Collisions During a collision, external forces are ignored. The time frame of the collision is very short. The forces are impulsive forces (high force, short duration).

Collision Types Elastic (hard, no deformation) –p is conserved, KE is conserved Inelastic (soft; deformation) –p is conserved, KE is NOT conserved Perfectly Inelastic (stick together) –p is conserved, KE is NOT conserved

Inelastic Collisions Only momentum is conserved. Kinetic Energy is not conserved. Some deformation of the object(s) will occur. Perfectly inelastic collision is when the objects actually “stick” together. Examples are: automobile crashes, catching a ball, recoil of a gun.

Perfectly Inelastic Collision #1 An 80 kg roller skating grandma collides inelastically with a 40 kg kid as shown. What is their velocity after the collision?

Perfectly Inelastic Collisions #2 A train of mass 4M moving 5 km/hr couples with a flatcar of mass M at rest. What is the velocity of the cars after they couple?

Perfectly Inelastic Collisions #3 A 1.14-kg skateboard is coasting along the pavement at a speed of 3.53 m/s, when a 1.1-kg cat drops from a tree vertically down on the skateboard. What is the speed of the skateboard-cat combination?

Explosions and Recoil When an object separates suddenly, this is the reverse of a perfectly inelastic collision. Mathematically, it is handled just like an ordinary inelastic collision. Momentum is conserved, kinetic energy is not. Examples: –Cannons, Guns, Explosions, Radioactive decay.

Recoil Problem #1 A gun recoils when it is fired. The recoil is the result of action-reaction force pairs. Calculate the Recoil velocity Mass of Gun = 2.1 kg Mass of Man= 75 kg Mass of Bullet = Kg Muzzle Velocity = 450 m/s

Elastic Collisions Momentum and Kinetic Energy are conserved. No deformation of objects occurs. Examples are: billiard balls (pool), particle collisions, marbles.

Elastic Collision #1 A 7-g marble has a head-on collision with a 3-g marble, initially at rest on a playing surface. The speed of the 7-g marble is reduced from 1.08 m/s to 0.75 m/s in the collision. What is the speed of 3-g marble after the collision?

Elastic Collision #2 A 4-gram object moving to the right with a speed of 3.9 cm/s makes an elastic head- on collision with a 6-gram object moving in the opposite direction with a speed of 6.6 cm/s. Find the velocities after the collision.