Chap 8.3 and 8.4 Conservation of Momentum Conservation of Linear Momentum Inelastic Collisions Elastic Collisions

Conservation of Linear Momentum Conservation of Momentum If the net force acting on an object is zero, its momentum is conserved

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 on body B by body A.

Conservation of Linear Momentum An example of internal forces moving components of a system:

Collisions Collision: two objects striking one another The collision between two billiard balls on a frictionless surface in isolated system.

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) momentum is conserved, KE is conserved Inelastic (soft; deformation) momentum is conserved, KE is NOT conserved Perfectly Inelastic (stick together)

Inelastic Collisions A completely inelastic collision:

Inelastic Collisions Ballistic pendulum: the height h can be found using conservation of mechanical energy after the object is embedded in the block.

Elastic Collisions One-dimensional elastic collision:

Conservation of Momentum Newton’s 2nd law becomes difficult or impossible to solve collisions. Let’s see Elastic head-on collision: before collision during collision A     B Forces during the collision are an action/reaction pair. According to Newton’s III law, = -

Elastic Head-on Collision       After collision   Change in momentum of A = - (Change in momentum of B) Conservation law of momentum – total momentum of a system remain constant before after

Conservation Law 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. ΔpB = ΔpA

Chubby, Tubby and Flubby are astronauts on a spaceship Chubby, Tubby and Flubby are astronauts on a spaceship. They each have the same mass and the same strength. Chubby and Tubby decide to play catch with Flubby, intending to throw her back and forth between them. Chubby throws Flubby to Tubby and the game begins. Describe the motion of Chubby, Tubby and Flubby as the game continues. If we assume that each throw involves the same amount of push, then how many throws will the game last? 14

Head-on Elastic Collisions

The coefficient of elasticity is a measure of the "restitution" of a collision between two objects. The coefficient, e is defined as the ratio of relative speeds after and before an impact  

E is usually positive, between 0-1 e=0, the perfect inelastic collision. e=1 the perfect elastic collision. 0<e<1, real world inelastic

Answer: Truck Collision Comparison of the collision variables for the two trucks: Ride in the bigger truck! There are good physical reasons! A greater change in velocity implies a greater change in kinetic energy and therefore more work done on the driver.

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 #3 A fish moving at 2 m/s swallows a stationary fish which is 1/3 its mass. What is the velocity of the big fish and after dinner?

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?

Explosion 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. As the gases from the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet pushes the gun backwards.