Momentum Chapter 6

Momentum ► Related to inertia, not the same. ► Symbol is p ► p=mv ► Units of kgm/s 1. What is the momentum of a 75kg rock rolling at 2m/s?

Impulse ► No symbol ► Impulse has the same unit as momentum. ► The relationship between impulse and momentum is called the Impulse-Momentum theorem. ► Examples  Airbags  Nets / Catching  Follow through  Padding

Practice Problems 2. A pro exerts a 150N force on a tennis ball with the racquet. If the ball has a mass of 0.060kg and is in contact with the strings for 0.030s, what is the change in kinetic energy of the ball when it leaves the racquet? Assume the ball starts from rest. 3. How much more force is needed to make a 0.7kg ball initially going at 4.2m/s to bounce back from a wall at 2m/s in 0.022s than to make it stop?

Conservation of Momentum ► In a closed system, the total momentum does not change. ► Requires that no outside force is present. ► In equation form, with two objects:  m 1 v 1 + m 2 v 2 = m 1 v 1 ’+ m 2 v 2 ’ ► If there are more than two objects, simply add the appropriate number of terms to each side.

Internal vs External forces ► Internal forces are those between objects in a system ► External forces are those coming from outside of the system ► Defining the system appropriately is key to observing conservation of momentum ► Examples  Gun / Bullet  Stepping off a boat

Practice 4. Two ducks on roller skates, one travelling at 6m/s and the other at 2.5m/s, collide head on. If the first duck has a mass of 7.8kg and a final speed of 7.1m/s backwards and the second duck has a final speed of 1.4m/s backwards, what is the mass of the second duck? 5. A kid on a skateboard, initially at rest, throws a 20kg cat he was holding at 4.5m/s. If the kid and the skateboard have a combined mass of 55kg, what is their final velocity?

#6 ► An 83g Pokey is thrown at Gumby with a speed of 16m/s. Gumby has a mass of 370g and is initially standing still. After the collision, the two stick together. What is their final speed?

Elastic vs Inelastic Collisions ► Elastic collisions  All energy that starts as kinetic ends as kinetic  No permanent deformation  Things don’t stick  Allows a problem to be solved with fewer givens. ► Inelastic collisions  While total energy is conserved, initial kinetic may switch to other forms  Frequently, there is deformation  When the book says perfectly inelastic collision, they mean that the two objects stick together after the collision.

#7 ► An 800 g billiard ball traveling at 3 m/sec collides head-on with a 900 g billiard ball at rest. What is the velocity of the balls after the collision? Assume that the collision is elastic.

The Elastic Collision Equation ► Can only be used if the problem explicitly states that the collision is elastic.

For 10 points ► In an elastic collision, both momentum and kinetic energy are conserved, therefore: ► If you start with those two equations and derive the elastic collision equation, you will earn 10 points.

Problems #8 & 9 ► Two pool balls collide elastically. The first, with a mass of 0.37kg, has an initial velocity of 1.5m/s and a final velocity of -1.85m/s. The second ball has a final velocity of 0.8m/s. What is:  The initial velocity of the second ball?  The mass of the second ball? ► A 1.2kg ball traveling at 2.3m/s collides elastically with a 4.5kg ball traveling at 1.7m/s in the opposite direction. What are the final velocities of the two balls?

#10 ► Two blocks collide elastically. The first has a mass of 0.77kg and an initial velocity of 12m/s. The second has a mass of 1.2kg and an initial velocity of 3m/s in opposite direction. What are their final velocities?

Conservation of Both Momentum and Energy - #11 ► m 1 =2kg ► m 2 =3kg ► Both start from rest ► v’ 1 =1.3m/s ► Initial height of box 1 is 3.1m ► v’ 2 =?

► A 200g bullet fired at 350m/s is fired into a block which then slides across the floor. If the block and the floor have a coefficient of friction equal to 0.57, how far will the block travel before coming to a stop? Assume that the block has a mass of 4kg. #12