Which takes more force to stop?• Big player @ 2m/s

Small player @ 2 m/s

• Big player @ 0.6 m/sSmall player @ 6 m/s

• Small player @ 2 m/sBullet @ 100 m/s

• Small player @ 100 m/sBullet @ 4 m/s

Which takes more force to stop?

• Big player @ 2m/sSmall player @ 2 m/s

Is there ever a time when it would take the same amount of force to stop both players?

Momentum

• Defined as “a mass in motion” (amount of motion)– Momentum equals mass times velocity– A vector quantity (has direction)

• The more momentum an object has– could mean it has a larger mass or velocity– it is harder to change its motion

Momentum

• Momentum is different from inertia– Inertia is the resistance to the change of motion– Momentum is how much motion there is• An object not moving has inertia but zero momentum• An object moving has inertia and momentum

Calculating Momentum

Determine the momentum of a ...• a. 100-kg halfback moving to the right at 4 m/s.

• b. 70-kg halfback moving to the left at 2 m/s.

Check Your Understanding

A car traveling down the road has momentum of 20,000 kg·m/s. What would be the car's new momentum if ...a.its velocity were doubled. b.its mass were tripled (by adding more passengers and a greater load)c.The car turned around.

Momentum and Impulse

• Impulse: a change in momentum created by a force exerted over a period of time

Impulse DefinedImpulse is defined as the product

force acting on an object and the time during which the force acts. The symbol for impulse is J. So, by

definition:

J = F t Example: A 50 N force is applied to a 100 kg boulder for 3 s. The impulse of this force is J = (50 N) (3 s) = 150

N · s. Note that we didn’t need to know the mass of the object in the above

example.

Impulse UnitsJ = F t shows why the SI unit for impulse is the Newton ·

second. There is no special name for this unit, but it is equivalent to a kg · m /s.

proof: 1 N · s = 1 (kg · m /s2) (s) = 1 kg ·

m /s {Fnet = m a shows this is

equivalent to a newton.

Therefore, impulse and momentum have the same units, which leads to a useful theorem.

Impulse - Momentum Theorem

The impulse due to all forces acting on an object (the net force) is equal to the change in momentum of the object:

Fnet t = p

We know the units on both sides of the equation are the same

(last slide), but let’s prove the theorem formally:

Fnet t = m a t = m ( v / t) t = m v = p

Determine the Impulse

• A baseball with a momentum of 5 kg·m/s is caught in a player’s glove.

• A billiard ball with a momentum of 0.7 kg·m/s to the right hits the rail of the table and bounces back with a momentum of 0.6 kg·m/s to the left.

• A boxer hits an opponent with a force of 300 N for a time of 0.021 seconds.

Same Impulse in Different Ways• The same change in momentum (impulse) can be

accomplished with different combinations of force and time.

• Large force, short time = small force, long time!

same change in momentum = same change in momentum

F·t = F·t

• Safety belts save lives because they cause the same change in momentum over an extended period of time.

same change in momentum = same change in momentum

F·t = F·t

Types of Collisions

• Elastic collision: objects bounce off each other– Bounce, snap back into shape (like a rubber band).

• Inelastic collision: objects stick together or change shape (break, compress)

The Law of Conservation of Momentum• In a collision– Force on each object is the same (Newton’s 3rd Law)

– The system’s total momentum is conserved (stays the same)

– Pbefore = Pafter

– The system’s total momentum is the same in the absence of external forces

Collisions and Momentum

• Objects collide• Objects push apart or explode

• In any system, momentum is conserved• Total momentum is the same before and after a

collision• http://youtu.be/4IYDb6K5UF8

Under what circumstances will:

--the first car stop completely after the collision?

--the first car bounce backward?

--the first car keep moving forward?

Elastic collision is a larger change

Inelastic collision• Object just comes to rest

Elastic collision• Object has a greater

momentum after impact

Bouncing has a larger

change in momentu

m!

Bouncing has a larger

impulse!

Bouncing is a larger impulse

• Water wheels used to turn because the weight of the water.

• Now, paddles are made to make water ‘bounce’

• Creates a larger impulse and moves water turbines faster

Solving Momentum Problems

• Draw pictures– Before picture (before the collision)– After picture

• Need to know the momentum of each object first

(p of all the objects)before = (p of all the objects)after

• A hunter spots his prey off to the right. He waits patiently and does not move. When the hunter fires, the bullet has a momentum of 284 kg·m/s. The hunter feels a kickback after the bullet is fired. Determine the momentum of the hunter after he fires the bullet.

• A van traveling East with a momentum of 1500 kg·m/s collides with a car moving West with a momentum of 800 kg·m/s. After they collide, they stick together and the van has a momentum of 500 kg·m/s. What is the momentum of the car?

• Playing a game of pool, the cue ball is hit so it moves with a momentum of -0.90 kg·m/s. It collides with the 1-ball that was at rest. After they hit, the 1-ball has a momentum of -0.75 kg·m/s. What is the momentum of the cue ball?

• Two figure skaters are standing next to each other on an ice rink. The skaters then push off from one another. One skater has a momentum of 120 kg·m/s to the right. What is the momentum of the other skater?

• Playing a game of pool, the cue ball (m = 0.17 kg) is hit with a speed of 3 m/s toward the 4-ball (m = 0.16 kg) that was at rest. After the two balls collide, the 4-ball has a speed of 2 m/s. What is the speed of the cue ball after the collision?

• An 80 kg hunter spots his prey off to the right. He waits patiently and does not move. When the hunter fires, the 5 gram bullet has a velocity of + 120 m/s. The hunter feels a kickback after the bullet is fired. Determine the speed of the of the hunter after he fires the bullet.

• A 1000 kg van traveling East with a velocity of of 1.5 m/s collides with a 600 kg car moving West with a velocity of 1.5 m/s. After they collide, they stick together. What is the velocity of the van and the car?

• Two children on ice skates start at rest and push off from each other. One has a mass of 30 kg and moves back at 2 m/sec. The other child has a mass of 15 kg, but what is their speed?

• Standing on an icy pond, you throw a 0.5 kg ball at 40 m/sec. You move back at 0.4 m/sec. What is your mass?