From a Consumer Reports article on Crash Tests of Cars… …..The tests don’t say what happens when a small car impacts a big car. Physics dictates that the smaller car bears the brunt of the collision. Why? What Physics?

1.Momentum = mass x velocity 2. A vector quantity 3. Its direction is parallel to the velocity 4. Units are kg · m/s v p

Large Momentum Examples  Huge ship moving at a small velocity  High velocity bullet P = m v

1.A 15 g bullet is moving with a speed of 300 m/s, what is the magnitude of its momentum. p = mv = (.015 kg) (300 m/s) = 4.5 kg  m/s 2.A 75 kg sprinter running with a speed of 10 m/s, what is the magnitude of her momentum? p = mv = (75 kg) (10 m/s) = 750 kg  m/s

Two identical objects move toward one another along the same line as shown. Which is correct? a.The magnitude of the total momentum before the impact is mv b.The magnitude of the total momentum before the impact is 3mv c.The magnitude of the total momentum after the impact is 2mv d.The total kinetic energy before the impact is 3mv 2 /2

Equivalent Formulation of Newton’s Second Law * The time rate of change of momentum equals the net force applied to it.*

Impulse Change in Momentum MOVIE The greater the change in momentum the greater the impulse!

Newton’s Second Law Derivation The rate of change of momentum of a body is equal to the net force applied to it.

Having a net force is not enough to cause a change in the motion of an object. It must be present for some time. A huge force acting for zero seconds accomplishes nothing. A small force acting for a long time can be as effective as a huge force acting for a short time.

You can abruptly stop a car by stomping on the brakes or gradually by lightly applying the brakes. In either case the car gets stopped. When we multiply the average force by the time, we find that in all three cases above is the same. It’s called the Impulse. The formula for it actually comes from a little manipulation of Newton's Second Law shown below.

Two ways to calculate the Impulse And since  p = F  t

Newton’s Second Law & Momentum  If there is a net force the momentum changes.   p = F  t = Impulse = J  If there’s no net force the momentum is constant.   p = F  t = 0 Louis

Fore! A golf ball of mass.05 kg is hit off the tee at 45 m/s. The golf club was in contact with the ball for 5.0 x s. 1.Find the force imparted to the golf ball by the club. 2.Find the impulse imparted to the ball. J = Impulse = F  t =  p = mv f – mv i J = Impulse = m(v f – v i ) = 0.05kg · (45 – 0)m/s J = Impulse = 2.25 kg·m/s = 2.25 N·s

2. Find the average force given to the golf ball by the club. J= F  t ( = 2.25 N· s ) J/  t = F F = 2.25 N·s/5.0 x10 -3 s = 450 N

How can you maximize the Impulse? Apply the force for a long time !!  Follow through on a golf swing  Pushing a car  Hitting a baseball FtFt

How can you minimize the force? Increasing  t decreases F !!  Catching a ball  Bungee jumping  Air bags  Bending knees Increasing the time decreases the force ! FtFt

When a boxer sees that he will be hit he relaxes his neck and allows his head to move backwards upon impact, it’s called riding the punch. A boxer does this to extend the time of impact of the glove with their head. Why?

A 1500 kg car initially moving with a speed of 15 m/s collides head on with a pole and is brought to rest in.3 seconds. a.What is its initial momentum? b.What is its final momentum? c.What is the change in momentum of the car? d.What impulse was imparted to the car? e.What is the average force exerted on the car?

A.15 kg tennis ball traveling to the right at 30 m/s strikes the racquet and rebounds at 30 m/s: 1.What impulse was delivered to the ball? 2.If the collision lasted.2 seconds what average force was given to the ball? 3.What impulse was delivered to the racquet? vivi vfvf

Estimate the Impulse imparted to the 100 kg passenger

Calculate: The impulse given to the 300 kg car in each case

A soccer player hits a ball (mass m = 440 g) coming at him at 20 m/s. After it was hit, the ball travels in The opposite direction with a velocity of 30 m/s. (a)What impulse acts on the ball while it is in contact with the foot? (b)The impact time is 0.1s. What is the force acting on the ball?

Force vs. Time  Area under the curve = Impulse

Force vs. Time  Area under the curve = Impulse  Area above the x-axis is positive Impulse  Area below the x-axis is negative Impulse  Total Impulse is the sum of all the individual areas

Impulse = Area J Net = Net Impulse J Net = J p + J n F t J n = Negative impulse J p = Positive impulse I II III Force vs. Time

Time (s) F(N) Calculate the Impulse from: seconds.

Force on a rubber ball during a bounce

Constant force What would the graph be for a rigid ball hitting the wall?

Time (sec) Force (N) Force on a human during a jump

1.In which case (A or B) is the change in momentum the greatest? Explain. 2.In which case (A or B) is the impulse the greatest? Explain 3.In which case (A or B) is the force which acts upon the ball the greatest (assume contact times are the same in both cases)? Explain

Lara, mass 60 kg, is riding at 25 m/s in her sports car when she must suddenly slam on the brakes to avoid hitting a dog crossing the road. She strikes the air bag, which brings her body to a stop in 0.4 s. Lara then picks up the “Lucky” puppy and they live happily ever after. 1.What average force does the seat belt exert on her? 2.If Lara had not been wearing her seat belt and not had an air bag, the windshield would have stopped her head in s. What average force would the windshield have exerted on her? Lucky

1.A hockey player applies an average force of 80 N to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced by the hockey puck. 2. If a 5 kg object experiences a 10 N force for a duration of 0.1 second, then what is the momentum change of the object? 80N