Chapter 6: Momentum and Collisions!

The Solar System (not to scale!) A Question for you to ponder… Why do the Sun and all of the planets (except Venus) rotate In the same direction?

The Answer lies in the Formation of the Solar System

4 billion miles away…do you see what I see? That’s us 

So What? What does this have to do with Chapter 6? Planet formation is directly tied to the law of conservation of momentum! Yay for more laws 

Linear Momentum Momentum describes how the motions of objects are changed Newton’s Laws explain why The Linear Momentum equation p=mv Momentum = mass x velocity MOMENTUM IS A VECTOR!!

Sample Problem A 3000kg elephant is chasing a 1 kg squirrel across the road at a velocity of 5 m/s to the west. What is the momentum of the elephant? If the squirrel is running at 7 m/s west what is its momentum?

Solve the Problem Momentum of the elephant Momentum of the squirrel p = mv = (3000 kg)(5m/s)= 15000 kgm/s West Momentum of the squirrel p=mv= (1kg)(7m/s)= 7 kgm/s West

Change in Momentum A change in momentum takes force and time It takes a lot of force to stop an object that has a lot of momentum

Impulse Momentum Theorem A net external force, F, applied to an object for a time interval, Δt, will cause a change in the object’s momentum equal to the product of the Force and the time interval. In other words…

What does that mean? A small force acting for a long time can produce the same change in momentum as a large force acting for a short time. In sports like baseball, this is why follow through is important. The longer the bat is in contact with the ball, the greater the change in momentum will be.

Sample Problem p. 211 #3 A 0.40 kg soccer ball approaches a player horizontally with a velocity of 18 m/s north. The player strikes the ball and causes it to move in the opposite direction with a velocity of 22 m/s. What impulse was delivered to the ball by the player?

What do we know? M = 0.40 kg Vi= +18 m/s Vf= -22 m/s What does impulse mean? Impulse is equal to FΔt Impulse is also equal to the object’s change in momentum

Solve the problem

Stopping Distance The stopping distance is the distance it requires an object to come to rest The greater the momentum, the more distance it takes to stop

Sample Problem p.213 #2 A 2500 kg car traveling to the north is slowed down uniformly from an initial velocity of 20.0 m/s by a 6250 N braking force acting opposite the car’s motion. Use the impulse momentum theorem to answer the following questions: A. What is the car’s velocity after 2.50 s? B. How far does the car move during 2.50 s? C. How long does it take the car to come to a complete stop.

Answer part a. m= 2500 kg Vi= 20 m/s North F= -6250 N t= 2.50 s Vf= ? Why is F negative? Because it is acting opposite the car’s motion! m= 2500 kg Vi= 20 m/s North F= -6250 N t= 2.50 s Vf= ?

Use the impulse-momentum theorem!!

Solve Part B How far does the car move in 2.5 s? Which kinematic equation should we use?

Solve Part c How long does it take for the car to come to a complete stop? Use impulse momentum theorem!

Summary of 6.1 Momentum is a vector quantity that is equal to the product of an object’s mass and its velocity (p=mv) Impulse = FΔt= Δp A small force applied over a long period of time produces the same change in momentum as a large force applied over a short period of time

Section 6.2: Conservation of Momentum Remember...we talked about the formation of the solar system and conservation of momentum.

Let’s Talk about the Moon

We are the only inner planet with a large moon…why? Our moon didn’t form with us in the nebula We acquired it later through a collision with another planetoid http://vimeo.com/2015273

The Moon is trying to leave us Every year, the moon moves about 4 cm away from the Earth and thus it’s velocity increases Conservation of Momentum says that velocity has to come from somewhere. So…the moon steals it from us So every year, our rotation slows down… adding about 0.0002 seconds to our day.

Momentum is Conserved The Law of Conservation of Momentum says: The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.

In mathematical form Be very careful with your signs when using this equation!!

Collisions There are many different ways to describe collisions between objects In any collision, the total amount of momentum is conserved but generally the total kinetic energy is not conserved

Perfectly Inelastic Collisions When two objects collide and move together as one mass, the collision is perfectly inelastic Since the two objects stick together and move as one, they have the same final velocity. Kinetic Energy IS NOT CONSERVED in PERFECTLY INELASTIC COLLISIONS

Sample Problem p. 219 #2 An 85.0 kg fisherman jumps from a dock into a 135 kg rowboat at rest on the west side of the dock. If the velocity of the fisherman is 4.30 m/s to the west as he leaves the dock, what is the final velocity of the fisherman and the boat?

What do we know M1= 85 kg M2= 135 kg V2,i=0 V1,i= -4.30 m/s What type of collision is this? PERFECTLY INELASTIC because they stick together and move as one mass

Rearrange the equation and solve for Vf Vf= 1.66 m/s West

What is the change in Kinetic Energy for this problem? Initial Kinetic Energy of the boat= 0 J Initial Kinetic Energy of the fisherman KE= 0.5mv^2= 0.5(85kg)(4.3m/s)^2=785.3 J Total Initial KE= 0+ 785.3 J= 785.3 J Final KE= 0.5(85+135)(-1.66)^2=303.1 J ΔKE=KEf – Kei = 482.2 J

Elastic Collisions In an elastic collision, two objects collide and return to their original shapes with no change in total energy. After the collision, the two objects move separately. Momentum is conserved Kinetic Energy is Conserved

Sample Problem p.229 #2 A 16.0 kg canoe moving to the left at 12 m/s makes an elastic head-on collision with a 4.0 kg raft moving to the right at 6.0 m/s. After the collision, the raft moves to the left at 22.7 m/s. Disregard any effects of the water. a. Find the velocity of the canoe after the collision.

What do we know? V1,i= -12 m/s V2,i = 6 m/s V1,f = ? V 2,f = -22.7 m/s M1= 16 kg M2= 4 kg

Conservation of Momentum says… This is an elastic collision, so we should use the following equation:

Rearrange and solve We need to solve for V1,f so we should rearrange the conservation of momentum equation So The final velocity of the canoe is 4.8 m/s Left.

Impulse In Collisions Think about Newton’s 3rd Law: Every action force has an equal and opposite reaction force Since Impulse = FΔt then in a collision between objects, the impulse imparted to each mass is the same!!!!

Comparison of Collisions Perfectly Inelastic Collisions Inelastic Collisions Elastic Collisions Objects stick together and move as one mass after the collision Momentum is conserved Kinetic Energy is not conserved because it is converted to other types of energy Objects are deformed and move separately after the collision KE is not conserved Objects return to their original shapes and move separately after the collision Kinetic Energy is conserved

Summary of Section 6.2 and 6.3 In all interactions between isolated objects, momentum is conserved Few collisions are elastic or perfectly inelastic Impulse imparted is the same for all objects in a collision