Momentum

Momentum and Sports "Going into the all-star break, the Chicago White Sox have the momentum." "Chicago Bears Gaining Momentum." “Figure skaters use their momentum to do jumps and spins.” What do all these phrases have in common? Objects in Motion!!!

Momentum in Sports Momentum: An object in motion ("on the move") has momentum. ** Please write this slide in your notes.

A loaded freight train _________ Place the following objects in the correct order from the HIGHEST momentum (#1) to the LOWEST momentum (#5) Assume that all the objects are at their maximum velocity. A loaded freight train _________ A bullet from a high-powered rifle _________ The space shuttle _________ A mosquito _________ A bowling ball making a strike _________ Explain how you arrived at your answer.

Would you rather…..? Be tackled by a large football player running really fast……… OR Be tackled by a small football player running really slow?

Which is Harder to Stop: a heavy truck vs. a small car moving at the same speed? A massive truck rolling down a steep hill has a LARGE momentum.

What is Momentum? Mass Velocity Momentum can be defined as MASS IN MOTION. The amount of momentum which an object has is dependent upon two variables… Mass Velocity In other words, how much stuff is moving and how fast the stuff is moving ** Please write this slide in your notes.

How can you remember? m&m mass in motion

A bullet has a small mass but a very LARGE velocity: m V For each object below write either a BIG or little letter m and v. A cruise ship slowly pulling into the dock. ______ x _____ A jet taking off from an air strip. _____ x _____ A turtle moving across a rock. _____ x ____ d. Hitting (driving) a golf ball. ______ x _____ Now RANK them from most to least momentum

What is Momentum? p = m ∙ v p m v Momentum = mass ∙ velocity Velocity (m/s) p = m ∙ v Momentum (kg ∙ m/s) p m v Mass (kg)

p = m ∙ v If an object has a large mass and velocity, …….it will have a greater momentum. If an object has a small m and v, …….it will have a smaller momentum. Ex: Which player has more momentum? Large football player running fast vs. Small football player running slow ** Please write this slide in your notes.

Example Problem What is the momentum of a 60 kg halfback moving eastward at 9 m/s? G U E S

What is the momentum of a parked airplane? Anything at rest has a momentum of “0”. Its “mass is NOT in motion.”

Momentum can transfer! What if 2 of the balls were lifted?

Momentum transfers!

Transfer of Momentum One object can transfer its momentum to another object when it comes into contact…. “Aka” a Collision!!! ** Please write this slide in your notes.

Types of Collisions 1) Elastic 2) Inelastic Colliding objects bounce off each other 2) Inelastic Colliding objects stick to each other ** Please write this slide in your notes.

Elastic Collision Elastic collision: colliding objects bounce off each other ** Please write this slide in your notes.

Inelastic Collision Inelastic collision: colliding objects stick to each other ** Please write this slide in your notes.

Types of Collisions Lab Carts on the Track

Conservation of Momentum

Law of Conservation of Momentum In the absence of an external force, the momentum of a system remains the same. Momentum is conserved in collisions!!!! Momentum before collision = Momentum after collision pinitial = pfinal m∙vi = m∙vf

Example Newton’s 3rd Law Consider a gun being fired. A gun recoils when it is fired. Newton’s 3rd Law The gun pushes the bullet forwards and the bullet pushes the gun backwards. What is the recoil momentum of the gun? The same as the momentum of the bullet it fires!

Why? The momentum gained by the bullet is equal and opposite to the momentum gained by the recoiling gun. They cancel each other out No momentum is gained, and no momentum is lost. They are within the same SYSTEM

Solution to Ex #1 6.25 m/s = Vafter (m∙ v)before = (m∙ v)after Total momentum before = Total momentum after (m∙ v)before = (m∙ v)after (m∙v) red + (m∙v) blue = (mred +mblue) ∙ vafter (5kg ∙ 10 m/s) + (3kg ∙ 0 m/s) = (5kg + 3kg) ∙Vafter 50 kg∙m/s + 0 = 8 kg ∙ Vafter 50 kg∙m/s = Vafter 8 kg 6.25 m/s = Vafter

Impulse Day 3

Impulse To stop such an object, it is necessary to apply a… force against its motion for a given period of time

Impulse The more momentum an object has, the harder that is to stop It would require a…… greater amount of force or a longer amount of time (or both) to bring an object with more momentum to a halt.

Impulse In order to change an objects momentum, it is necessary to apply a….. Force Against the objects motion For a given time Force (N) Impulse = F ∙ t Impulse (N ∙ s) Time (s)

Class Discussion Egg toss & Egg into sheet Explain why the goal posts have padding around their base. The padding will increase the time required to stop and decrease the force. What safety features in cars lengthen the time during a collision in order to decrease the maximum force during that collision. Examine the inside of a football helmet. How is the helmet constructed so that the player’s head will have more time to stop during a collision? There is space in the interior of the helmet for the head to move, thereby increasing the time.

Decreasing Momentum Over a Long Time If you are out of control in a car, would you rather hit a brick wall or a haystack? A haystack right? Why? Which has a greater impulse? They have the same impulse. Why? Because the result in both is a momentum of “0” However, stopping is a product, it doesn’t mean that the time or force was the same

Haystack vs. Wall By hitting the haystack instead of the wall, you Extend the time of impact The time it takes you to change your momentum to zero Ft mV

mV Ft

Decreasing Momentum over a Short Time For short impact times, the impact forces are large! Remember: for an object brought to rest, the impulse is the same no matter how it is stopped. But, if the time is short, the force will be large

Change in Momentum for an object

Impulse F ∙ t = m ∙ (vf – vi) Impulse is a change in momentum Impulse = Δp F ∙ t = m ∙ Δv F ∙ t = m ∙ (vf – vi) F ∙ t = m ∙ (vf – vi)

Change in Momentum #1 A 1800 kg police car at rest increases his velocity to 45 m/s in order to catch up to a speeding car. What is the police car’s change in momentum? Where did the momentum get transferred? G U E S

Change in Momentum #2 G U E S A 3 kg tennis ball travels east towards a wall at a speed of 10 m/s. The ball bounces off the wall and is now traveling 5 m/s west. What is the ball’s change in momentum? Where did the momentum get transferred? G U E S

Change in Momentum #3 G U E S A 75 kg quarterback running at 11m/s east gets tackled to a stop. What is the quarterback’s change in momentum? Where did the momentum get transferred? G U E S

Impulse-Momentum Practice Problem A 90 kg football player is moving at 7 m/s. Calculate the force required to stop him in 0.5 seconds. G U E S Find the change in momentum here: Find the force here:

Exit Slip List 3 safety features in cars which lengthen the time during a collision in order to decrease the maximum force during that collision.