Momentum & Impulse

Momentum The linear momentum of an object is defined as: Momentum = mass x velocity p = m x ѵ ‘p’ is used because the word "impetus" (formally in place of "momentum“) comes from the latin, "petere," to go towards or rush upon...so therefore we get "p"

What are the units of momentum? m x ѵ = So – the SI unit for momentum is defined as:

So let’s think about momentum… Momentum is a measure of mass in motion. So – think about: car traveling at 55 mph vs. 18-wheeler at 55 mph Which would you expect to have more momentum?

-Deyjah carries her violin to practice with a velocity of.6m/s. If the mass of Deyjah & her instrument combined is 66 kg, find her momentum.

-Peter has a mass of 72 kg and is riding his 25.9 kg dirt bike with a velocity of 4.5 m/s to the northwest. What is Peter’s momentum? What is the momentum of the bike? What is the momentum of the two together?

Before we define ‘impulse,’ I would like to work our way to it. Impulse is defined as the change in momentum. Let’s reason why…

p = m x ѵ So – how can we express change in momentum? Δp = mѵ f – mѵ i rewrite as: From kinematics, what equation do we know that has the expression (ѵ f – ѵ i )? Derive (ѵ f – ѵ i ) by itself to get: Substitute in for (ѵ f – ѵ i ) What equation = m x a? Substitute in… Your final equation is:

Impulse = Force x change in time I = FΔt The SI units of Impulse are: (Are these the same units of momentum?) Moreover, if Impulse = FΔt, then: Impulse = This is the ‘Impulse – Momentum Theorem’

Let’s discuss the idea of impulse… If impulse is defined as the change in momentum, then take an object, like an egg, that will: - have a mass of.10 kg -experience a change in velocity from 10 m/s to zero m/s. In terms of the definition of change in momentum, From the same height, compare the impulses of: Egg falling on the pavement vs. Egg falling on a pillow

The impulses are the same! So – why does one egg break and the other stay intact? What is the true definition of impulse? So, how are Force and Δt related? Hmmmmm…. So – if broken egg and whole egg experienced the same impulse, what was the difference?

How does impulse differ from force? 1. Force produces momentum; impulse produces acceleration. 2. Force is usually larger than momentum. 3. Force produces acceleration; impulse produces change in momentum. 4. Momentum is larger than force. 5. Force produces acceleration; impulse produces momentum. 6. None of these

- A.40 kg soccer ball approaches Jennifer with a velocity of 18 m/s. Jennifer strikes the ball and causes it to move in the opposite direction with a velocity of 22 m/s. What is the impulse delivered by Jennifer?

-Noah throws a.50 kg football with a velocity of 15 m/s to the right. If Bryan catches the ball and brings it to rest in.020 s, what is the force exerted on Bryan?

Stopping Distance - Riley slows her 2250 kg car to let a momma duck and her ducklings cross the street. If Riley slows from 20.0 m/s to 5.0 m/s how long does it take her car to decelerate if the force on the car is 8450 N in the opposite direction?

- Patrick drives his 3250 kg SUV to a stop from 20.0 m/s by a 6250 N braking force. What is his vehicle’s velocity after 1.5 s? How far does Patrick travel in 1.5 s? How long does it take him to come to a complete stop?

Conservation of Momentum Momentum is always conserved in collisions (and also for objects pushing away from each other) m 1 ѵ 1 + m 2 ѵ 2 = m 1 ѵ 1 + m 2 ѵ 2 initial final

- Sam and Jose are standing face-to-face on a frozen lake. Jose is carrying an extra 50kg on his back to give him a total mass of 125 kg. Sam has a mass of 75kg. If Sam pushes off Jose at 2.3m/s, what is Jose’s velocity?

- Dillon counts the fish that he caught while sitting in his rowboat next to the dock. If the boat has a mass of 45 kg and Dillon has a mass of 57 kg, What is the final velocity of the boat if Dillon steps on to the dock at 3.6 m/s?

-Andrew is standing on his 2.3 kg skateboard when he sees Priscila drive by (she sees Andrew and speeds up! Haha). Andrew attempts to throw his 7.7 kg backpack at her car with a velocity of 2.9 m/s. If Andrew and his skateboard move in the opposite direction at 2.5 m/s, find his mass.

- Yarelie (44 kg) is buckling on her rollerblades, when her brother, Jesus, yells, “think fast!” He throws a 15 kg exercise ball at her with a speed of 4.6 m/s, trying to knock her over. Much to her brother’s surprise, Yarelie catches the ball. Describe and calculate the motion she experiences after catching the ball.

Collisions There are 2 types of collisions: Elastic – These collisions are characterized by objects hitting and bouncing apart. Inelastic – Think of these as ‘not’ bouncing. In fact, inelastic collisions occur when objects collide and stick together.

Elasticvs. Inelastic 2 objects collide and bounce2 objects collide and stick final velocities are in different move together as one mass directionsmomentum is conserved kinetic energy is conservedkinetic energy is not conserved

Elastic Collisions Momentum is conserved m 1 ѵ 1i + m 2 ѵ 2i = m 1 ѵ 1f + m 2 ѵ 2f initial final Kinetic Energy is conserved ½ m 1 ѵ 1i 2 + ½ m 2 ѵ 2i 2 = ½ m 1 ѵ 1f 2 + ½ m 2 ѵ 2f 2

Technically – most collisions are neither perfectly elastic nor perfectly inelastic… -most objects do not collide and stick together -even in elastic collisions, such as a golf club hitting a golf ball, there is some amount of deformation of shape. This leads to kinetic energy loss in the form of elastic potential energy.

- You might think that pool balls hitting each other is a good example of elastic collisions with little or no kinetic energy loss. However, think about the sound pool balls make when they hit each other – this is kinetic energy lost as ‘sound energy.’

- A 4.0 kg bowling ball sliding to the right at 8.0 m/s has an elastic head-on collision with another 4.0 kg bowling ball initially at rest. The first ball stops after the collision. - Find the velocity of the second ball after the collision.

- Severin paddles a canoe (106 kg together) to the left at 12 m/s. He hits Bailey in a raft (55 kg together) traveling to the right at 6.0 m/s. After the collision, Bailey travels to the left at 18 m/s. - Find the velocity of Severin after the collision

Perfectly Inelastic Collisions -2 objects become one after colliding Momentum is conserved m 1 ѵ 1i + m 2 ѵ 2i = (m 1 + m 2 )ѵ f initial final But kinetic energy is not

- Billy drives his new truck (mass 1575 kg) right into Mr. Engel’s bumper while he is sitting at a traffic light in his car (mass 900kg). If Billy’s initial speed is 22m/s to the north before the collision, what is the velocity of the entangled mass after the collision? - How much kinetic energy is lost?

- During practice, Yazmin kicks a.40 kg soccer ball with a velocity of 8.5 m/s into a.15 kg bucket lying on its side. The bucket and ball move together after the collision. What is the final velocity of the final mass? - What is the decrease in kinetic energy after the collision?