MomentumLearning Intention:• Understand and be able to support the claim

of conservation of momentum in a system

Learning Intention:• Understand and be able to support the claim of

conservation of momentum in a systemSuccess Criteria: I can ….

– Define momentum– Solve for momentum, mass, or velocity– Compare to objects to determine which would have

more momentum– Derive the impulse equation – Explain how momentum is conserved in both elastic

and inelastic collisions using calculations to support my explanation

Momentum• Inertia in motion• momentum (p) is equal to mass x velocity

• units for momentum: kg· m/s

Which will have more momentum, a semi moving at 70 km/h or a Prius moving at 70 km/h?

Why?

• Will a large truck ALWAYS have more momentum than a Pruis?

• NO!!! If the truck is at rest, it has no momentum.

Problem Solving Practice!

Momentum practice: • A child on a sled is moving at 5 m/s. The mass of

the child and the sled is 90 kg. What is the momentum?

Given Equation Substitution Answer90kg p = mv p = (90kg)(5m/s) p = 450

kg·m/s

5m/s

Journal: Your Turn

A 70 kg skateboarder launches off of a ramp at a velocity of 14 m/s. What is the skateboarder’s momentum at that instant?

• p = (70kg)(14m/s) = 980 kg·m/s

A 725 kg car is moving at 115km/h. What is it’s momentum in kgm/s? (watch your units)

115 km/h (1000 m/km)( 1 hr/ 60 min) (1 min/ 60 sec) = 31.9 m/s

• p = mv• p = (725kg) (31.9 m/s) = 23,172.5 kg·m/s

Journal: When does momentum of an object change????

Use the equation for momentum as your reference!!!!

Momentum of an object changes if:

• mass changes• velocity changes • or both change!!

When do velocity changes occur???

Impulse: how long a force acts on an object

• impulse = FΔt

Change in momentum is called impulse.

or Ft = ΔmvFt = Δp

Knowing that

a= F/m a= v/t

Journal: Derive the impulse equation, Ft = Δmv,

from the two equations for acceleration. Show your work.

Increasing Momentum of an object:

apply a large force for as long as possible

Ft = Δp

Decrease momentum:

• Extending impact time reduces the force of the impact.

• Example: catching a baseball and pulling your arm back to slow the catch

Bouncing

• Impulses are great because the impulse required to both “stop” the object and then “throw it back again”

Law of Conservation of Momentum

• In the absence of an external force, the momentum of a system remains unchanged.

• initial momentum = final momentum

Example: Two cars colliding• The net momentum of the system is the

combined momentum of the cars colliding, so before and after the collision the total momentum of the system is the same.

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Law of Conservation of Momentum

Collisions:

• Elastic• Inelastic

Elastic: when objects collide without being deformed or generating heat

• bounce perfectly• Momentum is reversed• Kinetic Energy is conserved

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Example: A 300 kg bumper car travelling at 10 m/s collides with a 400 kg bumper car that is stopped. After the elastic collision, the 300 kg car is travelling in the opposite direction at 1.43 m/s. What is the resulting velocity of the 400 kg car after this collision?

[ (m1)(v1) + (m2)(v2) ] initial = [ (m1)(v1) + (m2)(v2) ] final

[ (300kg)(10 m/s) + (400kg)(0 m/s)] = [ (300kg)(-1.43 m/s) + (400 kg)v2]

• 3000 = - 429 + 400v2

• 3429 = 400 v2

• 3429/ 400 = v2

• 8.57 = v2

Inelastic : when objects collide and are deformed

• Kinetic Energy is NOT conserved, rather it is transferred into thermal or potential energy.

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Practice Problem

• A car weighing 200 kg and travelling at 25 m/s crashes and sticks to a 1500 kg car that was travelling at 20 m/s. What is the final velocity of the joined vehicles?

= • (2000)(25) + (1500)(20) = ( 2000+1500) Vf

• Vf = 22.86

For both Elastic and Inelastic collisions, TOTAL ENERGY IS CONSERVED!!!!

Practice Problem Solving