How can knowledge of forces and momentum be used to predict the behaviour of interacting bodies?

Understandings

• that linear momentum as given by p = mv remains constant unless the system is acted upon by a resultant external force
• that a resultant external force applied to a system constitutes an impulse J as given by J = Ft where F is the average resultant force and t is the time of contact
• that the applied external impulse equals the change in momentum of the system
• that Newton's second law in the form F = ma assumes mass is constant whereas F=pt allows for situations where mass is changing
• the elastic and inelastic collisions of two bodies
• explosions
• energy considerations in elastic collisions, inelastic collisions, and explosions

Guidance:

• The use of simultaneous equations involving conservation of momentum and energy in collisions is not required.
• A quantitative approach to collisions and explosions is for one-dimensional situations for standard level students and for two-dimensional situations for higher level students.

Demo - Momentum & Collisions

Task 4.1. Collision Lab

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In 4 groups, work on the following 4 scenarios

Which quantities remains constant in all four experiments?

Momentum

"Unstoppability"

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Momentum (kg.m.s^-1) = Mass (kg) x Velocity (m.s^-1)

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Momentum is a vector quantity

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Law of conservation of momentum

The total momentum of an isolated system remains constant.

Isolated here means no external forces act on the system

Total initial momentum = total final momentum

Elastic Collision

An elastic collision is when both momentum and kinetic energy is conserved in a collision.

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There are very few collisions in real life where kinetic energy is not lost as sound or heat.

Inelastic Collision

An inelastic collision is when kinetic energy is lost during a collision and converted into other types of energy.

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Momentum is conserved in all collisions, assuming no external forces apply; however, kinetic energy is not.

When bodies stick together after a collision, it is totally inelastic.

Max possible E_k is lost.

Practice Questions Slides 1-4

Why doesn’t the egg break?

Rewrite Newton’s Second Law of Motion terms of momentum to find an expression that relates the net force and the momentum.

Impulse

Impulse (J) is the product of average force and the time for which the force acts.

J = F Δt = Δp

An impulse on an isolated objects results in a change in momentum, which is numerically equal to the impulse.

u

How does a jet engine produce thrust?

The jet engine sucks in air (at about the speed that the plane is flying through the air), heats it up, and expels it at a greater velocity. The momentum of the air changes since its velocity does, and hence an impulse has been imparted to it by the engine. The engine feels an equal and opposite impulse. Hence the engine creates a thrust.

In the combustion chamber the gas particles have random directions. The shape of the nozzle is such that the particles in the sphere of combustion are deflected in such a way that they all come out antiparallel to the rocket. This maximizes the impulse on the gases. The rocket feels an equal and opposite (maximized) impulse, creating a maximized thrust.

What is the purpose of the rocket nozzle?

Find an expression that relates the kinetic energy and momentum.

Practice Questions Slides 5-8

Understandings

• that linear momentum as given by p = mv remains constant unless the system is acted upon by a resultant external force
• that a resultant external force applied to a system constitutes an impulse J as given by J = Ft where F is the average resultant force and t is the time of contact
• that the applied external impulse equals the change in momentum of the system
• that Newton's second law in the form F = ma assumes mass is constant whereas F=pt allows for situations where mass is changing
• the elastic and inelastic collisions of two bodies
• explosions
• energy considerations in elastic collisions, inelastic collisions, and explosions

If momentum must be conserved, how can an astronaut move in space?

Grade Gorilla Practice Set

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Hodder Practice Set

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Paper Plainz (Old Syllabus)

1. Try first

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• Then ask a buddy

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• Then look at the Answer (not the video solution) to see if you can work it out

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• Then look at the video solution

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• Then ask your teacher