Momentum

Momentum Momentum = mass x velocity Momentum is a measure of how hard it is to stop something. Momentum = mass x velocity Which has most momentum? v v

Which has most momentum? v 2v

Momentum Conservation The total momentum of a system is constant unless there is an external …. FORCE Δp = 0 if F = 0

Momentum is a vector quantity

Total initial momentum = mv + (-mv) = 0 Total final momentum = 0

Kinetic energy is a scalar. Bull’s Total Initial KE = Bull’s Total Final KE = 0 Kinetic energy is converted to heat

Total initial momentum = 0 Total final momentum = Mv + (-mV) = 0

Impulse Describe how you catch an egg to minimise the chance of it breaking. The damage to the egg (force on it) doesn’t just depend on how fast it’s travelling…. but also how fast it stops.

The momentum change for the egg does not depend on how you catch it ( ) A long stopping time causes a small force or

Summary of Key Ideas Momentum is always conserved if there are no outside forces. (the momentum of a sliding box decreases because friction is an outside force) Kinetic Energy is not usually conserved in most interactions KE is converted to HEAT

Centre of Mass Centre of mass This is the point where you can assume all the weight force acts through. Centre of mass

The centre of mass is normally above the support Where is the center of mass?

Will He Balance?

Where is her centre of mass?

mc x dc= mAC x dAC clockwise torque = anticlockwise torque (mc g) x dc= (mAC g) x dAC mc x dc= mAC x dAC

Center of Mass Where is the center of mass? 3 x d = 2 x (2 – d) 3 kg 2 kg 2 m d 2 - d Where is the center of mass? 3 x d = 2 x (2 – d) d = 4/5 =0.8 m

Center of Mass x - d d Where is the center of mass? m1 x d = m2 x (x – d)

If momentum is conserved, the centre of mass has constant velocity

Collisions in Two Dimensions Inelastic Collision

Collisions in Two Dimensions Inelastic Collision

Adding Momentum Vectors Total final momentum BEFORE pB after pA = 3 kgms-1 pA before pB = 3 kgms-1

Collisions in Two Dimensions Elastic Collision

Vector Triangle Method

Total final momentum pB after Same as initial momentum pA = 3 kgms-1 Σp = 3 kgms-1 pA after

Total final momentum Same as initial momentum pA = 3 kgms-1 pB after pA after

pi = 6 kgms-1 Σp = 6 kgms-1 pX = 3 pf = 5 kgms-1 pY = 4 370 370 pY = 4

Components Method

What is the momentum of the red ball after the collision? pX = 6 pA = 10 kgms-1 pY = 8 pi = 12 kgms-1 Σp = 12 kgms-1 370 What is the momentum of the red ball after the collision? pY = 8 P B= 10 kgms-1 pX = 6

Momentum Change Find the momentum change of the ball Recall Δp = pf-pi or Δp = pf + (-pi) pf Δp pi Check momentum change of the ball is in the same direction as the force

Momentum Change Δp Find the momentum change of the ball Recall Δp = pf-pi or Δp = pf + (-pi) pf -pi pi pf Δp Check momentum change of the ball is in the same direction as the force

Force of racket on ball Force of ball on racket

Find the momentum change of the 300g soccer ball. Find the average force on the ball if she was in contact for 0.10s 15 ms-1 20 ms-1

Circular Motion

A car goes around a circle as shown. What direction is the net force? B A C D

The car hits an icy patch as shown. What direction will it slide? B C

Objects moving in a circle are always accelerating towards the centre. Centripetal acceleration is…. This requires a centripetal force.

We will look at circular motion with two forces

Don’t watch this if you’re a cat lover……..

A bird swings in a horizontal circle on a string. What are the individual forces? What is the total force? What direction is the acceleration? What happens as it speeds up?

Why do motorcyclists lean when cornering?

Consider the forces Straight line

Consider the forces Cornering upright Centripetal force Which way is he turning? What will happen? (consider Torque about center of mass)

Consider the forces Cornering leaning Centripetal force What will happen? (consider Torque about center of mass) clockwise torque = anticlockwise torque

Vertical Circular Motion

Why doesn’t he fall at the highest point?

What happens to the penguin if the lift is stationary? Why? acceleration = 0 Gravity pulls the penguin down, the elevator produces an equal and opposite force up

What happens to the penguin if the lift is accelerates up at 10ms-2? Why? acceleration Gravity pulls it down, the elevator produces a force up that is twice its weight.

What happens to the penguin if the lift is accelerates down at 10ms-2? Why? acceleration The penguin is in freefall. There is no upward force on the penguin from the elevator. When we feel “weight”, it is the upward force from the floor. The penguin thinks she is weightless

What happens to the penguin if the lift is accelerates down at 15ms-2? Why? acceleration The penguin is stuck to the ceiling of the elevator. She is accelerating at more than 10 ms-2, so an extra force is needed. (this is from the elevator floor)

Roller Coaster Why does the car not fall? It is falling!! But it’s also moving sideways. If the centripetal acceleration is greater than 10 ms-2 the car will stay on the track This is like being in an elevator accelerating down at › 10ms-2. You will be on the ceiling.

Gravity and Satellites How are you able to watch the All Blacks on TV when they are playing in France? How are you able to have a cellphone conversation with your friend in the USA?

International Space Station

Other Uses of Satellites Tracking endangered animals

Satellite Weather Forecasting

Satellites Satellites are above the atmosphere (no air resistance), so the only force on them is…………. Gravity

Why don’t satellites fall? link to Newton's mountain Satellites are falling, but they are moving sideways, They fall at the same rate that the earth curves away under them

Weightlessness. You don’t feel the gravity force on your body, you feel the support force pushing up. You can feel weightless for two reasons. 1: You are weightless in outer space. There is no gravity force so there is no reaction force

You feel weightless in orbit You feel “weight” due to the support force on you. The astronaut and their satellite are in free fall. There is no support force acting on them

Newton’s Law of Gravitation

Can a satellite have any speed? At a certain height, a satellite must have one particular speed. Satellite Speed:

Period of a satellite The period of a satellite orbiting around the earth only depends on the altitude.

Notice the mass of the satellite doesn’t appear in the equation. All masses have the same acceleration due to gravity:

A geostationary satellite has a period of 24 hours It must have the earth’s centre as its orbital centre It must be above the equator

Geostationary Satellites AUS NZ

AUS NZ

AUS NZ

AUS NZ

AUS NZ

AUS NZ

AUS NZ