Forces and motion

Speed

Speed = distance travelled

time taken

seconds

metres

Metres per second (m/s)

Speed

Speed = distance travelled

time taken

hours

kilometres

Kilometres per hour (km/h)

triangle

s tx

d

No movement

distance

time

Constant speed

distance

time

fast

slow

The gradient of the graph gives the

speed

Getting faster (accelerating)

distance

time

A car accelerating from stop and then hitting a wall

distance

time

Let’s try a simulation

Speed against time graphs

speed

time

No movement

speed

time

Constant speed

speed

time

fast

slow

Getting faster? (accelerating)

speed

time

Constant acceleration

Getting faster? (accelerating)

speed

time

a = v – u

t

(v= final speed, u = initial speed)

v

u

The gradient of this graph gives the acceleration

Getting faster? (accelerating)

speed

time

The area under the graph gives the distance travelled

A dog falling from a tall building (no air resistance)

speed

time

Area = height of building

Forces

• Remember a force is a push (or pull)

Forces

• Force is measured in Newtons

Forces

• There are many types of forces; electrostatic, magnetic, upthrust, friction, gravitational………

Which of the following is the odd one out?

MassSpeedForce

TemperatureDistanceElephant

Scalars and vectors

Scalars

Scalar quantities have a magnitude (size) only.

For example:

Temperature, mass, distance, speed, energy.

1 kg

Vectors

Vector quantities have a magnitude (size) and direction.

For example:

Force, acceleration, displacement, velocity, momentum.

10 N

Scalars and Vectors

scalarsvectors

Magnitude (size)

No direction

Magnitude and direction

temperature mass

speed

velocity

force

acceleration

Copy please!

Representing vectors

Vectors can be represented by arrows. The length of the arrow indicates the magnitude, and the direction the direction!

Adding vectors

When adding vectors (such as force or velocity) , it is important to remember they are vectors and their direction needs to be taken into account.

The result of adding two vectors is called the resultant.

Adding vectors

For example;

6 N 4 N 2 N

Resultant force

Copy please!

An interesting example

velocity

We have constant speed but changing velocity.

Of course a changing velocity means it must be accelerating! We’ll come back to this in year 12!

Friction opposes motion!

Newton’s 1st Law

If there is no resultant force acting on an object, it will move with constant velocity. (Note the constant velocity could be zero).

Does this make sense?

Newton’s second law

Newton’s second law concerns examples where there is a resultant force.

I thought of this law myself!

Newton’s 2nd law

There is a mathematical relationship between the resultant force and acceleration.

Resultant force (N) = mass (kg) x acceleration (m/s2)

FR = maIt’s physics,

there’s always a mathematical relationship!

An example

Resultant force = 100 – 60 = 40 N

FR = ma

40 = 100a

a = 0.4 m/s2

Pushing force (100 N)

Friction (60 N)

Mass of Mr Porter and bike = 100 kg

Newton’s 3rd lawIf a body A exerts a force on body B, body B will exert an equal but opposite force on body A.

Hand (body A) exerts force on table (body B)

Table (body B) exerts force on hand (body A)

Gravity

Gravity is a force between ALL objects!

Gravity

Gravity

Gravity is a very weak force.

The force of gravitational attraction between Mr Porter and his wife (when 1 metre apart) is only around 0.0000004 Newtons!

Gravity

The size of the force depends on the mass of the objects. The bigger they are, the bigger the force!

Small attractive force

Bigger attractive force

Gravity

The size of the force also depends on the distance between the objects.

Gravity

The force of gravity on something is called its weight. Because it is a force it is measured in Newtons.

Weight

Gravity

On the earth, Mr Porter’s weight is around 800 N.

800 N

I love physics!

Gravity

On the moon, his weight is around 130 N.

Why?

130 N

Mass

Mass is a measure of the amount of material an object is made of. It is measured in kilograms.

Mass

Mr Porter has a mass of around 77 kg. This means he is made of 77 kg of blood, bones, hair and poo!

77kg

Mass

On the moon, Mr Porter hasn’t changed (he’s still Mr Porter!). That means he still is made of 77 kg of blood, bones, hair and poo!

77kg

Mass and weight

Mass is a measure of the amount of material an object is made of. It is measured in kilograms.

Weight is the force of gravity on an object. It is measured in Newtons.

Calculating weight

To calculate the weight of an object you multiply the object’s mass by the gravitational field strength wherever you are.

Weight (N) = mass (kg) x gravitational field strength (N/kg)

Gravity = air resistanceTerminal velocity

gravity

As the dog falls faster and air resistance increases, eventually the air resistance becomes as big as (equal to) the force of gravity.

The dog stops getting faster (accelerating) and falls at constant velocity.

This velocity is called the terminal velocity.

Air resistance

Falling without air resistance

gravity

Without air resistance objects fall faster and faster and faster…….

They get faster by 10 m/s every second (10 m/s2)

This number is called “g”, the acceleration due to gravity.

Can you copy the words please?

Where did I come from?

Falling without air resistance?

distance

time

Falling without air resistance?

speed

time

Gradient = acceleration = 9.8 m.s-2

Falling with air resistance?

distance

time

Falling with air resistance?

speed

time

Terminal speed

Stopping distances

The distance a car takes to stop is called the stopping distance.

Two parts

The stopping distance can be thought of in two parts

Stopping distancesThinking distance is the distance traveled whilst the driver is thinking (related to the driver’s reaction time).

Thinking distance

This is affected by the mental state of the driver (and the speed of the car)

Braking distance

This is the distance traveled by the car once the brakes have been applied.

Braking distance

This affected by the speed and mass of the car

Braking distance

It is also affected by the road conditions

Braking distance

And by the condition of the car’s tyres.

Typical Stopping distances YouTube - Top Gear 13-5: RWD Braking Challenge

YouTube - Think! - Slow Down (Extended) (UK)

Momentum

• What makes an object hard to stop?

• Is it harder to stop a bullet, or a truck

travelling along the highway?

• Are they both as difficult to stop as each other?

Momentum

• Momentum is a useful quantity to consider when thinking about "unstoppability". It is also useful when considering collisions and explosions. It is defined as

Momentum (kgm/s) = Mass (kg) x Velocity (m/s)

p = mv

An easy example

• A lorry has a mass of 10 000 kg and a velocity of 3 m/s. What is its momentum?

Momentum = Mass x velocity

= 10 000 x 3

= 30 000 kgm/s

Law of conservation of momentum

• The law of conservation of linear momentum says that

“in an isolated system, momentum remains constant”.

We can use this to calculate what happens after a collision (and in fact during an “explosion”).

Conservation of momentum

• In a collision between two objects, momentum is conserved (total momentum stays the same). i.e.

Total momentum before the collision = Total momentum after

Momentum is not energy!

A harder example!

• A car of mass 1000 kg travelling at 5 m/s hits a stationary truck of mass 2000 kg. After the collision they stick together. What is their joint velocity after the collision?

A harder example!

5 m/s1000kg

2000kgBefore

After

V m/s

Combined mass = 3000 kg

Momentum before = 1000x5 + 2000x0 = 5000 kgm/s

Momentum after = 3000v

A harder example

The law of conservation of momentum tells us that momentum before equals momentum after, so

Momentum before = momentum after

5000 = 3000v

V = 5000/3000 = 1.67 m/s

Momentum is a vector

• Momentum is a vector, so if velocities are in opposite directions we must take this into account in our calculations

An even harder example!

Snoopy (mass 10kg) running at 4.5 m/s jumps onto a skateboard of mass 4 kg travelling in the opposite direction at 7 m/s. What is the velocity of Snoopy and skateboard after Snoopy has jumped on?

I love physics

An even harder example!

10kg

4kg-4.5 m/s7 m/s

Because they are in opposite directions, we make one velocity negative

14kg

v m/s

Momentum before = 10 x -4.5 + 4 x 7 = -45 + 28 = -17

Momentum after = 14v

An even harder example!

Momentum before = Momentum after

-17 = 14v

V = -17/14 = -1.21 m/s

The negative sign tells us that the velocity is from left to right (we choose this as our “negative direction”)

Impulse

Ft = mv – mu

The quantity Ft is called the impulse, and of course mv – mu is the change in momentum (v =

final velocity and u = initial velocity)

Impulse = Change in momentum

Units

Impulse is measured in Ns

or kgm/s

Impulse

Note; For a ball bouncing off a wall, don’t forget the initial and final velocity are in

different directions, so you will have to make one of them negative.

In this case mv – mu = 5m - -3m = 8m

5 m/s

-3 m/s

Example

• Jack punches Chris in the face. If Chris’s head (mass 10 kg) was initially at rest and moves away from Jack’s fist at 3 m/s, and the fist was in contact with the face for 0.2 seconds, what was the force of the punch?

• m = 10kg, t = 0.2, u = 0, v = 3• Ft = mv – mu• 0.2F = 10x3 – 10x0• 0.2F = 30• F = 30/0.2 = 150N

The turning effect of a force depends on two things;

The size of the force

Obviously!

The turning effect of a force depends on two things;

The distance from the pivot (axis of rotation)

Not quite so

obvious!

Axis of rotation

Turning effect of a force – moment of a force

Moment (Nm) = Force (N) x distance from pivot (m)

Note the unit is Nm, not N/m!

A simple example!

nut

spanner (wrench)

50 N

0.15 m

Moment = Force x distance from pivot

Moment = 50 N x 0.15 m

Moment = 7.5 Nm

If the see-saw balances, the turning effect anticlockwise must equal the

turning effect clockwise

pivot

1.2 m 2.2 m

110 N? N

Anticlockwise moment clockwise moment=

Anticlockwise moment = clockwise moment? X 1.2 = 110 x 2.2

? X 1.2 = 242? = 242/1.2? = 201.7 N

pivot

1.2 m 2.2 m

110 N? N

Anticlockwise moment clockwise moment=

Principal of Moments

Rotational equilibrium is when the sum of the anticlockwise moments equal the sum of the clockwise moments.

YouTube - Alan Partridge's Apache office

COPY PLEASE!

Centre of gravity

The centre of gravity of an object is the point where the object’s weight seems to act.

I think he wants you

to copy this

Complex shapes

How do you find the centre of

gravity of complex shapes?

Complex shape man

Finding the centre of mass

i. Place a compass or needle through any part of the card.

ii. Make sure that the card “hangs loose”.iii. Hang a plumb line on the needle.iv. After it has stopped moving, carefully draw a

line where the plumb line is.v. Place the needle in any other part of the card.vi. Repeat steps ii to iv.vii. Where the two drawn lines cross is where the

centre of mass is.viii. Physics is the most interesting subject.

Hooke’s law

Force (N)

Extension (cm)

Elastic limit

The extension of a spring is proportional to the force applied (until the elastic limit is reached)

Steel, glass and wood!

Force

Extention

Even though they don’t stretch much, they obey Hooke’s law for the first part of the graph

Rubber

Force

Extension

The Solar System

Main points

• Know the names of the planets!• My very easy method just speeds up naming

planets• They orbit in ellipses with the sun at one foci• Inner planets small and rocky• Outer planets large and mainly gas• Asteroid belt between Mars and Jupiter

• Giant dirty snow balls (ice and dust) (diameter 100m - 50 km?)

• Very elliptical orbits

• Short period (T < 200 yrs) and long period (could be thousands of years)

• Oort cloud

• Tail(s) always point away from the sun

• Evaporate as they get closer to the sun

Comets

Orbital motion

• Space objects

• use the relationship between orbital speed, orbital radius and time period

• orbital speed = 2× π ×orbital radius/(time period)

• v = 2× π × r

T

My address

11507 Meadow Lake Drive

Houston

Texas 77077

USA

Earth

Solar System

My address

11507 Meadow Lake DriveHoustonTexas 77077USAEarthSolar SystemMilky wayLocal groupUniverse

Galaxies

• A large collection of stars held together by their mutual gravity.

• Dwarf galaxies might have only a few million stars, many galaxies have hundreds of billions.

• The Universe has around 100 billion galaxies

Orbital speed

• Speed = distance/time

• v = (2πr)/T

• r = radius of orbit

• T = Period (time for one orbit)