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 st x 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? Mass Speed Force Temperature Distance Elephant

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 scalars vectors Magnitude (size) No direction Magnitude and direction temperaturemass 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 N4 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 1 st 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 2 nd law There is a mathematical relationship between the resultant force and acceleration. Resultant force (N) = mass (kg) x acceleration (m/s 2 ) F R = ma It’s physics, there’s always a mathematical relationship!

An example Resultant force = 100 – 60 = 40 N F R = ma 40 = 100a a = 0.4 m/s 2 Pushing force (100 N) Friction (60 N) Mass of Mr Porter and bike = 100 kg

Newton’s 3 rd law If 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 is a very weak force. The force of gravitational attraction between Mr Porter and his wife (when 1 metre apart) is only around 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 resistance Terminal 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/s 2 ) 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 distances Thinking 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) 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 kg and a velocity of 3 m/s. What is its momentum? Momentum = Mass x velocity = x 3 = 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/s 1000kg 2000kg Before After V m/s Combined mass = 3000 kg Momentum before = 1000x x0 = 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/s 7 m/s Because they are in opposite directions, we make one velocity negative 14kg v m/s Momentum before = 10 x x 7 = = -17 Momentum after = 14v

An even harder example! Momentum before = Momentum after -17 = 14v V = -17/14 = 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 m2.2 m 110 N ? N Anticlockwise momentclockwise moment=

Anticlockwise moment = clockwise moment ? X 1.2 = 110 x 2.2 ? X 1.2 = 242 ? = 242/1.2 ? = N pivot 1.2 m2.2 m 110 N ? N Anticlockwise momentclockwise 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 Meadow Lake Drive Houston Texas USA Earth Solar System

My address Meadow Lake Drive Houston Texas USA Earth Solar System Milky way Local group Universe

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)