# Physics Paper 2 AQA NEW SPEC (Incomplete)

## What's the difference between a scalar and a vecto

• Scalar quantities have magnitude only. E.g.  speed, distance, mass, temperature, time etc.
• Vector quantities have magnitude and an associated direction. E.g. force, velocity, displacement, acceleration, momentum etc.
• A vector quantity may be represented by an arrow.
• The length of the arrow represents the magnitude, and the direction of the arrow the direction of the vector quantity.
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## What's the difference between contact and non-cont

• A force is a push or pull that acts on an object due to the interaction with another object. ]
• All forces between objects are either:
• contact forces – the objects are physically touching. Examples of contact forces include friction, air resistance, tension and normal contact force.
• non-contact forces – the objects are physically separated. Examples of non-contact forces are gravitational force, electrostatic force and magnetic force.
• Force is a vector quantity.
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## What happens when two objects interact?

• When two objects interact, there is a force produced on both objects. An interaction pair is a pair of forces that are equal and opposite and act on two interacting objects. (Newton's third law). E.g.:
• The Sun and the Earth are attracted to each other by the gravitational force. This is a non-contact force. An equal but opposite force of attraction is felt by both the Sun and the Earth.
• A chair exerts a force on the ground, whilst the ground pushes back at the chair with the same force (the normal contact force). Equal but opposite forces are felt by both the chair and the ground.
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## What is gravitational force?

• Gravity attracts all masses, but you only notice it when one of the masses is really big, e.g. a planet.
• Anything near a planet or a star is attracted to it very strongly.
• This has two important effects:
• On the surface of a planet, it makes all things fall towards the ground.
• It gives everything a weight.
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## What is the difference between mass and weight?

• Mass is the amount of material a substance is made up of. For any given object this will have the same value anywhere in the universe.
• Weight is the force acting on an object due to gravity. Its a force measured in N. You can think of the force as acting from a signle point on the object, called its centre of mass (a point at which you assume the whole mass is concentrated). For a uniform object (one that's the same density throughout and is a regular shape), this would be at the centre of the object.
• The force of gravity close to the Earth is due to the gravitational field around the Earth. Gravitational field strength varies with location. It's stronger the closer you are to the mass causing the field, and stronger for larger masses.
• The weight of an object depends on the gravitational field strength at the point where the object is. The weight changes with location. Weight is measured using a calibrated spring balance (newtonmeter).
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## EQUATION - Weight, Mass and GFS.

weight = mass × gravitational field strength

W = m g

• weight, W, in newtons, N
• mass, m, in kilograms, kg
• gravitational field strength, g, in newtons per kilogram, N/kg (In any calculation the value of the gravitational field strength (g) will be given.)

The weight of an object and the mass of an object are directly proportional. On Earth, GFS = 9.8 N/kg.

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## What is a resultant force?

• A number of forces acting on an object may be replaced by a single force that has the same effect as all the original forces acting together.
• This single force is called the resultant force.
•  A single force can be resolved into two components acting at right angles to each other. The two component forces together have the same effect as the single force.
• If the forces all act along the same line (they're all parallel), the overall effect is found by adding those going in the same direction and subtracting any going in opposite directions.
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## What do free body diagrams show?

• You need to be able to describe all the forces acting on an isolated object or a system - i.e. every force acting on the object or system but none of the forces the object or system exerts on the rest of the world.
• For example, a skydiver's weight acts on him, pulling him towards the ground, and drag (air resistance) also acts on him, in the opposite direction to his motion. This can be shown on a free body diagram.
• The sizes of the arrows show the relative magnitudes of the forces and the directions show the directions of the forces acting on the object.
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## If a resultant force moves on an object, what happ

• When a force causes an object to move through a distance work is done on the object.
• To make something move (or keep it moving if there are frictional forces), a force must be applied.
• The thing applying the force needs a source of energy (like fuel or food).
• The force does 'work' to moe the object and energy is transferred from one store to another.
• Whether energy is transferred 'usefully' (e.g. lifting a load) or is 'wasted' you can say that work is done. Work done is the same as energy transferred.
• When you push something along a rough surface (like a carpet) you are doing work against friction forces. Energy is being transferred to the kinetic energy store of the object because it starts moving but some is also being transferred to thermal energy stores due to the friction. This causes the overall temperature of the object to increase. (Like rubbing your hands together to warm them up).
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## EQUATION - Work done, force, distance.

work done = force × distance moved along the line of action of the force

W = F s

• work done, W, in joules, J
• force, F, in newtons, N
• distance, s, in metres, m

One joule of work is done when a force of one newton causes a displacement of one metre.

1 joule = 1 newton-metre

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## How do you use scale drawing to find resultant for

• Draw all the forces acting on an object, to scale, tip-to-tail.
• Then, draw a straight line from the start of the first force to the end of the last force - this is the resultant force.
• Measure the length of the resultant force on the diagram to find the magnitude and the angle to  find the direction of the force.
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## What happens if an object is in equilibrium?

• If all of the forces acting on an object combine to give a resultant force of 0, the object is at equilbrium.
• On a scale diagram, this means that the tip of the last force you draw should end where the tail of the first force you drew begins.
• You might be given forces acting on an object and told to find a missing force, given that the object is in equilibrium. To do this, draw out the forces you do know (to scale and tip-to-tail), join the end of the last force to the start of the first force.
• The line is the missing force so you can measure its size and direction.
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## How can you split a force into compounds?

• Not all forces act horizontally or vertically - some act at angles.
• To make these easier to deal with, they can be split into two components at right angles to each other (usually horizontal and vertical).
• Acting together, these components have the same effect as the single force.
• You can resolve a force (split it into components) by drawing it on a scale grid.
• 1 cm  =  1 N.
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## Stretching, compressing or bending transfers energ

• When you apply a force to an object, you may cause it to stretch, compress or bend.
• To do this, you need more than one force acting on the object - otherwise the object would simply move in the direction of the applied force, instead of changing the shape.
• Work is done when a force stretches or compresses an object and causes energy to be transferred to the elastic potential energy store of the object.
• If it is elastically deformed, all this energy is transferred to the object's elastic potential energy store.
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## What is directly proportional in elasticity?

• The extension of an elastic object, such as a spring, is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.
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## What is the difference between elastic and inelast

Elastic deformation:

• An object has been elastically deformed if it can go back to its original shape and length after the force has been removed.
• Objects that can be elastically deformed are called elastic objects (e.g. a spring).

Inelastic deformation:

• An object has been inelastically deformed if it doesn't return to its original shape and length after the force has been removed.
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## EQUATION - Force, extension, spring constant

force  = spring constant  × extension

F = k e

• force, F, in newtons, N
• spring constant, k, in newtons per metre, N/m
• extension, e, in metres, m
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## Force, extension and spring constant

• This relationship also applies to the compression of an elastic object, where ‘e’ would be the compression of the object.
• A force that stretches (or compresses) a spring does work and elastic potential energy is stored in the spring.
• Provided the spring is not inelastically deformed, the work done on the spring and the elastic potential energy stored are equal.
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## What is extension directly proportional to?

• The extension of a stretch spring (or certain other elastic objects) is directly proportional to the load of force applied.
• The spring constant, k, depends on the material you are stretching - a stiffer spring has a greater spring constant.
• The equation also works for compression (where e is just the difference between the natural and compressed lengths - the compression.
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## What is the limit of proportionality?

• There's a limit to the amount of force you can apply to an object for the extension to keep on increasing proportionally.
• A graph showing force against extension for an elastic object has a maximum force above which the graph curves, showing that the extension is no longer proportional to the force.
• This is known as the limit of proportionality.
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## REQUIRED PRACTICAL - Force and extension

• Measure the natural length of the spring (when no load is added) with a ruler clamped to the stand. Make sure you take the reading at eye level and add a marker to the bottom of the spring to make your reading more accurate.
• Add a mass to to spring and allow the spring to come to rest. Record the mass and measure the new length of the spring. The extension is the change in length.
• Repeat this process until you have enough measurements.
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## REQUIRED PRACTICAL - Pilot experiment

• To check if your masses are an appropriate size for your investigation:
• Using an identical spring to the one you'll be testing, load it with masses one at a time to a total of five. Measure the extension each time you add another mass.
• Work out the increase in the extension of the spring for each of your masses. If any of them cause a bigger increase in extension than the previous masses, you've gone past the spring's limit of proportionality. If this happens, you'll need to use smaller masses, or else you won't get enough measurements for you graph.
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## REQUIRED PRACTICAL - Check elastic and inelastic

• To check whether the deformation is elastic or inelastic, you can remove each mass temporarily and check to see if the spring has gone back to its previous extension.
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## REQUIRED PRACTICAL - Results

• Once you've collected your results, plot it on a force-extension graph. It will only start to curve if you've exceeded the limit of proportionality.
• When the line of best fit is a straight line, it means there is a linear relationship between the force and extension (directly proportional). F = ke, so the gradient of the straight line is equal to k, the spring constant.
• When the line begins to bend, the relationship is now non-linear between the force and extension - the spring stretches more for each unit increase in force.
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## EQUATION - Elasticity.

elastic potential energy  = 0.5  × spring constant  × (extension)2

Ee = 1 2 k e2

• Elastic potential energy, E, is measured in J.
• Spring constant, k, is measured in N/m.
• Extension, e, is measured in m.
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## Elasticity equation...

• You only use the formula if the spring is not stretched past its limit of proportionality, work done can also be found through this.
• For elastic deformation, this formula can be used to calculate the energy stored in a spring's elastic potential energy store.
• It's also the energy transferred to the spring as it's deformed (or transferred by the spring as it returns to its original shape).
• The energy in the elastic potential energy store of a spring is equal to the area under the force-extension graph up to that point.
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## What may cause an object to rotate?

• A force or a system of forces may cause an object to rotate.
• The turning effect of a force is called the moment of the force.
• If the total anticlockwise moment equals the clockwise moment about a pivot, the object is balanced and won't turn.
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## Spanners and moments....

• The force on the spanner causes a turning effect or moment on the nut (which acts as a pivot). A larger force or a longer distance (spanner) would mean a larger moment.
• To get the maximum moment (or turning effect) you need to push at right angles (perpendicular) to the spanner. Pushing at any other angle means a smaller distance, so a smaller moment.
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## EQUATION - Moments...

moment of a force = force  × distance

M = F d

• moment of a force, M, in newton-metres, Nm
• force, F, in newtons, N
• distance, d, is the perpendicular distance from the pivot to the line of action of the force, in metres, m.
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## What do levers do?

• Levers increase the distance from the pivot at which the force is applied. SInce M = fd this means less force is needed to get the same moment.
• This means levers make it easier to do work, e.g. lift a load or turn a nut.
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## What do gears transmit?

• Gears are circular disks with 'teeth' around their edges.
• Their teeths interlock so that turning in one direction causes another to turn in the opposite direction.
• They are used to transmit the rotational effect of a force from one place to another.
• Different sized gears can be used to change the moment of the force. A force transmitted to a larger gear will cause a bigger moment, as the distance to the pivot is greater.
• The larger gear will turn slower than the smaller gear.
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## What can be used to transmit rotational effects?

A simple lever and a simple gear system can both be used to transmit the rotational effects of forces.

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## What is pressure?

• Fluids are substances that can 'flow' because their particles are able to move around.
• As these particles move around, they collide with surfaces and other particles.
• Particles are light, but they can still have a mass and exert a force on the object they collide with. Pressure is the force per unit area, so this means the particles exert a pressure.
• The pressure of a fluid means a force is exerted normal (at right angles) to any surface in contact with the liquid.
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## EQUATION - Pressure

pressure = force normal to a surface / area of that surface

p = f / a

• pressure, p, in pascals, Pa
• force, F, in newtons, N
• area, A, in metres squared, m2
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## Pressure in a liquid...

• Density is a measure of the 'compactness' of a substance, i.e. how close together the particles in a substance are. For a given liquid, the density is uniform (the same everywhere) and it doesn't vary with shape or size. The density of a gas can vary.
• The more dense a given liquid is, the more particles is has in a certain space. This means there are more particles that are able to collide soo the pressure is higher.
• As the depth of the liquid increases, the number of particles above that point increases. The weight of these particles adds to the pressure felt at that point, so liquid pressure increases with depth.
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## EQUATION - Pressure in a liquid.

pressure = height of the column × density of the liquid × gravitational field strength

[ p = h ρ g ]

• pressure, p, in pascals, Pa
• height of the column, h, in metres, m
• density, ρ, in kilograms per metre cubed, kg/m3
• gravitational field strength, g, in newtons per kilogram, N/kg (In any calculation the value of the gravitational field strength (g) will be given.)
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## What do objects in fluids experience?

• When an object is submerged in a fluid (either partially or completely), the pressure of the fluid exerts a force on it from every direction.
• Pressure increases with depth, so the force exerted on the bottom of the object is larger than the force acting on the top of the object.
• This causes a resultant force upwards, known as upthrust.
• The upthrust is equal to the weight of the fluid that has been displaced (pushed out of the way) by the object. E.g. the upthrust on a pineapple in water is equal to the weight of a pineapple-shaped volume of water.
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## How does an object float?

• Weight = upthrust. If the upthrust on the object is equal to the object's weight, then the forces balance and the objects floats.
• If the objects' weight is more than the upthrust, the object sinks.
• This means that whether or not an object will float depends on its density.
• An object that is less dense than the fluid it is placed in weighs less than the equivalent volume of the fluid. This means that it displaces a volume of fluid that is equal to its weight before it is completely submerged.
• At this point, the objects weight is equal to the upthrust so the object floats.
• An object that is denser than the fluid it is placed in is unable to displace enough fluid to equal its weight. This means that its weight is always larger than the upthrust so it sinks.
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## How do submarines use upthrust?

• Submarines make use of upthrust.
• To sink, large tanks are filled with water to increase the weight of the submarine so that it is more than the upthrust.
• To rise to the surface, the tanks are filled with compressed air to reduce the air to reduce the weight so that it's less than the upthrust.
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## What is the atmosphere?

• The atmosphere is a thin layer (relative to the size of the Earth) of air round the Earth.
• Atmospheric pressure is created on a surface by air molecules colliding with the surface.
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## Atmospheric pressure decreases with height....

• As the altitude (height above the Earth) increases, atmospheric pressure decreases.
• This is because as the altitude increases, the atmosphere gets less dense so there are fewer air molecules that are able to collide within the surface.
• There are also fewer air molecules above a surface as the height increases. This means that the weight of the air above it, which contributes to atmospheric pressure, decreases with altitude.
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## What is the difference between distance and displa

Distance:

• Distance is how far an object moves.
• Distance does not involve direction.
• Distance is a scalar quantity.

Displacement:

• Displacement includes both the distance an object moves, measured in a straight line from the start point to the finish point and the direction of that straight line.
• Displacement is a vector quantity
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## What is the difference between speed and velocity?

• Speed and velocity both measure how fast you're going, but speed is scalar and velocity is a vector.
• Speed is just how fast you're going (e.g. 30 mph or 20 m/s) with no regard to the direction. Velocity is a speed in a given direction, e.g. 30 mph north or 20 m/s 060 degrees.
• This means that you can have objects travelling at a constant speed with a changing velocity. This happens when the object is changing direction whilst staying at the same speed. An object moving in a circle at a constant speed has a constantly changing velocity, as the direction is always changing, e.g. a car going around at a roundabout.
• Objects rarely travel at constant speed. E.g. when you walk, run or travel in a car, your speed is always changing. The equation in this case would be used to give the average (mean) speed.
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## Typical everyday speeds...

• walking ~ 1.5 m/s
• running ~ 3 m/s
• cycling ~ 6 m/s
• car ~ 25 m/s
• train ~ 55 m/s
• plane ~ 250 m/s
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## What factors affect the speed of travel?

The speed at which a person can walk, run or cycle depends on many factors including:

• age
• terrain - what kind of land they're moving over.
• fitness
• distance travelled.

It's not only the speed of objects that varies. The speed of sound - 330 m/s - changes depending on what the sound waves are travelling through, and the speed of wind is affected by many factors.

Wind speed can be affected by things like temperature, atmospheric pressure and if there are any large buildings or structures nearby (e.g. forests reduce the speed of air travelling through them).

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## What is acceleration?

• Acceleration is the change in velocity in a certain amount of time.
• Decceleration is just negative acceleration - an object slowing down, and the change in velocity is negative.
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## EQUATION - Acceleration.

acceleration = change in velocity / time taken

a = ∆ v / t

• acceleration, a, in metres per second squared, m/s2
• change in velocity, ∆v, in metres per second, m/s
• time, t, in seconds, s
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## What is uniform acceleration?

• Constant acceleration is sometimes called uniform acceleration.
• Acceleration due to gravity (g) is uniform for obkects in free fall. It's roughly equal to 9.8 m/s2 near the Earth's surface and has the same value as gravitational field strength.
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## EQUATION - Uniform acceleration.

(final velocity)2 − (initial velocity)2 = 2 × acceleration × distance

v2 − u2 = 2 a s

• final velocity, v, in metres per second, m/s
• initial velocity, u, in metres per second, m/s
• acceleration, a, in metres per second squared, m/s2
• distance, s, in metres, m
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## What do distance-time graphs show?

• If an object moves in a straight line, its distance travelled can be plotted on a distance-time graph. You can show journeys on them.
• The shape of the graph shows how the object is moving:
• Gradient = speed. The steeper the graph, the faster the object is going. This is because speed = distance / time.
• Flat sections = stationary - it's stopped.
• Straight uphill sections = steady speed.
• Curves = acceleration or deceleration.
• A steepening curve means that the object's speeding up.
• A levelling off curve means that it's slowing down.
• If the object is changing speed (accelerating) you can find its speed at a point by finding the gradient to the tangent to the curve.
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## What do velocity-time graphs show?

• How an object's velocity changes as it travelled can be shown on a distance-time graph.
• Gradient = acceleration, since acceleratio is change in velocity / time.
• Flat sections = steady speed.
• Steeper the graph, the greater the acceleration or deceleration.
• Uphill sections are accelerations. Downhill sectiosn are deceleration.
• Curve = changing acceleration.
• The area under any section of the graph is equal to the distance travelled in that time interval. If the section under the graph is irregular, it's easier to count the squares under the line and multiplying it by the value of one square.
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## What force slows objects down?

• If an object has no force propelling it along it will always slow down and stop because of friction.
• Friction always acts in the opposite direction to movement.
• To travel at a steady speed, the driving force needs to balance the frictional forces.
• You get friction between two surfaces in contact, or when an object passes through a fluid (drag).
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## Drag and air resistance.

• Drag is the resistance you get in a fluid (a gas or a liquid). Air resistance is a type of drag - it's the frictional force produced by the air acting on a moving object.
• The most important factor by far in reducing drag is keeping the shape streamlined. This is where the object is designed to allow fluid to flow easily across it, reducing drag.
• Paracutes work in the opposite way - they want as much drag as they can get.
• Air flows easily over a streamlined object, e.g. car.
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## What happens when drag increases?

• Frictional forces from fluids always increase with speed.
• A car has much more friction to work against when travelling at 70 mph compared to 30 mph. So at 70 mph, the engine has to work much harder just to maintain a steady speed.
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## What do objects falling through fluids reach?

• When falling objects first set off, the force of gravity is much more than the frictional force slowing them down, so they accelerate.
• As the speed increases, friction builds up.
• This gradually reduces the acceleration until eventually the frictional force is equal to the accelerating force (so the resultant force is 0).
• It will have reached its maximum speed or terminal velocity and will fall at a steady speed.
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## What does terminal velocity depend on?

• The accelerating force acting on all falling objects is gravity and it would make them all fall at the same rate, if it wasn't for air resistance.
• This means that on the Moon, where there's no air, hammers and feathers dropped simultaneously would hit the ground together.
• However, on Earth, air resistance causes things to fall at different speeds, and the terminal velocity of any object is determined by its drag in comparison to its weight.
• The frictional force depends on its shape and area. An important example is the human skydiver.
• Without his parachute open he has quite a small area and a force of "w=mg" pulling him down.
• He reaches terminal velocity of about 120 mph.
• But with the parachute open, there's much more air resistance (at any given speed) and still only the same force "w=mg" pulling him down.
• This means his terminal velocity comes right down to about 15 mph, which is a safe speed to hit the ground at.
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## What is Newton's First Law?

Newton’s First Law:

If the resultant force acting on an object is zero and:

• the object is stationary, the object remains stationary
• the object is moving, the object continues to move at the same speed and in the same direction. So the object continues to move at the same velocity.

So, when a vehicle travels at a steady speed the resistive forces balance the driving force. The velocity will only change if there's a non-0 resultant force acting on the object.

• A non-0 resultant force will always produce acceleration (or deceleration) in the direction of the force.
• This "acceleration" can take 5 different forms: starting, stopping, speeding up, slowing down and changing direction.
• On a free body diagram, the arrows will be unequal.
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## What is Newton's First Law?

Newton’s First Law:

If the resultant force acting on an object is zero and:

• the object is stationary, the object remains stationary
• the object is moving, the object continues to move at the same speed and in the same direction. So the object continues to move at the same velocity.

So, when a vehicle travels at a steady speed the resistive forces balance the driving force. The velocity will only change if there's a non-0 resultant force acting on the object.

• A non-0 resultant force will always produce acceleration (or deceleration) in the direction of the force.
• This "acceleration" can take 5 different forms: starting, stopping, speeding up, slowing down and changing direction.
• On a free body diagram, the arrows will be unequal.
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## EQUATION - Describe Newton's Second Law.

The acceleration of an object is proportional to the resultant force acting on the object, and inversely proportional to the mass of the object.

resultant force  = mass × acceleration

F = m a

• force, F, in newtons, N
• mass, m, in kilograms, kg
• acceleration, a, in metres per second squared, m/s2
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## What is inertia?

• Until acted upon by a result force, objects at rest stay at rest and objects moving at a steady speed will stay moving at this speed - Newton's First Law. This tendency to continue in the same state of motion is called inertia - the tendency for motion to remain unchanged.
• An object's inertial mass measures how difficult it is to change the velocity of an object.
• Inertial mass can be found using Newton's Second Law of F=ma. Rearranging this gives m= F / a, so intertial mass is just the ratio of force over acceleration.
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## Describe Newton's Third Law.

Whenever two objects interact, the forces they exert on each other are equal and opposite.

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## Newton's Third Law and Equilibrium.

• An example of Newton's Third Law in an equilibrium situation is a man pushing against a wall. As the man pushes the wall, there is a normal contact acting back on him.
• These two forces are the same size. As the man applies a force and pushes the wall, the wall 'pushes back' on him with an equal force.
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## Forces and Newton's Third Law.

• It can be easy to get confused with Newton's Third Law when an object is in equilibrium. E.g. a book resting on a table is in equilibrium. The weight of the book is equal to the normal contact force. The weight of the book pulls it down, and the normal reaction force from the table pushes it up. This is NOT Newton's Third Law. These forces are different types and they're both acting on the book.
• The pairs of foces due to Newton's Third Law in this case are:
• The weight of the book is pulled down by gravity by Earth and the book also pulls back up on the Earth.
• The normal contact force from the table pushing up on the book and the normal contact force from the book pushing down on the table.
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## REQUIRED PRACTICAL - Mass, Force and Acceleration.

• Set up the ttrolley so it holds a piece of card with a gap in the middle that will interrupt the signal on the light gate twice. If you measure the length of each bit of card that will pass through the light gate and input this into te software, the light gate can measure the velocity for each bit of card. It can use this to work out the acceleration of the trolley.
• Connect the trolley to a piece of string that goes over a pulley and is connected on the other side to a hook (that you know the masss of and can add more masses to).
• The weight of the hook and any masses attatched to it will provide the accelerating force, equal to the mass of the hook x acceleration due to gravity.
• The weight of the hook and masses accelerates both the trolley and the masses, so you are investigating the acceleration of the system (the trolley and masses together).
• Mark a starting line on the table the trolley is on, so that the trolley always travels the same distance to the light gate.
• Place the trolley on the starting line and hold it in place. You should let the hook and any masses on the hook hang so the string is taut (not loose and touching the table). Then, release the trolley.
• Record the acceleration measured by the light gate as the trolley passes through it. This is the acceleration of the whole system. Repeat this twice to get an average acceleration.
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## REQUIRED PRACTICAL - Varying mass and force.

• To investigate the effect of mass, add masses to the trolley, one at a time, to increase the mass of the system.
• Don't add masses to the hook, or you'll change the force.
• Record the average acceleration for each mass.

• To investigate the effect of force, you need to keep the total mass of the system the same, but change the mass on the hook.
• To do this, start with all the masses loaded onto the trolley and transfer the masses to the hook one at a time, to increase the accelerating force (the weight of the hanging masses),
• The mass of the system stays the same as you're only transferring the masses from one part of the system (the trolley) to another (the hook).
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## REQUIRED PRACTICAL - What could affect results?

• The friction between the bench might affect your acceleration measurements. You could use an air track to reduce the friction (a track which hovers a trolley on jets of air).
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## REQUIRED PRACTICAL - Results...

• Newton's Second Law can be written as F = ma. Here, F = weight of the hanging masses, m= mass of the whole system and a = acceleration of the system.
• By addding masses to the trolley, the mass of the whole system increases, but the force applied to the system stays the same. This should lead to a decrease in the acceleration of the trolley, as a = F / m.
• By transferring masses to the hook, you are increasing the accelerating force without changing the mass of the whole system. So increasing the force should lead to an increase in the acceleration of the trolley.
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## What is a stopping distance?

• The stopping distance of a vehicle is the sum of the distance the vehicle travels during the driver’s reaction time (thinking distance) and the distance it travels under the braking force (braking distance).
• Stopping distance = thinking distance + braking distance.
• In an emergency, a driver may perform an emergency stop. This is where maximum force is applied by the brakes in order to stop the car in the shortest possible distance.
• Thinking distance = how far the car travels during the driver's reaction time (the time between the driver seeing a hazard and applying the brakes).
• Braking distance - the distance taken to stop under the braking force (once the brakes are applied).
• Typical car braking distances are 14 m at 30 mph, 55 m at 60 mph and 75 m at 70 mph.
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## What factors affect your thinking distance?

• Your speed - the faster you're going the further you'll travel during the time you take to react.
• Your reaction time 0 the longer your reaction time, the longer your thinking distance. This can be affected by tiredness, drugs or alcohol. Distractions can affect your ability to react.
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## What factors are braking distance affected by?

• Your speed - for a given braking force, the faster a vehicle travels, the longer it takes to stop it.
• The weather or road surface - if it is wet or icy, or there are leaves or oil on the road, there is less grip (and so less friction) between a vehicle's tyres and the road, which can cause tyres to skid.
• The conditions of your tyres - if the tyres of a vehicle are bald (they don't have any thread left), then they cannot get rid of water in wet conditions. This leads to them skidding on top of the water.
• How good your brakes are - if the brakes are worn or faulty, they won't be able to apply as much force as well-maintained brakes, which could be more dangerous when you need to brake hard.
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## For example...

• Icy conditions increase the chance of skidding and so increase the stopping distance so driving too close to other cars in icy conditions is unsafe. The longer your stopping distance, the more space you need to leave in front in order to stop safely.
• Speed limits are really important becasue speed affects the stopping distance so much.
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## REQUIRED PRACTICAL - Ruler drop test...

• Sit with your arm resting on the edge of a table (this should stop you moving your arm up or down during the test). Get someone else to hold the ruler so it hangs between your thumb and forefinger lined with 0. You may need a third person to be at eye level with the ruler to check it's lined up.
• Without any warning, the person holding the ruler should drop it. Catch the ruler as quickly as possible.
• The measurement on the ruler at the point where it is caught is how far the ruler dropped in the time it takes you to react.
• The longer the distance, the longer the reaction time.
• You can calculate how long the ruler falls for (the reaction time) because acceleration due to gravity is constant. E.g. uniform equation.
• Repeat the experiment - you can use a blob of modelling clay to the bottom to stop it from waving about.
• Make sure it's a fair test - use the same ruler for each repeat, and have the same person dropping it.
• Investigate other factors by providing distractions. Work out the mean for this and the normal mean and compare.
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## What does the braking rely on?

• When the brake pedal is pushed, this causes brake pads to be pressed onto the wheels. This contact causes friction, which causes work to be done.
• The work done between the brakes and the wheels transfers energy from the kinetic energy store of the wheels to the thermal energy store of the brakes. The brakes increase in temperature.
• The faster a vehicle is going, the more energy it has in its kinetic energy store, so more work needs to be donne to stop it. This means that a greater braking force is needed to make it stop within a certain distance.
• A larger breaking force means a larger deceleration. Very large decelerations can be dangerous because they can cause brakes to overheat or could cause the vehcile to skid.
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## Leave enough space to stop.

• To avoid an accident, drivers need to leave enough space between their car and the one in front so that if they had to stop suddenly they would have time to do so safely.
• Enough space means that the stopping distance or whatever speed they're going at.
• So even at 30 mph you should drive no closer that 6 or 7 car lengths away from the car in front.
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## Reaction time varies...

Reaction times vary from person to person. Typical values range from 0.2 s to 0.9 s.

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## Speed affects braking distance more than thinking

• As a car speeds up, the thinking distance increases at the same rate as speed. The graph is linear.
• This is because the thinking time (how long it takes to apply the brakes) stays constant - but the higher the speed, the more distance you cover in that time.
• Braking distance, however, increases faster the more you speed up. The work is done to stop the car is equal to the energy in the car's kinetic energy store (1/2 m v 2). So as speed doubles, the kinetic energy increases 4-fold (2 squared), and so work is done to stop the car increases 4 fold. Since W = f s, and the braking force is constant, the braking force increases 4 fold.
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## What is momentum?

• The greater the mass of an object, or the greater its velocity, the more momentum the object has.
• Momentum is a vector quantity - it has size and direction.
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## EQUATION - Momentum

momentum = mass  × velocity

p = m v

• momentum, p, in kilograms metre per second, kg m/s
• mass, m, in kilograms, kg
• velocity, v, in metres per second, m/s
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## Momentum before = momentum after.

• In a closed system, the total momentum before an event is equal to the total momentum after the event. This is called conservation of momentum.
• A moving car hits into the back of the parked car. The crash causes the two cars to lock together, and they continue moving in the direction that the original moving car was travelling, but at a lower velocity.
• Before: the momentum was equal to the mass of a moving car x its velocity.
• After: the mass of the moving object has increased, but its momentum is equal to the momentum before the collision. So an increase in mass causes a decrease in veloctiy.
• In snooker, balls of the same size and mass collide with each other. Each collision is an event wheere the momentum of each ball changes, but the overall momentum stays the same (momentum is conserved). Red ball and white ball.
• Before: The red ball is stationary, so it has 0 momentum. The white ball is moving with velocity, v, so has a momentum of p = mv.
• After: the white ball hits the red ball, causing it to move. The red ball now has a momentum. The white ball continues moving, but a much smaller velocity (and so a smaller momentum). The combined momentum of the red and white ball is equal to the original momentum of the white ball, mv.
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## Forces cause what?

• When a non-0 resultant force acts on a moving object, it causes its velocity to change. This means that there is a change in momentum. F = ma and that a = change in velocity / time.
• So, f = m x (change in velocity / time).
• The force causing the change is equal to the rate of momentum.
• A larger force means a faster change of momentum.
• Likewise, if someone's momentum changes very quickly like in a car crash, the forces on the body will be very large and more likely to cause an injury.
• This is why cars are designed to slow people down over a longer time when they have a crash - the longer it takes for a change in momentum, the smaller the rate of change of momentum, and so the smaller the force. Smaller forces mean the injuries are likely to be less severe.
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## What safety features do vehicles have?

Cars:

• Crumple zones crumple on impact, increasing the time taken for the car to stop.
• Seat belts stretch slightly, increasing the time taken for the wearer to stop.
• Air bags inflate before you hit the dashbard of a car. The compressing air inside it slows you down more gradually than if you had just hit the hard dashboard.
• Helmets, e.g. bike helmets contain a crushable layer of foam which helps to lengthen the time taken for your head to stop in a crash. This reduces the impact on your brain.
• Crush mats and cushioned playground flooring increase the time taken for you to stop if you fall on them. This is because they are made from soft, compressible materials.
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## Waves transfer energy...

• in the direction they're travelling.
• When waves travel through a medium, the particles of the medium oscillate and transfer energy between each other. BUT overall, the particles stay in the same place - only energy is transferred.
• For e.g. if you drop a twif into a calm pool of water, ripples form on the water's surface. The ripples don't carry the water or the twig away with them though.
• Similarly, if you strum a guitar string and create sound waves, the sound waves don't carry the air away from the guitar and create a vaccum.
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## What are the amplitudes, wavelengths and frequenci

• Amplitude = maximum displacement of a point on the wave from its undisturbed position.
• Wavelength = the distance between the same point on two adjacent waves (e.g. from trough to trough or peak to peak).
• Frequency = the number of complete waves passing a cerain point per second. Frequency is measured in hertz, Hz. 1 Hz is 1 wave per second.
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## EQUATION - Frequency and period.

period =  1 / frequency

T = 1 / f

• period, T, in seconds, s
• frequency, f, in hertz, Hz
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## What is wave speed?

The wave speed is the speed at which the energy is transferred (or the wave moves) through the medium.

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## Describe transverse waves.

• In transverse waves, the oscillations are perpendicular to the direction of energy transfer. A spring wiggled from side to side gives a transverse wave.
• Most waves are transverse, including:
• All EM waves
• Ripples and waves in water
• A wave on a string
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## Describe longitudinal waves.

• In longitudinal waves, the oscillations are parallel to the direction of energy transfer. If you push the end of a spring, you'll get a longitudinal wave:
• Examples:
• Sound waves in air, e.g. ultrasound.
• Shock waves e.g. some seismic waves.
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## EQUATION - Wave speed.

wave speed  = frequency × wavelength

v = f  λ

• wave speed, v, in metres per second, m/s
• frequency, f, in hertz, Hz
• wavelength, λ, in metres, m
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## Oscilloscope to measure speed of sound:

• Set up the oscilliscope so the detected waves at each microphone are shown as separate waves.
• Start with both microphones next to the speaker, then slowly move one away until the two waves are aligned on the display, but have moved exactly one wavelength apart.
• Measure the distance between the microphones to find one wavelength.
• You can then use the formula wave speed = frequency x wavelength to find the speed of the sound waves passing through the air - the frequency is whatever you set the signal generator to (around 1kHz is sensible).
• The speed of sound is also arround 330 m/s so check your results roughly agree with this.
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## REQUIRED PRACTICAL - Speed of water ripples.

• Use a signal generator attatched to the dipper of a ripple tank, you can create water waves at a set frequency.
• Dim the lights and turn on the strobe light - you'll see a wave pattern made by the shadows of the wave crests on the screen below the tank.
• Increase the frequency of the strobe light until the wave pattern on the screen appears to 'freeze' and stop moving. This happens when the frequency of the strobe light is equal to the frequency of the waves.
• The strobe is a suitable piece of equipment to use because it allows you to measure a still pattern instead of a constantly moving one.
• The distance between each shadow line is equal to one wavelength. Measure the distance between shadow lines that are 10 wavelengths apart, then divide this distance by 10 to find the average wavelength. This is a suitable method for measuring small wavelengths.
• Use wave speed = frequency x wave length to calculate the speed of the waves.
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## REQUIRED PRACTICAL - Wave equation for waves on st

• In this practical, you create a wave on a string. Again, you use a signal generator, but this time you attatch it to a vibration transducer which converts the signals to vibrations.
• Set up the equipment, then turn on the signal generator and vibrations transducer. The string will start to vibrate.
• You can adjust the frequency setting on the signal generator to change the length of the wave created on the string. You should keep adjusting the frequency of the signal generator until there appears to be a clear wave on the string (you want at least 4/5 half wavelengths). The frequency you need will depend on the length of string between the pulley and the transducer, and the masses you have used.
• You need to measure the wavelength of the wave. The best way to do this accurately is to measure the length of all the half-wavelengths on the string in one go, then divide by the total number of half-wavelengths to get the mean half-wavelength. You can then double this value to get a full wavelength.
• The frequency of the wave is whatever the signal generator is set to (you could also measure it with a strobe, as in the previous experiment).
• You can find the speed of the wave length, speed = frequency x length.
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## What 3 things can all waves do?

When waves arrive at a boundary between two different materials, three things can happen:

• The waves are absorbed by the material the wave is trying to cross into - this transfers energy to the material's energy stores (this is how a microwave works).
• These waves are transmitted - the waves carry on travelling through the new material. This often leads to refraction.
• These waves are reflected.

What actually happens depends on the wavelength of the wave and the properties of the materials involved.

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## Drawing ray diagrams.

• Angle of incidence = angle of reflection.
• The angle of incidence is the angle between the incoming wave and the normal.
• The angle of reflection is the angle between the reflected wave and the normal.
• The normal is an imaginary line that's perpendicular to the surface of the point of incidence (the point where the wave hits the boundary).
• The normal is usually shown as a dotted line.
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## Reflection can be specular or diffuse...

• Waves are reflected at different boundaries in different ways.
• Specular reflection happens when a wave is reflected in a single direction by a smooth surface, e.g. when light is reflected by a mirror, you get a reflection.
• Diffuse reflection is when a wave is reflected by a rough surface (e.g. a piece of paper) and the refracted rays are scattered in lots of different directions.
• This happens because the normal is different for each incoming ray, which means that the angle of incidence is different for each ray. The rule of angle of incidence = angle of reflection still applies.
• When light is reflected by a rough surface, the surface appears matte (not shiny) and you don't get a clear reflection of objects.
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## What is refraction?

• When a wave crosses a boundary between materials at an angle, it changes direction - it's refracted.
• How much it's refraced by depends on how much the wave speeds up or slows down, which usually depends on the density of the two materials. Usually, the higher the density of a material, the slower a wave travels through it.
• If a wave crosses a boundary and slows down it will bend towards the normal. If it crosses into a material and speeds up it will bend away from the normal.
• The wavelength of a wave changes when it's refracted, but the frequency stays the same.
• If the wave is changed along the normal, it will change speed but it's not refracted.
• If a light wave hits a boundary face on, it carries on in the same direction, but if a wave meets a different medium at an angle, the wave changes direction and it has been refracted.
• The optical density of a material is a measure of how quickly light can travel through it - the higher the optical density, the slower light waves travel through it.
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## Constructing ray diagrams.

• First, draw the boundary between your two materials and the normal perpendicular to it.
• Draw an incident ray that meets the normal at the boundary. The angle between the ray and normal is the angle of incidence. Protractor.
• Now, draw the refracted ray on the other side of the boundary. If the second material is optically denser than the first, the refracted ray bends towards the normal. The angle between the refracted ray and the normal is smaller than the angle of incidence. If the second material is less optically dense, the angle of refraction is larger than the angle of incidence.
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## REQUIRED PRACTICAL - Light....

• Set up the ray box, slit and lens so that a narrow ray of light is produced.  Then darken the room. Place the ruler near the middle of the A3 paper and draw a straight line parallel to its long side Use the protractor to draw a second line at right angles to this line.
• Label this line with an ‘N’ for ‘normal’
• Draw around the transparent block.  Be careful not to move it.
• Use the ray box to direct a ray of light at the point where the normal meets the block. This is called the ‘incident ray’.
• The angle between the normal and the incident ray is called ‘the angle of incidence’.
• Mark the path of the reflected ray with another cross. Mark the path of the ray that leaves the block (the transmitted ray) with two crosses.  One cross needs to be near the block and the other cross further away.
• Draw the incident ray by drawing a line through your first cross to the point where the normal meets the block. Draw the reflected ray by drawing a line through your second cross to the point where the normal meets the block.
• Draw the transmitted ray by drawing a line through the two crosses on the other side of the block to that side of the block.  Label this point with a ‘P’.
• Draw a line that represents the path of the transmitted ray through the block.
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## REQUIRED PRACTICAL - Refraction...

• Place a transparent rectangular block on a piece of paper and trace around it. Use a ray box or a laser to shine a ray of light at the middle of one side of the block.
• Trace the incident ray and mark where the light ray emerges on the other side of the block. Remove the block and, with a straight line, join up the incident ray and the emerging point to show the path of the refracted ray through the block.
• Draw the normal at the point where the light ray entered the block. Use a protractor to measure the angle of incidence and the angle of refraction.
• Repeat this experiment using rectangular blocks made from different materials, keeping the incident angle the ame throughout.
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## What are EM waves?

• Electromagnetic waves are transverse waves that transfer energy from the source of the waves to an absorber.
• Electromagnetic waves form a continuous spectrum and all types of electromagnetic wave travel at the same velocity through a vacuum (space) or air.
• The waves that form the electromagnetic spectrum are grouped in terms of their wavelength and their frequency. Going from long to short wavelength (or from low to high frequency) the groups are: radio, microwave, infrared, visible light (red to violet), ultraviolet, X-rays and gamma rays.
• Our eyes only detect visible light and so detect a limited range of electromagnetic waves.
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## List the EM waves...

Mate - Microwaves

In - Infrared

Very - Visible Light

eXpensive - X-ray

Gardens - Gamma ray

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•  Radio waves can be produced by oscillations in electrical circuits.
• Ac are made up of oscillating charges. As the charges oscillate, they produce oscillating electric and magnetic fields, i.e. EM waves.
• The frequency of the waves produced will be equal to the frequency of the AC.
• You can produce radio waves using an AC in an electrical circuit. The object in which charges (electrons) oscillate to create the radio waves is called a transmitter.
• The energy transferred by the waves is transferred to the electrons in the material of the receiver.
• This energy causes the electrons to oscillate and, if the receiver is part of a complete electrical circuit, it generates an AC.
• This current has the same frequency as the radio waves that generated it.
• MRI scanners.
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## Radio waves are used for communications.....

• EM radiation with a wavelength greater than 10cm.
• Long-wave radio waves (wavelengths of about 1-10 km) can be transmitted from London and received halfway around the world. That's because long wavelengths diffract (bend) around the curved surface of the Earth. Long wave radio wavelengths can also diffract around hills, into tunnels and all sorts.
• This makes it possible for radio signals to be received even if the receiver isn't in line of sight of the transmitter.
• Short-wave radio signals (wavelengths of about 10 -100 m) can, like long-wave, be received from long distances from the transmitter. That's because they are reflected from the ionosphere - an electrically charged layer in the Earth's upper atmosphere.
• Bluetooth uses short-wave radio waves to send data over short distances between devices without wires.
• Medium wave signals can also reflect from the ionosphere, depending on atomospheric conditions and the time of day.
• The radio waves used for TV and FM radio transmission have very short wavelengths. To get reception, you must be in direct sight of the transmitter - the signal doesn't bend or travel far through buildings.
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## Microwaves are used by satellites....

• Communication to and from satellites uses microwaves. But you need to use microwaves whcih can pass easily through the Earth's watery atmosphere.
• For satellite TV, the signal from a transmitter is transmitted into space where it's picked up by the satellite receiver dish orbiting thousands of km above the Earth. The satellite transmits the signal back to the Earth in a different direction where it's received by a satellite dish on the ground. There's a slight time delay between the signal being sent and received because of the long distance the signal has to travel.
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## Microwave ovens use a different wavelength.

• In communications the microwaves used need to pass through the Earth's watery atmosphere.
• In microwae ovens, the microwaves need to be absorbed by water molecules in food - so they can use a different wavelength to those used in satellite communications.
• The microwaves penetrate up to a few cm in the food before being absorbed and transferring the energy they are carrying to the water molecules in the food, causing water to heat up.
• The water molecules then transfer this energy to the rest of the molecules in the food by heating - which quickly cooks the food.
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