Download Velocity-time graphs

PHYSICS
Representing motion
The speed of an object can be calculated if the distance travelled and the time taken is known.
The faster an object moves, the steeper is the line representing it on a distance-time graph. The
speed is equal to the gradient of the line on a distance-time graph.
The velocity of an object is its speed in a particular direction. The acceleration of an object is
equal to the gradient of the line on a velocity-time graph. The distance travelled is equal to the
area under a velocity-time graph.
Speed, distance and time
You should recall from your Key Stage 3 studies how to calculate the speed of an object from the
distance travelled and the time taken.
The equation
When an object moves in a straight line at a steady speed, you can calculate its speed if you
know how far it travels and how long it takes. This equation shows the relationship between
speed, distance travelled and time taken:
Distance-time graphs
You should be able to draw and explain distance-time graphs for objects moving at steady
speeds or standing still.
Background information
The vertical axis of a distance-time graph is the distance travelled from the start, and the
horizontal axis is the time from the start.
Features of the graphs
When an object is stationary, the line on the graph is horizontal.
When an object is moving at a steady speed, the line on the graph is straight, but sloped.
The diagram shows some typical lines on a distance-time graph.
Note that the steeper the line, the greater the speed of the object. The blue line is steeper than
the red line because it represents an object moving faster than the one represented by the red
line.
The red lines on the graph represent a typical journey where an object returns to the start again.
Notice that the line representing the return journey slopes downwards.
Velocity-time graphs
You should be able to explain velocity-time graphs for objects moving with a constant velocity or
a constant acceleration.
Background information
The velocity of an object is its speed in a particular direction. This means that two cars traveling
at the same speed, but in opposite directions, have different velocities.
The vertical axis of a velocity-time graph is the velocity of the object and the horizontal axis is the
time from the start.
Features of the graphs
When an object is moving with a constant velocity, the line on the graph is horizontal. When an
object is moving with a constant acceleration, the line on the graph is straight, but sloped. The
diagram shows some typical lines on a velocity-time graph.
The steeper the line, the greater the acceleration of the object. The blue line is steeper than the
red line because it represents an object with a greater acceleration than the one represented by
the red line.
Notice that a line sloping downwards (with a negative gradient) represents an object with a
constant deceleration (slowing down).
Acceleration
You should be able to calculate the acceleration of an object from its change in velocity and the
time taken.
The equation
When an object moves in a straight line with a constant acceleration, you can calculate its
acceleration if you know how much its velocity changes and how long this takes. This equation
shows the relationship between acceleration, change in velocity and time taken:
For example, a car accelerates in 5s from 25m/s to 35m/s.
Its velocity changes by 35 – 25 = 10 m/s.
So, its acceleration is 10 ÷ 5 = 2m/s2.
Velocity-time graphs (Higher Tier)
You should be able to calculate gradients of velocity-time graphs and the areas under the graphs.
The gradient
The gradient of a line on a velocity-time graph represents the acceleration of the object. Study
this velocity-time graph.
What is the acceleration represented by the sloping line?
The object increases its velocity from 0m/s to 8m/s in 4s.
Its acceleration is 8 ÷ 4 = 2m/s2.
The area
The area under the curve in a velocity-time graph represents the distance travelled. To find the
the distance travelled in the graph above we need to find the area of the light blue triangle and
the dark blue square
Step 1 - Area of light blue triangle
The width of the triangle is 4 seconds and the height is 8 metres per second. To find area you use
the equation:
area of triangle = 1/2 x base x height
so the area of the light blue triangle is 1/2 x 8 x 4 = 16m.
Step 2 - Area of dark blue rectangle
The width of the rectangle is 6 seconds and the height is 8 metres per second so the area is 8 x 6
= 48m.
Step 3 - Area under the whole graph
The area of the light blue triangle plus the area of the dark blue rectangle is:
16 + 48 = 64m.
This is the total area under the distance time graph and this area represents the distance
covered.
To summarise:
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the gradient of a velocity time graph represents the acceleration
the area under a distance time graph represents the distance covered
Friction and non-uniform motion
A falling object accelerates because of the force of gravity, but as it speeds up, the frictional
forces on it increase. Eventually, the gravitational force is balanced by the frictional forces and
the object falls at a constant speed, called the terminal velocity.
The distance travelled by a car between the time it takes for its driver to start reacting to a hazard
and the car stopping depends on two things: the thinking distance and the braking distance.
Several factors influence the thinking distance and the braking distance, and can increase the
overall stopping distance.
Falling objects
You should be able to describe the forces affecting a falling object at different stages of its fall.
Outline
When an object is dropped, we can identify three stages before it hits the ground:
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At the start, the force of gravity pulls the object down towards the Earth, and it
accelerates downwards.
As it gains speed, frictional forces on the object increase and oppose the downwards
movement.
Eventually, the force of gravity acting on the object is balanced by the frictional forces.
The object reaches a steady speed called the terminal velocity.
Terminal velocity
What happens if you drop a feather and a coin together? The feather and the coin have roughly
the same surface area, so when they begin to fall they have about the same drag.
As the feather falls, its drag increases until it soon balances the weight of the feather. The feather
now falls at its terminal velocity. But the coin is much heavier, so it has to travel quite fast before
drag is large enough to balance its weight. In fact, it probably hits the ground before it reaches its
terminal velocity.
On the moon
An astronaut on the moon carried out a famous experiment. He dropped a hammer and a feather
at the same time and found that they landed together. The moon's gravity is too weak for it to
hold onto an atmosphere, so there is no air resistance. When the hammer and feather were
dropped they fell together with the same acceleration.
Stopping distances
You should know some of the factors affecting the stopping distance of a car.
Thinking distance
It takes a certain amount of time for a driver to react to a hazard and to start applying the brakes.
During this time, the car is still moving. The faster the car is travelling, the greater this thinking
distance will be.
The thinking distance will also increase if the driver's reactions are slower because the driver is:
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Under the influence of alcohol.
Under the influence of drugs.
Tired
Braking distance
The braking distance is the distance the car travels from where the brakes are first applied to
where the car stops. If the braking force is too great, the tyres may not grip the road sufficiently
and the car may skid. The faster the car is travelling, the greater the braking distance will be.
The braking distance will also increase if:
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The brakes or tyres are worn.
The weather conditions are poor, such as icy or wet roads.
The car is more heavily laden, for example with passengers and luggage.
Stopping distance
The stopping distance is the thinking distance added to the braking distance. The graph shows
some typical stopping distances.
Force, mass and acceleration
If the forces acting on an object are balanced, a stationary object remains stationary, and a
moving object keeps moving at the same speed and in the same direction.
If the forces acting on an object are unbalanced, a stationary object begins to accelerate in the
direction of the force, and a moving object speeds up, slows down or changes direction.
Acceleration depends on the force applied to an object and the mass of the object.
Balanced and unbalanced forces
You should be able to use the idea of balanced and unbalanced forces to determine the
movement of an object.
Balanced forces
When all the forces acting on an object cancel out, we say that they are balanced. If the forces
are balanced:
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A stationary object remains stationary.
A moving object keeps on moving at the same speed in the same direction.
For example, a book resting on a table has balanced forces. Its weight acting downwards is
balanced by the upward force on the book provided by the table. In the diagram of the
weightlifter, the forces on the bar are balanced, so it does not move.
The longer the arrow, the bigger the force. In this diagram, the arrows are the same length, so we
know they are the same size.
Unbalanced forces
When all the forces acting on an object do not cancel out, we say they are unbalanced. If the
forces are unbalanced:
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A stationary object begins to move in the direction of the unbalanced force.
A moving object speeds up, slows down or changes direction depending on the direction
of the unbalanced force.
In this diagram of the weightlifter, the forces on the bar are unbalanced. The upwards force is
bigger than the downwards force, so the bar moves upwards.
In this diagram of the weightlifter, the forces on the bar are also unbalanced. The upwards force
is smaller than the downwards force, so the bar moves downwards.
Forces and acceleration
You should know that unbalanced forces cause objects to accelerate, and understand the factors
that affect the size of the acceleration.
Size of the force
An object will accelerate in the direction of an unbalanced force. The bigger the force, the greater
the acceleration. Click on the animation (below) to double the force applied to the trolley, and see
what happens.
Doubling the size of the unbalanced force doubles the acceleration.
The mass
An object will accelerate in the direction of an unbalanced force. The bigger the mass of the
object, the smaller the acceleration. Click on the animation below to increase the mass on the
trolley, and see what happens.
Doubling the mass halves the acceleration.
Forces and acceleration (Higher Tier)
You should know the equation that shows the relationship between force, mass and acceleration,
and be able to use it.
The equation
You should see that 1N is the force needed to give 1kg an acceleration of 1m/s 2.
For example, the force needed to accelerate a 10kg mass by 5m/s2 is 10 x 5 = 50N.
The same force could accelerate a 1kg mass by 50m/s2 or a 100kg mass by 0.5m/s2.
Example
A truck has a mass of 2,000kg.
The driving force created by the engine is 3,000 newtons.
Calculate the acceleration caused by this unbalanced force.
Answer
1. Write down and rearrange the equation. force = mass x acceleration
2. Rearrange the equation.
acceleration = force/mass
3. Put in the values.
acceleration = 3,000N/2,000kg
4. Work out the answer and write it down.
acceleration = 1.5m/s2
1. Air resistance (drag)
When an object moves through the air, the force of air resistance acts in the opposite direction
to the motion. Air resistance depends on the shape of the object and its speed.
2. Contact force
This happens when two objects are pushed together. They exert equal and opposite forces on
each other. The contact force from the ground pushes up on your feet as you push down to walk
forwards.
3. Friction
This is the force that resists movement between two surfaces, which are in contact.
4. Gravity
This is the force that pulls objects towards the Earth. We call the force of gravity on an object its
weight. The Earth pulls with a force of about 10 newtons on every kilogram of mass.
Sample questions
Question 1
Look at the animation of the parachutist falling at a steady speed. Name the forces acting on the
parachutist and state how they are acting.
Answer 1
There are just two forces acting on the parachutist. Gravity (weight) pulls the parachutist down.
Air resistance (drag) pushes up on the canopy of the parachute.
Question 2
Look at the animation of the car moving at a steady speed. Name the forces acting on the car and
state how they are acting.
Answer 2
There are several forces acting on the car. Gravity pulls down on the car. The contact force from
the road pushes up on the wheels. The driving force from the engine pushes the car along. There
is friction between the road and the tyres. There is friction in the wheel bearings. Air resistance
acts on the front of the car.
Circuits
Electrical circuits can be represented by circuit diagrams. The various electrical components are
shown by using standard symbols in circuit diagrams. Components can be connected in series, or
in parallel. The characteristics of the current and potential difference (voltage) are different in
series and parallel circuits.
Circuit symbols
You need to be able to draw and interpret circuit diagrams.
Standard symbols
The diagram below shows the standard circuit symbols you need to know.
Circuit diagrams
Two things are important for a circuit to work:
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
There must be a complete circuit.
There must be no short circuits.
To check for a complete circuit, follow a wire coming out of the battery with your finger. You
should be able to go out of the battery, through the lamp and back to the battery.
To check for a short circuit, see if you can find a way past the lamp without going through any
other component. If you can, then there is a short circuit and the lamp will not light.
Series and parallel connections
You should know the difference between series and parallel connections in circuits.
Series connections
Components that are connected one after another on the same loop of the circuit are connected
in series. The current that flows across each component connected in series is the same.
The circuit diagram shows a circuit with two lamps connected in series. If one lamp breaks, the
other lamp will not light.
Parallel connections
Components that are connected on separate loops are connected in parallel. The current is
shared between each component connected in parallel.
The circuit diagram shows a circuit with two lamps connected in parallel. If one lamp breaks, the
other lamp will still light.
Current and potential difference
You need to know how to measure the current that flows through a component in a circuit and the
potential difference or voltage across it.
Current
A current flows when an electric charge moves around a circuit. No current can flow if the circuit
is broken, for example, when a switch is open. Click on the animation to see what happens to the
charge when the switch is opened or closed.
We can't detect if you have flash or not.
Measuring current:
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Current is measured in amperes.
Amperes is often abbreviated to amps or A.
Current flowing through a component in a circuit is measured using an ammeter.
The ammeter must be connected in series with the component.
Potential difference
A potential difference or voltage across an electrical component is needed to make a current flow
through it. Cells or batteries often provide the potential difference needed.
Measuring potential difference:
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Potential difference is measured in volts, V.
Potential difference across a component in a circuit is measured using a voltmeter.
The voltmeter must be connected in parallel with the component.
Cells and circuits
You should know what happens to the potential difference and current when the number of cells
in a circuit is changed.
Potential difference
A typical cell produces a potential difference of 1.5V. When two or more cells are connected in
series in a circuit, the total potential difference is the sum of their potential differences. For
example, if two 1.5V cells are connected in series in the same direction, the total potential
difference is 3.0V. If two 1.5V cells are connected in series, but in opposite directions, the total
potential difference is 0V, so no current will flow.
Current
When more cells are connected in series in a circuit, they produce a bigger potential difference
across its components. More current flows through the components as a result.
Series circuits
You should know the characteristics of the current and potential difference in series circuits.
Current
When two or more components are connected in series, the same current flows through each
component.
Potential difference
When two or more components are connected in series, the total potential difference of the
supply is shared between them. This means that if you add together the voltages across each
component connected in series, the total equals the voltage of the power supply.
Parallel circuits
You should know the characteristics of the current and potential difference in parallel circuits.
Current
When two or more components are connected in parallel, the total current flowing through the
circuit is shared between the components.
Potential difference
When two or more components are connected in parallel, the potential difference across them is
the same. This means that if a voltage across a lamp is 12V, the voltage across another lamp
connected in parallel is also 12V.
Resistance and resistors
In this section, we will look at resistance (measured in ohms) and how it is calculated in different
types of circuit. We will look at how the resistance in the filament of a lamp changes when the
filament heats up. You will also learn about diodes, heat-dependent resistors (called thermistors)
and light-dependent resistors (LDRs).
Resistance and Ohm's Law
You should know and understand the relationship between potential difference, current and
resistance.
Why do we get resistance?
An electric current flows when charged particles called electrons move through a conductor. The
moving electrons can collide with the atoms of the conductor. This makes it more difficult for the
current to flow, and causes resistance. Electrons collide with atoms more often in a long wire than
they do in a short wire. A thin wire has fewer electrons to carry the current than a thick wire. This
means that the resistance in a wire increases as:
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The length of the wire increases.
The thickness of the wire decreases.
Ohm’s Law
Resistance is measured in ohms,
. The greater the number of ohms, the greater the resistance.
The equation below shows the relationship between potential difference (voltage), current and
resistance:
The current flowing through a resistor at a constant temperature is directly proportional to the
voltage across the resistor. So, if you double the voltage, the current also doubles. This is called
Ohm’s Law. The graph shows what happens to the current and voltage when a resistor follows
Ohm’s Law.
Try this calculation:
Question
Bicycles with battery operated lights often have different size bulbs for the front and rear lights.
The filament in the front lamp has a resistance of 3 ohms. It takes a current of 0.6A. What voltage
does it work at?
1.
2.
3.
4.
0.2V
1.5V
1.8V
5V
The Answer
The answer is 1.8V. If you didn't get the correct answer make sure you have used the formula
correctly.
Changing the resistance
You should know how to change the resistance in a circuit and how to work out the resistance in
a series circuit.
Series circuits
When components are connected in series, their total resistance is the sum of their individual
resistances. For example, if a 2 resistor, a 1 resistor and a 3 resistor are connected side by
side, their total resistance is 2 + 1 + 3 = 6 .
If you increase the number of lamps in a series circuit, the total resistance will increase and less
current will flow.
The filament lamp
You should be able to recognise the graph of current against voltage for a filament lamp.
Background
The filament lamp is a common type of light bulb. It contains a thin coil of wire called the filament.
This heats up when an electric current passes through it and produces light as a result.
Ohm’s Law revisited
Remember that the current flowing through a resistor at a constant temperature is directly
proportional to the voltage across the resistor. The graph shows what happens to the current and
voltage when a resistor follows Ohm’s Law.
The filament lamp
The filament lamp does not follow Ohm’s Law. The resistance of a filament lamp increases as the
temperature of its filament increases. As a result, the current flowing through a filament lamp is
not directly proportional to the voltage across it. This is the graph of current against voltage for a
filament lamp.
The diode
You should be able to recognise the graph of current against voltage for a diode.
Background
Diodes are electronic components that can be used to regulate the voltage in circuits and to make
logic gates. Light-emitting diodes (LEDs) give off light and are often used for indicator lights in
electrical equipment such as computers and television sets.
The diode
The diode has a very high resistance in one direction.This means that current can only flow in the
other direction. This is the graph of current against voltage for a diode.
Energy transfer and efficiency
Different types of energy can be transferred from one form to another. For example, chemical
energy is transferred into kinetic energy in a car engine. The process of transferring energy is
shown using an energy transfer diagram. A very efficient device can transfer a greater
proportion of useful energy.
Heat can be transferred by conduction, convection and radiation. Dark matt surfaces are better at
absorbing heat energy than light shiny surfaces. Heat energy can be lost from homes in many
different ways. There are different ways to reduce these heat losses.
Forms of energy
You should be able to recognise the main types of energy.
Type of energy
Magnetic
Energy in magnets and electromagnets
Kinetic
The energy in moving objects. Also called movement
energy.
Heat
Also called thermal energy.
Light
Also called radiant energy.
Gravitational
potential
Stored energy in raised objects.
Chemical
Stored energy in fuel, foods and batteries.
Sound
Energy released by vibrating objects.
Electrical
Energy in moving or static electric charges.
Elastic potential
Stored energy in stretched or squashed objects.
Nuclear
Stored in the nuclei of atoms.
Energy transfer diagrams
The energy transfer diagram (below) shows the useful energy transfer in a car engine. You can
see that a car engine transfers chemical energy, which is stored in the fuel, into kinetic energy in
the engine and wheels.
This diagram shows the energy transfer diagram for the useful energy transfer in an electric lamp.
You can see that the electric lamp transfers or converts electrical energy into light energy.
Notice that these energy transfer diagrams only show the useful energy transfers. However, car
engines are also noisy and hot, and electric lamps also give out heat energy.
Sankey diagrams
Sankey diagrams summarise all the energy transfers taking place in a process. The thicker the
line or arrow, the greater the amount of energy involved. The Sankey diagram for an electric lamp
(below) shows that most of the electrical energy is transferred as heat rather than light.
Efficiency
You should know that energy can be 'wasted' during energy transfers, and you should be able to
calculate the efficiency of a device.
'Wasted' energy
Energy cannot be created or destroyed. It can only be transferred from one form to another or
moved. Energy that is 'wasted', like the heat energy from an electric lamp, does not disappear.
Instead, it is transferred into the surroundings and spreads out so much that it becomes very
difficult to do anything useful with it.
Electric lamps
Ordinary electric lamps contain a thin metal filament that glows when electricity passes through it.
However, most of the electrical energy is transferred as heat energy instead of light energy. This
is the Sankey diagram for a typical filament lamp.
Modern energy-saving lamps work in a different way. They transfer a greater proportion of
electrical energy as light energy. This is the Sankey diagram for a typical energy-saving lamp.
From the diagram, you can see that much less electrical energy is transferred, or "wasted", as
heat energy.
Calculating efficiency
The efficiency of a device such as a lamp can be calculated using this equation:
efficiency = useful energy transferred/energy supplied × 100
The efficiency of the filament lamp is 10 ÷ 100 ×100 = 10%. This means that 10% of the
electrical energy supplied is transferred as light energy (90% is transferred as heat energy).
The efficiency of the energy-saving lamp is 75 ÷ 100 × 100 = 75%. This means that 75% of the
electrical energy supplied is transferred as light energy (25% is transferred as heat energy).
Note that the efficiency of a device will always be less than 100%.
Heat transfer
You should know that heat energy can be transferred from one place to another by conduction,
convection and radiation.
Conduction
Heat energy can move through a substance by conduction. Metals are good conductors of heat,
but non-metals and gases are usually poor conductors of heat. Poor conductors of heat are called
insulators. Heat energy is conducted from the hot end of an object to the cold end.
Convection
Liquids and gases are fluids. The particles in these fluids can move from place to place.
Convection occurs when particles with a lot of heat energy in a liquid or gas move and take the
place of particles with less heat energy. Heat energy is transferred from hot places to cooler
places by convection.
Radiation
Objects release heat energy as infrared radiation. The hotter an object is, the more infrared
radiation it emits or radiates. No particles are involved in radiation, unlike conduction and
convection, so radiation can even work through the vacuum of space. This is why we can still
feel the heat of the sun although it is 150 million km away from the Earth.
Some surfaces are better than others at reflecting and absorbing infrared radiation. The table
below summarises this.
Colour Finish
Ability as a reflector Ability as an absorber
dark
dull or matt poor
good
light
shiny
poor
good
Many domestic radiators are painted with white gloss paint. They would be better at radiating
heat if they were painted with black matt paint.
Heat transfer (Higher Tier)
You should be able to explain how conduction in metals works and how convection works. You
should also know that radiation involves waves.
Conduction
Metals consist of metal ions (charged particles formed when the metal atoms lose electrons)
packed closely together. Metals have free electrons that can move through the structure of the
metal. This is why metals are good conductors of electricity.
The hotter a piece of metal, the more kinetic energy its ions have as they vibrate. Free electrons
can transfer this energy to cooler parts of the metal. They diffuse through the metal structure,
colliding with other electrons and metal ions as they go.
Convection
Liquids and gases expand when they are heated. This is because the particles in liquids and
gases move faster when they are heated than they do when they are cold. As a result, the
particles take up more volume. This is because the gap between particles widens, while the
particles themselves stay the same size.
The liquid or gas in hot areas is less dense than the liquid or gas in cold areas, so it rises into the
cold areas. The denser cold liquid or gas falls into the warm areas. In this way, convection
currents are set up that transfer heat from place to place.
Radiation
Radiation involves the transfer of heat by infrared radiation. This is a type of electromagnetic
radiation and involves waves.
Reducing heat loss
You should be able to describe how heat energy is lost from buildings and to explain how these
losses can be reduced.
Heat escape routes
The diagram shows some of the sources of heat loss from a house and how to reduce them.
Heat energy is transferred from homes by conduction through the walls, floor, roof and windows.
It is also transferred from homes by convection. For example, cold air can enter the house
through gaps in doors and windows, and convection currents can transfer heat energy in the loft
to the roof tiles. Heat energy also leaves the house by radiation through the walls, roof and
windows.
Ways to reduce heat loss
There are some simple ways to reduce heat loss, including fitting carpets, curtains and draught
excluders.
Heat loss through windows can be reduced using double glazing. There may be air or a vacuum
between the two panes of glass. Air is a poor conductor of heat, while a vacuum can only transfer
heat energy by radiation.
Heat loss through walls can be reduced using cavity wall insulation. This involves blowing
insulating material into the gap between the brick and the inside wall, which reduces the heat loss
by conduction. The material also prevents air circulating inside the cavity, therefore reducing heat
loss by convection.
Heat loss through the roof can be reduced by laying loft insulation. This works in a similar way to
cavity wall insulation.
Energy, work and power
Work done and energy transferred are measured in joules (J). The work done on an object can
be calculated if the force and distance moved are known. Power is the rate of energy transfer
and it is measured in watts (W).
Objects raised against the force of gravity contain gravitational potential energy. The weight of a
1kg mass on Earth is 10N.
Elastic objects gain elastic potential energy when they are squashed or stretched. Moving objects
have kinetic energy. The more mass they contain and the faster they move, the more kinetic
energy they contain.
Work, force and distance
You should know and be able to use the relationship between work done, force applied and
distance moved.
Background
Work and energy are measured in the same unit, the joule (J). When an object is moved by a
force, energy is transferred and work is done. But work is not a form of energy, it is one of the
ways in which energy can be transferred.
The equation
This equation shows the relationship between work done, force applied and distance moved:
The distance involved is the distance moved in the direction of the applied force.
For example, a force of 10N is applied to a box to move it 2m along the floor. What is the work
done on the box?
The work done is 10 × 2 = 20J.
Weight and gravitational potential energy
Weight
You should know and be able to use the relationship between weight, mass and gravitational field
strength. Gravitational field strength is often simply reffered to as gravity or g.
This equation shows the relationship between weight, mass and gravitational field strength:
The gravitational field strength on the Earth’s surface is about 10N/kg. This is quite handy
because all you need to do to convert between weight and mass is to multiply the mass by 10.
For example, a 1kg bag of sugar weighs 1 × 10 = 10N.
Gravitational potential energy
If you lift a book up onto a shelf you have to do work against the force of gravity. The book has
gained gravitational potential energy. Any object that is raised against the force of gravity stores
gravitational potential energy.
Elastic potential energy
You should know how objects store elastic potential energy.
Stretching and squashing
Elastic objects such as elastic bands and squash balls can change their shape. They can be
stretched or squashed, but energy is needed to change their shape. This energy is stored in the
stretched or squashed object as elastic potential energy.
Bouncing balls
Several energy transfers happen when a squash ball is dropped onto a table and bounces up
again.
When the ball is stationary above the table, its gravitational potential energy (GPE) is at a
maximum. It has no kinetic energy (KE), or elastic potential energy (EPE).
As the ball falls, its GPE is transferred to KE and the ball accelerates towards the table.
When the ball hits the table, the KE is transferred to EPE as the ball squashes. As the ball
regains its shape, the EPE is transferred to KE and it bounces upwards.
When the ball reaches the top of its travel, all the KE has been transferred to GPE again. Note
that the ball will be lower than it was when it was first dropped, because some energy is also
transferred as heat and sound to the surroundings.
Kinetic energy
You should know that moving objects have kinetic energy.
Bigger and faster
Every moving object has kinetic energy (sometimes called movement energy). The more mass an
object has and the faster it is moving, the more kinetic energy it has.
The pendulum
The pendulum is a simple machine for transferring gravitational potential energy to kinetic
energy, and back again.
When the bob is at the highest point of its swing it has no kinetic energy, but its gravitational
potential energy is at a maximum. As the bob swings downwards, gravitational potential energy is
transferred to kinetic energy and the bob accelerates.
At the bottom of its swing, the bob’s kinetic energy is at a maximum and its gravitational potential
energy is at a minimum.
As the bob swings upwards, its kinetic energy is transferred to gravitational potential energy
again. At the top of its swing, it once again has no kinetic energy, but its gravitational potential
energy is at a maximum.
Note that the bob’s swing will become lower with each swing, because some energy is also
transferred as heat to the surroundings.
Power
You should know and be able to use the relationship between power, work done and time taken.
Background
Power is a measure of how quickly energy is transferred. The unit of power is the watt (W).
The equation
This equation shows the relationship between power, work done and time taken:
The more energy that is transferred in a certain time, the greater the power. A 60W light bulb
transfers less electrical energy each second than a 100W light bulb.
An example
A winch lifts a 10N weight by 2m in 5s.
What is the power of the motor?
First calculate the work done by the motor
Work done = force × distance, so:
Work done = 10 × 2 = 20J
Next calculate the power of the motor:
Power = work ÷ time, so:
Power = 20 ÷ 5 = 4W
Energy, work and power (Higher Tier)
It is possible to calculate the change in gravitational potential in an object if its weight and change
in height are known. It is also possible to calculate the kinetic energy of an object if its mass and
speed are known.
Gravitational potential energy
You should know and be able to use, the relationship between change in gravitational potential
energy, weight and change in height.
The equation
This equation shows the relationship between weight, mass and gravitational field strength:
For example, if a 1N weight is raised by 5m it gains 1 × 5 = 5J of gravitational potential energy.
An example
What is the change in gravitational potential energy when a 1kg mass is raised from 1m above
ground to 3m above ground?
First work out the weight of the object:Weight = mass × gravitational field strength
Weight = 1 × 10 = 10N
Next work out the change in height:
Change in height = end height – start height = 3 – 1 = 2m
Finally, work out the change in gravitational potential energy:
Change in gravitational potential energy = weight × change in height
Change in gravitational potential energy = 10 × 2 = 20J
Kinetic energy
You should know and be able to use, the relationship between kinetic energy, mass and speed.
The equation
This equation shows the relationship between kinetic energy, mass and speed:
An example
What is the kinetic energy of a 1000kg car travelling at 10m/s?
kinetic energy = 1/2 × mass × speed²
kinetic energy = 1/2 × 1000 × 10² = 1/2 × 1000 × 100 = 50,000J (or 50kJ)