IGCSE Co-ordinated Sciences · Area 3 · Physics

Motion, Forces and Energy

Motion, forces and energy brings together the mechanics of everything that moves: measuring physical quantities, describing motion, mass and weight, density, forces and momentum, energy, work and power, and pressure.

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Syllabus coverage

  • Describe the use of rulers and measuring cylinders to find a length or a volume
  • Describe how to measure a variety of time intervals using clocks and digital timers
  • Determine an average value for a small distance and for a short interval of time by measuring multiples, including the period of oscillation of a pendulum
  • Understand that a scalar quantity has magnitude (size) only and that a vector quantity has magnitude and direction
  • Know that the following quantities are scalars: distance, speed, time, mass, energy and temperature
  • Know that the following quantities are vectors: force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength
  • Determine, by calculation or graphically, the resultant of two vectors at right angles, limited to forces or velocities only
  • Define speed as distance travelled per unit time, and recall and use the equation v = s / t
  • Define velocity as speed in a given direction
  • Recall and use the equation average speed = total distance travelled / total time taken
  • Sketch, plot and interpret distance-time and speed-time graphs
  • Determine, qualitatively, from given data or the shape of a distance-time or speed-time graph when an object is at rest, moving with constant speed, accelerating or decelerating
  • Calculate speed from the gradient of a straight-line section of a distance-time graph
  • Calculate the area under a speed-time graph to determine the distance travelled for motion with constant speed or constant acceleration
  • State that the acceleration of free fall g for an object near to the surface of the Earth is approximately constant and is approximately 9.8 m/s2

Part of the IGCSE Co-ordinated Sciences syllabus 0654 / 0973.

Measuring instruments on a physics benchPick the instrument whose range covers the whole quantity, with the finest division you need.Rulerlength, to the nearest millimetre012345678cm5.0 cmStart from the 0 mark, not the end of the rule.Smallest division 1 mm, so read to 0.1 cm.Measuring cylindervolume of a liquid, to the nearest cm320406080100read the bottom of the meniscuseye levelnot from above or belowRead at the bottom of the meniscus, with theeye level with the mark.Digital stopwatchtime interval, to the nearest 0.01 s0:36.42minutes : seconds . hundredthsResolution 0.01 s, but a handstart and stop adds about 0.2 sof reaction time to a reading.The display reads 36.42 s, that is 36 s and 42 hundredths.A digital display has no parallax error.Time many oscillations, then divideA single short time is hard to measure, because thereaction time error is the same for a short interval and along one.20 swings take 36.0 s, so the period isT = t / n = 36.0 / 20 = 1.8 sRepeat and average to reduce random error.Range first, then precision: cover the whole quantity, then pick the instrument with the finer division.Each reading carries the smallest division as its uncertainty: + or - 0.1 cm on a rule, + or - 0.2 s on a stopwatch.
A set of measuring instruments: a metre rule with a millimetre scale, a measuring cylinder showing the meniscus read at eye level, a digital stopwatch and a pair of vernier calipers, with the smallest division of each instrument marked.

Physical Quantities and Measurement Techniques

Physics starts with measurement, so this topic covers the instruments you use to find a length, a volume and a time, and the methods that make those readings reliable. It then splits quantities into scalars and vectors, and shows how to find the resultant of two vectors at right angles.

Measuring instruments on a physics benchPick the instrument whose range covers the whole quantity, with the finest division you need.Rulerlength, to the nearest millimetre012345678cm5.0 cmStart from the 0 mark, not the end of the rule.Smallest division 1 mm, so read to 0.1 cm.Measuring cylindervolume of a liquid, to the nearest cm320406080100read the bottom of the meniscuseye levelnot from above or belowRead at the bottom of the meniscus, with theeye level with the mark.Digital stopwatchtime interval, to the nearest 0.01 s0:36.42minutes : seconds . hundredthsResolution 0.01 s, but a handstart and stop adds about 0.2 sof reaction time to a reading.The display reads 36.42 s, that is 36 s and 42 hundredths.A digital display has no parallax error.Time many oscillations, then divideA single short time is hard to measure, because thereaction time error is the same for a short interval and along one.20 swings take 36.0 s, so the period isT = t / n = 36.0 / 20 = 1.8 sRepeat and average to reduce random error.Range first, then precision: cover the whole quantity, then pick the instrument with the finer division.Each reading carries the smallest division as its uncertainty: + or - 0.1 cm on a rule, + or - 0.2 s on a stopwatch.

Motion

Motion is the study of how objects move: speed, velocity and acceleration, and the graphs that describe them. This topic covers the equations for speed and acceleration, how to read distance-time and speed-time graphs, and why a falling object reaches terminal velocity.

Mass and Weight

Mass measures the quantity of matter in an object and is the same everywhere, while weight is the gravitational force on that object and changes with the strength of the gravitational field. This topic defines gravitational field strength, uses the equation g = W/m, and explains why g is also the acceleration of free fall.

Density

Density is the mass per unit volume, and it decides whether an object floats or sinks. This topic covers the density equation, how to measure the density of regularly shaped solids, irregular solids and liquids, and how a comparison of densities explains floating, sinking and the layers formed by liquids that do not mix.

Forces

Forces are pushes and pulls that change the motion, size and shape of objects. This topic covers load-extension graphs and the spring constant, resultant forces and Newton's first law, the equation F = ma, friction and drag, motion in a circle, the turning effect of a force and the principle of moments, and the centre of gravity and stability.

Momentum

Momentum is the product of mass and velocity, and it is conserved in every collision and explosion where no external resultant force acts. This topic covers the equation p = mv, impulse as force times time, the link between resultant force and the rate of change of momentum, and the calculations that explain car safety, recoil and collisions.

Energy, Work and Power

Energy is stored in a small number of ways and transferred between them by forces, currents, heating and waves. This topic covers the seven energy stores, the conservation of energy, the equations for kinetic and gravitational potential energy, work done and power, efficiency and Sankey diagrams, and how electricity is generated from renewable and non-renewable resources.

Pressure

Pressure is the force acting on each square metre of a surface, and it explains why a sharp knife cuts and a snowshoe does not sink. This topic covers the pressure equation p = F / A, how the pressure changes with force and with area, how the pressure beneath the surface of a liquid depends on depth and density, and the Extended equation change in p = rho x g x change in h.

Key terms you must be able to define

Scalar quantity
A quantity that has magnitude (size) only, for example distance, speed, time, mass, energy or temperature.
Vector quantity
A quantity that has both magnitude and direction, for example force, weight, velocity, acceleration or momentum.
Resultant
The single vector that has the same effect as two or more vectors acting together.
Displacement
The distance moved in a stated direction from the starting point; a vector quantity, measured in metres (m).
Period
The time for one complete oscillation or cycle, measured in seconds (s).
Meniscus
The curved surface of a liquid in a container; read the bottom of the meniscus, with the eye level with the mark.
Parallax error
An error caused by reading a scale from the wrong angle, so that the eye is not level with the mark.
Resolution
The smallest change in a quantity that an instrument can measure, for example 1 mm on a metre rule.
Speed
The distance travelled per unit time, given by v = s / t and measured in m/s.
Velocity
Speed in a given direction; a vector, measured in m/s, so '20 m/s due east' is a velocity and '20 m/s' is a speed.
Average speed
The total distance travelled divided by the total time taken; the single steady speed that would cover the same journey in the same time.
Acceleration
The change in velocity per unit time, given by a = (v - u) / t and measured in m/s2.

Applied to the real world

Cambridge sets Co-ordinated Sciences in unfamiliar contexts - a hospital, a power station, a farm, a laboratory. Use these as models for how to apply the science, then write your own.

On a building site

Builders check that a corner is a true right angle by marking 3 m along one side and 4 m along the other, then measuring the diagonal between the marks. If the diagonal is 5 m, the angle is exactly 90 deg, because 3, 4 and 5 form a right-angled triangle. The same Pythagoras relationship is used to find the resultant of two forces at right angles.

In a hospital

A nurse measures out a liquid medicine in a small measuring cylinder, reading the bottom of the meniscus at eye level so that the dose is accurate. The volume must be measured in a cylinder of the right size: using a large cylinder for a few cm3 would make the reading far less precise. Pulse rate is timed with a digital timer, counting the beats over a full minute.

In a car

A car's speedometer shows speed, which is a scalar: it tells you how fast but not which way. The satellite navigation system works with displacement and velocity, because it must know the direction of travel as well as the distance covered. This is why the navigation system can tell that you have arrived back where you started, even after driving several kilometres.

At home

A measuring cylinder is used in the kitchen to measure liquid for a recipe, and the oven timer is a digital timer used to measure an interval of minutes. A pendulum clock uses the regular period of a swinging pendulum to keep time: the period depends only on the length of the pendulum, not on the mass of the bob, so it stays the same swing after swing.

In a sports science laboratory

Sprinters are timed with light gates, which start and stop automatically as the runner breaks a beam of light. This removes the reaction-time error that a hand-held stopwatch would introduce. The same laboratory measures the forces a rower applies with a force plate, and combines two forces at right angles to find the resultant the boat actually experiences.

On the road

A speed camera times a car over a measured stretch of road and divides the distance by the time to get the average speed. A car that covers the 500 m between the marks in 25 s has an average speed of 500 / 25 = 20 m/s, which is 72 km/h. The camera uses average speed because it is the steady speed that would cover the section in the same time, and that is what the law limits.

Flashcards

Click a card to flip it. Mark honestly — the tracker uses this.

Q1What is a scalar quantity?
A quantity that has magnitude (size) only, such as distance, speed, time, mass, energy or temperature.
Q2What is a vector quantity?
A quantity that has both magnitude and direction, such as force, weight, velocity, acceleration or momentum.
Q3Give three scalar quantities.
Any three of: distance, speed, time, mass, energy, temperature.
Q4Give three vector quantities.
Any three of: force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength.
Q5How do you measure the volume of an irregular solid?
Use the displacement method: record the starting water volume in a measuring cylinder, lower the solid in gently, and subtract the starting reading from the final reading.
Q6Where do you read the level of water in a measuring cylinder, and how?
At the bottom of the meniscus, with your eye level with the mark, to avoid a parallax error.
Q7How do you find the period of a pendulum accurately?
Time 20 complete oscillations, then divide the total time by 20: period = total time / number of oscillations.
Q8Why is it better to time 20 oscillations of a pendulum than one?
The total time is much longer, so the reaction-time error of the stopwatch is a much smaller fraction of the measurement.
Q9State the equation for the resultant of two vectors at right angles.
resultant = sqrt(a2 + b2), where a and b are the two vectors, and tan theta = a / b gives the angle.
Q10Two forces of 3.0 N and 4.0 N act at right angles. What is the resultant?
5.0 N, because sqrt(3.0 x 3.0 + 4.0 x 4.0) = sqrt(9 + 16) = sqrt(25) = 5.0 N.
0 of 10 marked as known

Exam-style questions

9 questions, 24 marks. Write your answer, then reveal the mark scheme and tick each point you actually made. Answering honestly here is what makes the rest of the site useful.

StateAO12 marks
From the list below, state one scalar quantity and one vector quantity. distance, force, mass, time, velocity, energy

Mark scheme — tick each point you actually made

Examiner tip: A scalar has magnitude only and a vector has magnitude and direction. Do not give the same quantity twice, and do not swap the two lists.
DescribeAO23 marks
Describe how a student would use a measuring cylinder to find the volume of an irregularly shaped stone.

Mark scheme — tick each point you actually made

Any 3 of these score full marks. The examiner only needs 3 distinct points - pick the ones you actually made.
Examiner tip: The two readings and the subtraction earn the marks. Mention that the stone is fully covered, and that you read at eye level to avoid a parallax error.
ExplainAO23 marks
A student times 20 complete oscillations of a pendulum instead of one, and then divides the total time by 20. Explain why this gives a more accurate value for the period.

Mark scheme — tick each point you actually made

Examiner tip: The key word is fraction, or percentage. The reaction time itself does not change, but it matters far less when the interval being measured is longer.
CalculateAO23 marks
A student times 20 complete oscillations of a pendulum and records a total time of 36.0 s. Calculate the period of the pendulum and its frequency.

Mark scheme — tick each point you actually made

Examiner tip: Show the division and give the unit for each answer. The period is in seconds and the frequency is in hertz, and frequency = 1 / period.
DetermineAO24 marks
A boat is rowed with a force of 6.0 N towards the east while a current pushes it with a force of 8.0 N towards the north. Determine the resultant force on the boat, giving its magnitude and its direction.

Mark scheme — tick each point you actually made

Examiner tip: Do not add 6.0 and 8.0. Use Pythagoras for the magnitude and tan theta = opposite / adjacent for the angle, then state the direction as well as the size.
ExplainAO23 marks
Explain why velocity is a vector quantity while speed is a scalar quantity.

Mark scheme — tick each point you actually made

Examiner tip: The mark is for direction. Use an example where the speed stays the same but the direction changes, so that the velocity changes.
CompareAO23 marks
Compare distance and displacement, and state which is a scalar and which is a vector.

Mark scheme — tick each point you actually made

Examiner tip: Use the round-trip example to show that you understand the difference. 'Distance is how far, displacement is how far in a stated direction' earns the first two marks.
SuggestAO32 marks
A student must measure the thickness of a single sheet of paper using a ruler that has millimetre divisions. Suggest a method that would give a reliable value.

Mark scheme — tick each point you actually made

Examiner tip: This is the measure-a-multiple-and-divide idea again. One sheet on its own is far thinner than the smallest division on the ruler, so a single measurement would be meaningless.
StateAO11 mark
State what is meant by the velocity of an object.

Mark scheme — tick each point you actually made

Examiner tip: The direction is the mark. A statement of speed alone is not a definition of velocity.

Exam technique for this topic

  • Write the unit with every value. A period of 1.8 on its own scores nothing; it must be 1.8 s, and a frequency must be in hertz (Hz).
  • When you time a multiple, show the division clearly: period = 36.0 / 20 = 1.8 s. The mark is for dividing the total time by the number of oscillations, not for the total itself.
  • For a vector answer, state the direction as well as the size, for example '10 N at 37 deg to the north'. A magnitude on its own is only half an answer.
  • Use Pythagoras for the magnitude of two perpendicular vectors and tan theta = opposite / adjacent for the angle. Never add the magnitudes together.
  • In a method question about a measuring cylinder, say that you read the bottom of the meniscus with your eye level with the mark. That one sentence usually carries a mark.

Why students lose marks here

A student wroteA student read the volume of water in a measuring cylinder by looking down on the surface from above, and recorded the reading.
Why it loses marksReading a scale from the wrong angle gives a parallax error, and the reading is too high or too low depending on which way you look. The volume is also read from the top of the curved surface instead of the bottom, which adds a second error.
The answer that scoresThe cylinder should be standing on a level bench and the eye should be level with the mark, looking straight at the scale. The volume is read at the bottom of the meniscus, the lowest point of the curved water surface. Read this way, the value is the true volume of liquid in the cylinder.
A physics bench with the measuring equipment laid out: a metre rule, a measuring cylinder of water, a digital stopwatch and a pair of vernier calipers.
A student wroteA student timed one complete oscillation of a pendulum, wrote the value down as the period and claimed it was accurate to 0.1 s.
Why it loses marksA hand-operated stopwatch has a reaction-time error of about 0.2 s, which is larger than the value being measured. The student is quoting a precision that the method cannot possibly achieve.
The answer that scoresTime 20 complete oscillations and divide the total time by 20 to get the period. The total time is much longer, so the reaction-time error is only a small fraction of it, and the period comes out far more accurately. Repeat the measurement and average the results to reduce random error further.
A student wroteA student wrote: 'The resultant of a 6.0 N force and an 8.0 N force acting at right angles is 14 N.'
Why it loses marksThe student simply added the two magnitudes. That is only correct when the vectors act along the same line. When they act at right angles, they form a right-angled triangle and the resultant is the hypotenuse.
The answer that scoresresultant = sqrt(6.0 x 6.0 + 8.0 x 8.0) = sqrt(36 + 64) = sqrt(100) = 10 N. The direction is found from tan theta = 6.0 / 8.0 = 0.75, so the resultant is 10 N at 37 deg to the 8.0 N direction, between the two original forces.
A student wroteA student wrote: 'Speed is a vector because it tells you how fast something is going.'
Why it loses marksSpeed has magnitude only, so it is a scalar. The student has confused speed with velocity, which is speed in a stated direction and is the vector quantity.
The answer that scoresSpeed is a scalar quantity, because it has magnitude only: 8 m/s tells you how fast the car moves but not which way. Velocity is a vector quantity, because it is speed in a stated direction, for example 8 m/s due north. A car going round a roundabout at a steady speed has a changing velocity, because its direction is changing.

Where this fits in IGCSE Co-ordinated Sciences

This page is one topic of Cambridge IGCSE Co-ordinated Sciences 0654 / 0973. IGCSE Co-ordinated Sciences is the course home: every area and every topic in Cambridge's own order, the papers you sit and what each one tests, and the exam-practice tools. The full topic list, with each topic linked to its revision page, is on the IGCSE Co-ordinated Sciences syllabus page.