Forces

1. Meet the main forces

A force is a push or pull caused by objects interacting. Forces can change an object’s motion or shape. We measure them in newtons (N).

On the ground: weight, support and friction

Moving through air or water

Pulling and stretching

Across a gap: magnets and charges

2. Describe the push or pull

A force is a push or pull caused by an interaction between objects. Force is measured in newtons, N.

Magnitude means size. “20 N” gives the magnitude; “20 N east” also gives the direction.

3. What is touching what?

Normal contact force acts at right angles to a surface. Tension is a pulling force transmitted through a stretched rope or cable. Identify both objects in an interaction, not just one.

4. Mass and weight are different

Mass is measured in kilograms. Weight is the gravitational force on an object, measured in newtons. A gravitational field is a region where a mass experiences a force.

• Use a calibrated spring balance or newtonmeter to measure weight.
• Weight acts towards Earth’s centre. In a diagram, draw it acting at the object’s centre of mass.
• At a fixed g, W ∝ m: doubling the mass doubles the weight.

Rearrange: m = W ÷ g. For W = 49 N and g = 9.8 N/kg, m = 5.0 kg.

5. Combine forces on one object

The resultant force is one force with the same effect as all the forces on an object together.

1. Same line and same direction: add the forces.
2. Same line and opposite directions: subtract the smaller from the larger.
3. Give the direction of the larger force.

6. Higher only: forces in two dimensions

A free-body diagram shows only the forces acting on the chosen object. Replace the object with a dot or simple outline; label each force and its direction.

1. Choose a scale, such as 1 cm represents 1 N.
2. Draw the first force, then draw the second from its arrowhead.
3. The resultant runs from the first tail to the final head.

Resolving does the reverse: replace one force with two perpendicular components. Draw a rectangle with the original arrow as its diagonal. The two sides show forces with the same combined effect.

For equilibrium, the resultant is zero. A force polygon drawn head to tail closes.

7. A force can transfer energy

Work done is energy transferred by a force moving an object. The distance must be measured along the force’s line of action.

Rearrange: F = W ÷ s and s = W ÷ F. Convert centimetres to metres first. Friction transfers energy to thermal stores, increasing the temperature of objects and surroundings.

8. Stretch, compress or bend

Changing an object’s shape is deformation. A stationary object needs forces at more than one point: pulling both ends of a spring, pressing both ends of a foam block, or supporting a ruler while pushing its middle.

9. A spring as a force meter

Up to its limit of proportionality, extension is directly proportional to force. A graph of force against extension is a straight line through the origin.

Worked example: F = 6.0 N and e = 0.030 m. Then k = F ÷ e = 200 N/m. A larger spring constant means more force is needed for the same extension.

10. Store energy by stretching

A stretching force does work and stores elastic potential energy. If the object is not permanently deformed, the work done equals the energy stored.

• Convert extension to metres before squaring it.
• Doubling extension stores four times as much energy if k stays constant.
• Do not use the final force × extension: the force increased during stretching.

11. Required practical 18: force and extension

1. Measure the unloaded spring length.
2. Add a known weight and wait for the spring to stop moving.
3. Read the new length at eye level. Calculate extension.
4. Repeat for a range of weights. Repeat readings to identify anomalies and calculate means.
5. Plot force against extension. Use the straight region to calculate k.
6. Remove weights to check whether the spring returns to its starting length.

Keep the spring and ruler position the same. Secure the stand, place a tray below the masses and avoid stretching the spring so far that it breaks.

12. Distance or displacement?

Distance is the total path travelled. Displacement is the straight-line change of position, with a direction. A completed lap has a distance greater than zero but zero displacement.

13. How quickly does it move?

Age, fitness, terrain and distance affect a person’s speed. Vehicle, wind and sound speeds also vary with conditions.

Worked example: 600 m in 5.0 min means 600 ÷ 300 = 2.0 m/s. To convert km/h to m/s, multiply by 1000 then divide by 3600.

14. Velocity includes direction

Velocity is speed in a stated direction: for example, 8 m/s north. Two cyclists can have the same speed but different velocities if they travel in opposite directions.

15. Distance–time graphs

Speed = gradient = change in distance ÷ change in time. For the first section: 20 ÷ 4 = 5.0 m/s. Use two well-separated points on a straight line.

16. Higher only: an instant on a curved graph

1. Draw a tangent at the time required.
2. Choose two widely spaced points on the tangent.
3. Calculate its gradient in m/s. This is the speed at that instant.

For the illustrated tangent, (75 − 0) ÷ (10 − 2.5) = 10 m/s. Using the start and finish of the curved journey gives an average instead.

17. Changing velocity

Acceleration is change in velocity per second. Deceleration means slowing down. A positive/negative sign depends on the direction you chose as positive.

A car reaching 20 m/s in 10 s accelerates at about 2 m/s². Free fall close to Earth, without air resistance, is about 9.8 m/s².

Higher only: the area under a velocity–time graph gives displacement. If motion stays in one direction, this is also distance. Split the area into rectangles and triangles or count grid squares. If velocity becomes negative, calculate signed areas for displacement and add the magnitudes for distance.

18. Constant acceleration and distance

For uniform (constant) acceleration, use:

• Square the velocities, not their difference.
• For slowing down, keep signs consistent.
• Take the square root at the end if finding velocity.

19. Why falling objects stop accelerating

1. At release, weight is greater than air resistance: the object accelerates downwards.
2. As it speeds up, air resistance increases. The resultant force and acceleration decrease.
3. Eventually air resistance equals weight. The resultant is zero.
4. The object keeps falling at constant terminal velocity.

The same idea applies to falling through a liquid: the resisting force increases with speed.

20. Newton’s first and second laws

• For constant mass, doubling the resultant force doubles acceleration.
• For constant force, doubling mass halves acceleration.
• Calculate the resultant, not just the driving force, before using F = ma.

Higher only: inertia is the tendency to remain at rest or at constant velocity. Inertial mass measures how difficult velocity is to change: m = F ÷ a.

21. Required practical 19: force, mass and acceleration

1. Measure the card length. Gate speed = card length ÷ time blocking the beam.
2. Use speeds at two gates and travel time between them to find acceleration, or use a motion sensor/data logger.
3. Release from the same position without a push. Repeat each setting and calculate a mean.
4. Use a low-friction track. Account for friction rather than assuming hanger weight is exactly the resultant.
5. Plot a against F at constant mass. For the mass investigation, plot a against 1/m to test inverse proportionality.

Use a catch tray and a trolley stop. Keep the hanging mass from striking the floor during measurement.

22. Newton’s third law

Whenever two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction. They are the same type of force and act on different objects.

23. Stopping takes distance

Example: at 20 m/s with a 0.70 s reaction time, thinking distance = 14 m. Add a 25 m braking distance to get a 39 m stopping distance.

24. Measure reaction time fairly

A partner holds a ruler with zero level with the top of your thumb. They release it without warning; you catch it. Read the fall distance and use a conversion table to find reaction time. Repeat and calculate a mean.

• Keep the hand position, ruler, person and release method the same when testing one factor.
• Practise first; learning can change results.
• Typical reaction times are about 0.2–0.9 s.
• A small laboratory test is not a complete model of driving in traffic.

25. Braking transfers energy

Friction in the brakes does work, reducing the vehicle’s kinetic energy and warming the brakes. Road–tyre grip also limits the braking force.

• Greater speed means greater kinetic energy to transfer.
• At the same braking force, more kinetic energy means a longer braking distance.
• At the same mass, doubling speed makes kinetic energy four times larger. With constant braking force, braking distance is then four times larger.
• A larger braking force gives a larger deceleration, but very large decelerations can overheat brakes or cause loss of control.

26. Higher only: momentum and collisions

Momentum = mass × velocity: p = mv, in kg m/s. Momentum has a direction.

1. Choose a positive direction and give opposite motion a negative sign.
2. Add the momenta of all objects before the event.
3. Set this equal to total momentum afterwards.
4. Do not assume kinetic energy is conserved in a collision. Momentum and energy are different quantities.

1. Follow the force arrows

• Explain why the two force sizes are subtracted here.
• What would happen to the resultant if resistance increased to 700 N?
• Could the car still be moving when its resultant force is zero? Explain.

2. Required practical 18: spring extension

1. Identify the spring, ruler, pointer and load. Explain how you would read the length without parallax error.
2. Plan how to change the force, measure extension and repeat readings.
3. Choose a safety precaution and explain the hazard it reduces.

Read the graph: identify its proportional region. Choose two points in that region and calculate the spring constant in N/m. Explain why you must not use the whole graph as one straight line.

3. Required practical 19: trolley acceleration

• Change force: explain why masses are transferred from the trolley to the hanger rather than simply added.
• Change mass: decide which mass stays fixed and where to add extra masses.
• Measure acceleration: explain how card length, gate timings and the time between speed readings are used.
• Choose controls, repeats and a way to stop the trolley or falling masses safely.

4. Read two different motion graphs

Identify when the robot is stationary. Compare the speeds in the two sloping sections. Use distances and times from the axes to support your answer.

Identify acceleration, constant velocity and deceleration. Explain why a horizontal line has a different meaning on these two graphs.

Higher only: divide the area under the velocity–time graph into simple shapes to find the distance travelled.

5. Higher only: add force vectors

Draw the two forces on squared paper using the stated scale. Measure the resultant’s size and direction. Explain why adding 4 + 3 does not give its magnitude. Enter your measured result in the notebook.

Your practical notebook — RP18 and RP19

Use the figures above to record or plan the spring investigation and both trolley investigations. You can also record your force-arrow and graph observations here.

• State the independent, dependent and control variables.
• Make a table with units and repeated measurements.
• Show how you calculate extension or acceleration and means.
• Describe the graph, what it tells you, uncertainties and a safety precaution.

Your answer sheet

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One final thought

Use a scientific idea and a specific example in your reflection.