Cambridge IGCSE Physics 0625
1.5 Forces
Detailed Core and Extended notes covering effects of forces, springs, friction, circular motion, moments, equilibrium and centre of gravity.
2026-2028 syllabus
Syllabus checklist
1.5.1 Effects of forces
Core
- Know that forces may produce changes in the size and shape of an object.
- Sketch, plot and interpret load-extension graphs for an elastic solid and describe the associated experimental procedures.
- Determine the resultant of two or more forces acting along the same straight line.
- Know that an object either remains at rest or continues in a straight line at constant speed unless acted on by a resultant force.
- State that a resultant force may change the velocity of an object by changing its direction of motion or its speed.
- Describe solid friction as the force between two surfaces that may impede motion and produce heating.
- Know that friction, or drag, acts on an object moving through a liquid.
- Know that friction, or drag, acts on an object moving through a gas, for example air resistance.
Supplement
- Define the spring constant as force per unit extension and recall and use the equation k = F ÷ x.
- Define and use the term limit of proportionality for a load-extension graph and identify this point on the graph.
- Recall and use the equation F = ma and know that the force and acceleration are in the same direction.
- Describe qualitatively motion in a circular path caused by a force perpendicular to the motion.
1.5.2 Turning effect of forces
Core
- Describe the moment of a force as a measure of its turning effect and give everyday examples.
- Define the moment of a force as moment = force × perpendicular distance from the pivot, and recall and use this equation.
- Apply the principle of moments to situations with one force on each side of the pivot, including the balancing of a beam.
- State that when there is no resultant force and no resultant moment, an object is in equilibrium.
Supplement
- Apply the principle of moments to other situations, including those with more than one force on each side of the pivot.
- Describe an experiment to demonstrate that there is no resultant moment on an object in equilibrium.
1.5.3 Centre of gravity
Core
- State what is meant by centre of gravity.
- Describe an experiment to determine the position of the centre of gravity of an irregularly shaped plane lamina.
- Describe qualitatively the effect of the position of the centre of gravity on the stability of simple objects.
Key scientific language
Definitions
Force
A push or pull that can change an object's motion, size or shape.
Resultant force
The single force that has the same effect as all the forces acting on an object together. It is also called the net force.
Friction
A force between surfaces that opposes or impedes relative motion and may produce heating.
Drag
A resistive force that opposes an object's motion through a liquid or gas.
Spring constant
The force required per unit extension of a spring. Its SI unit is N/m.
Limit of proportionality
The point beyond which extension is no longer directly proportional to the applied load.
Moment
The turning effect of a force about a pivot.
Principle of moments
For an object in rotational equilibrium, total clockwise moment equals total anticlockwise moment about the same pivot.
Equilibrium
A state in which there is no resultant force and no resultant moment.
Centre of gravity
The point through which the whole weight of an object may be considered to act.
Plane lamina
A thin, flat object whose mass can be considered to lie in a single plane.
Core
Effects of forces
What can a force do?
A force is a push or a pull. It can cause an object at rest to begin moving. If an object is already moving, a resultant force can increase its speed, decrease its speed or change its direction.
Because velocity includes both speed and direction, changing either the speed or direction changes the object's velocity. A force can also stretch, compress, bend or otherwise change the size or shape of an object.
Resultant force
Usually, more than one force acts on an object. The resultant force is the single force that would have the same overall effect as all these forces acting together. Force is a vector quantity, so both magnitude and direction must be considered.
For forces acting along the same straight line, choose one direction as positive. Add the forces acting in that direction and subtract forces acting in the opposite direction. The direction of the larger total determines the direction of the resultant.
Example
A force of 25 N acts forwards and a force of 10 N acts backwards.
Resultant force = 25 N - 10 N = 15 N forwards.
Motion when the resultant force is zero
If there is no resultant force on an object, an object at rest remains at rest. An object that is already moving continues at constant speed in a straight line.
An object resting on a table has a downward weight and an upward support force from the table. Because it remains at rest, these forces are balanced and the resultant force is zero.
Friction
Friction is a force between two surfaces that opposes or impedes their relative motion. The interaction between the surfaces can transfer energy by heating, so both surfaces may become warmer.
If friction acts on a moving object and there is no sufficient forward force, the resultant force acts backwards. The object slows down and may eventually stop.
Solid friction
Solid friction acts when two solid surfaces are in contact. It resists movement between the surfaces and can produce heating. The amount of friction is affected by the nature and roughness of the surfaces and by how strongly the surfaces are pressed together.
Drag in a liquid
An object moving through a liquid experiences drag. This force acts opposite to the motion, making movement through the liquid more difficult. Drag generally increases when the object's speed increases and also depends on the liquid's viscosity and the object's shape.
Drag in a gas
An object moving through a gas also experiences drag. Air resistance is drag caused by motion through air. It acts opposite to the object's motion and generally increases with speed and exposed surface area.
A bicycle, car or aircraft experiences air resistance. A larger drag force means that more driving force and energy are required to maintain a constant speed. This increases fuel use in a vehicle or the effort required by a cyclist.
Core practical method
Load-extension experiment
This experiment investigates how the extension of a spring changes as the applied load increases.
Apparatus
Clamp stand, boss and clamp, spring, metre rule, pointer, mass hanger and known masses.
Method
- 1
Secure the spring to the clamp stand and place a vertical metre rule beside it. The ruler should be close to the spring without touching it.
- 2
Measure and record the spring's initial unloaded length, L0. At this stage, the extension is zero.
- 3
Add a 20 g mass to the end of the spring. Allow the spring to stop moving, then record its new length, L.
- 4
Calculate the extension by subtracting the original length from the new length.
- 5
Add another 20 g mass. Record the total mass, new spring length and extension.
- 6
Continue adding masses in equal steps, allowing the spring to become stationary before every reading.
- 7
Convert each total mass from grams to kilograms and calculate its weight. This weight is the load applied to the spring.
- 8
Plot extension on the vertical axis against load on the horizontal axis. Draw a suitable straight line or smooth curve of best fit.
Calculating extension
- x is extension.
- L is the loaded length.
- L0 is the original unloaded length.
Calculating the load
- W is weight or load in newtons (N).
- m is mass in kilograms (kg).
- g is gravitational field strength, approximately 9.8 N/kg near Earth's surface.
Accuracy and safety
- Read the ruler at eye level to reduce parallax error.
- Use a pointer to make the spring's position easier to read.
- Wait for the spring to stop moving before taking each measurement.
- Repeat readings and calculate averages where appropriate.
- Add masses carefully and do not overload the spring.
- Keep feet clear of the masses in case they fall.
Example results
| Mass (g) | Mass (kg) | Load (N) | Spring length (cm) | Extension (cm) |
|---|---|---|---|---|
| 0 | 0 | 0 | 20 | 0 |
| 20 | 0.020 | 0.20 | 22 | 2 |
| 40 | 0.040 | 0.39 | 24 | 4 |
| 60 | 0.060 | 0.59 | 26 | 6 |
| 80 | 0.080 | 0.78 | 28 | 8 |
| 100 | 0.100 | 0.98 | 30 | 10 |
| 120 | 0.120 | 1.18 | 34 | 14 |
| 140 | 0.140 | 1.37 | 42 | 22 |
The loads are calculated using g = 9.8 N/kg and are rounded to two decimal places.
Interpreting the graph
The initial straight section shows that equal increases in load produce equal increases in extension. When the graph begins to curve, extension is no longer directly proportional to load.
A steeper extension-against-load graph represents a spring that extends more for each newton of force. Such a spring has a smaller spring constant than a spring with a less steep graph.
Supplement only
Extended forces
Hooke's law and spring constant
Up to the limit of proportionality, the extension of a spring is directly proportional to the applied force. Therefore, doubling the force doubles the extension while the spring remains within this proportional region.
Spring constant
- k is the spring constant in N/m.
- F is the applied force in N.
- x is the extension in m.
A larger spring constant means that the spring is stiffer because more force is required to produce the same extension. The force and extension units must match the unit used for the spring constant. For an answer in N/m, extension must be converted to metres.
Limit of proportionality
The limit of proportionality is the point on a load-extension graph where extension stops being directly proportional to load. Up to this point, the graph is a straight line through the origin and F ∝ x.
Beyond the limit of proportionality, the graph curves because equal increases in load no longer produce equal increases in extension.
The limit of proportionality should not be confused with the elastic limit. The elastic limit concerns whether the object returns to its original shape after the force is removed, while the syllabus point here concerns proportionality on the graph.
Resultant force and acceleration
A non-zero resultant force causes acceleration. Acceleration may involve an increase in speed, a decrease in speed or a change in direction.
Force, mass and acceleration
- F is resultant force in newtons (N).
- m is mass in kilograms (kg).
- a is acceleration in m/s2.
The acceleration is always in the same direction as the resultant force. For a fixed mass, a larger resultant force produces a larger acceleration. For a fixed resultant force, a larger mass produces a smaller acceleration.
Motion in a circular path
An object moving in a circle requires a force directed towards the centre of the circle. This force is perpendicular, at 90 degrees, to the object's instantaneous direction of motion.
The inward force changes the direction of the velocity continuously. Therefore, an object moving at constant speed in a circle is still accelerating because its velocity is changing.
- If mass and radius remain constant, a larger force is required for a greater speed.
- If mass and speed remain constant, increasing the force decreases the radius of the circular path.
- If speed and radius remain constant, a larger mass requires a larger inward force.
Motion of the satellite
The satellite moves at constant speed, but its direction changes at every point in the orbit. Its velocity therefore changes continuously, which means that the satellite is accelerating.
Earth's gravitational force acts towards the centre of the orbit and perpendicular to the satellite's instantaneous direction of travel. This inward force prevents the satellite from continuing in a straight line and continually turns its velocity, producing the circular path.
Core and Supplement
Turning effect of forces
Moment of a force
A moment is the turning effect of a force about a pivot. The size of the moment depends on the force and the perpendicular distance between the pivot and the force's line of action.
- A bottle opener turns about the edge of a bottle cap.
- A door turns about its hinges when a force is applied to its handle.
- A spanner turns a nut about the nut's centre.
Moment of a force
- F is force in newtons (N).
- d is perpendicular distance from the pivot in metres (m).
- The SI unit of moment is newton metre (N m).
Worked example: calculating a moment
Force = 40 N and perpendicular distance = 20 cm.
Convert the distance: 20 cm ÷ 100 = 0.20 m.
moment = 40 × 0.20
moment = 8.0 N m
Worked example: finding the force
A moment of 8.0 N m must be produced using a spanner with a perpendicular distance of 0.15 m.
8.0 = F × 0.15
F = 8.0 ÷ 0.15
F = 53.3 N
A shorter distance from the pivot requires a larger force to produce the same moment.
Principle of moments
When an object is balanced and has no resultant moment, the total clockwise moment about a pivot equals the total anticlockwise moment about the same pivot.
For rotational equilibrium
- Calculate every moment about the same pivot.
- Use perpendicular distances.
- Use consistent units throughout the calculation.
Worked example 1 (Fig 10)
On each side, a 0.50 kg mass acts 0.80 m from the pivot.
Weight = 0.50 × 9.8 = 4.9 N
Anticlockwise moment = 4.9 × 0.80 = 3.92 N m
Clockwise moment = 4.9 × 0.80 = 3.92 N m
The moments are equal, so the beam balances.
Worked example 2 (Fig 11)
Clockwise side: mass = 0.40 kg and distance = 0.80 m.
Clockwise moment = (0.40 × 9.8) × 0.80 = 3.14 N m
Anticlockwise side: mass = 0.64 kg and distance = 0.50 m.
Anticlockwise moment = (0.64 × 9.8) × 0.50 = 3.14 N m
The moments are equal, so the beam balances.
Supplement: several forces on each side
When several forces act, calculate the moment of every force separately. Add all clockwise moments and add all anticlockwise moments. For balance, the two totals must be equal.
Several forces
Worked example with several forces (Fig 13)
Anticlockwise moments:
(10 N × 90 cm) + (30 N × 50 cm) = 900 N cm + 1500 N cm = 2400 N cm
Clockwise moments:
(30 N × 20 cm) + (20 N × 90 cm) = 600 N cm + 1800 N cm = 2400 N cm
The total moments are equal, so the beam balances.
Equilibrium
An object is in equilibrium only when both of the following conditions are satisfied:
- There is no resultant force, so there is no linear acceleration.
- There is no resultant moment, so there is no turning acceleration.
Experiment: demonstrating no resultant moment
- Place a metre rule on a pivot and adjust it until the unloaded rule is horizontal.
- Hang a known weight at a measured perpendicular distance on one side of the pivot.
- Hang another known weight on the opposite side.
- Adjust its distance until the metre rule is horizontal and stationary.
- Calculate the clockwise and anticlockwise moments.
- The two moments should be equal within experimental uncertainty, showing that the resultant moment is zero.
Core
Centre of gravity
The centre of gravity is an imaginary point through which the whole weight of an object may be considered to act. For a regularly shaped object of uniform density, it is usually at the geometric centre. For an irregular object, its position can be found experimentally.
Experiment: centre of gravity of an irregular plane lamina
A plane lamina is a thin, flat object whose mass is concentrated approximately in one plane.
- 1
Cut an irregular shape from cardboard or another thin, rigid material.
- 2
Make at least three small holes close to different edges of the lamina.
- 3
Suspend the lamina freely from the first hole using a pin or nail.
- 4
Hang a plumb line from the same suspension point.
- 5
Wait until the lamina and plumb line are stationary. Draw a line on the lamina along the plumb line.
- 6
Repeat the procedure using the other holes.
- 7
The point where the lines intersect is the centre of gravity of the lamina.
Centre of gravity and stability
An object is generally more stable when it has a low centre of gravity and a wide base. It must then be tilted through a larger angle before the vertical line through its centre of gravity reaches the edge of its base.
When the vertical line through the centre of gravity remains inside the base, the object's weight produces a restoring moment and the object returns towards its original position.
When this vertical line moves outside the base, the object's weight produces a moment that makes it topple. Objects with a high centre of gravity and narrow base therefore topple more easily.
Cambridge-style practice
Practice questions
State three different effects that a force may have on an object.
- Change its speed.
- Change its direction of motion.
- Change its size or shape.
Two horizontal forces act on a box: 18 N to the right and 7 N to the left. Determine the resultant force.
resultant force = 18 - 7
resultant force = 11 N to the right
State the possible motion of an object when no resultant force acts on it.
The object remains at rest, or it continues moving at constant speed in a straight line.
Explain why a moving car slows down when the driving force is removed.
- Friction and air resistance continue to act backwards.
- There is a resultant force opposite to the motion.
- The car decelerates and slows down.
A spring has an original length of 18.0 cm and a loaded length of 24.5 cm. Calculate its extension.
extension = loaded length - original length
extension = 24.5 - 18.0
extension = 6.5 cm
A force of 35 N acts at a perpendicular distance of 0.40 m from a pivot. Calculate the moment.
moment = force × perpendicular distance
moment = 35 × 0.40
moment = 14 N m
A 12 N force acts 0.30 m to the left of a pivot. Calculate the force required 0.20 m to the right to balance it.
anticlockwise moment = 12 × 0.30 = 3.6 N m
clockwise moment = F × 0.20
F × 0.20 = 3.6
F = 3.6 ÷ 0.20
F = 18 N
Explain why a low centre of gravity and a wide base improve stability.
- The object must be tilted further before the vertical line through its centre of gravity reaches the edge of the base.
- It is therefore less likely to topple.
A spring extends by 0.060 m under a load of 12 N. Calculate its spring constant.
k = F ÷ x
k = 12 ÷ 0.060
k = 200 N/m
A resultant force of 24 N acts on a 6.0 kg object. Calculate its acceleration.
F = ma
a = F ÷ m
a = 24 ÷ 6.0
a = 4.0 m/s2
Explain why an object moving at constant speed in a circle is accelerating.
- The object's direction changes continuously.
- Velocity includes direction, so its velocity changes.
- A change in velocity means that the object is accelerating.
- The acceleration is directed towards the centre of the circle.
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