AQA GCSE Physics Foundation (8463), Foundation tier · Forces
Practise Forces and elasticity. 10 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Stretching, squashing or bending an object needs more than one force. You need F = k e, the difference between elastic and inelastic deformation, the limit of proportionality, force–extension graphs and the required practical on a spring. The equation for elastic potential energy, Ee = ½ k e2, is given on the equations sheet.
Key facts
F = k e (force = spring constant × extension)
Units: F in N, k in N/m, e in m
Extension = stretched length − original length
Elastic deformation: returns to original shape; inelastic deformation: does not
F ∝ e up to the limit of proportionality
Gradient of a force–extension graph (force on the y-axis) = k
Notes
Changing shape
To stretch, bend or compress an object you need more than one force. To stretch a spring, you pull on both ends, or hang a weight from it while a clamp holds the top.
Elastic deformation: the object returns to its original length and shape when the forces are removed.
Inelastic deformation: the object does not return to its original length and shape when the forces are removed.
Force and extension: F = k e
diagram
force = spring constant × extension: F = k e
F in newtons (N), k in newtons per metre (N/m), e in metres (m).
Extension is the increase in length: extension = stretched length − original length. The same equation works for compression.
Extension = stretched length − original length.
The extension of an elastic object is directly proportional to the force applied, provided the limit of proportionality is not exceeded.
A stiffer spring has a larger spring constant: it needs a bigger force for each metre of extension.
Force–extension graphs
diagram
With force on the y-axis and extension on the x-axis, the graph is a straight line through the origin (linear) up to the limit of proportionality.
The gradient of this straight section is the spring constant, k.
Beyond the limit of proportionality the line curves (non-linear): extension is no longer proportional to force.
Straight up to the limit of proportionality (here k = 4.0 ÷ 0.16 = 25 N/m), then it curves.
Required practical: force and extension of a spring
diagram
Clamp the spring next to a vertical metre rule and measure its original length.
Hang weights in equal steps. Each time, measure the new length and calculate the extension. Read the ruler at eye level, using a pointer on the bottom of the spring.
Force and extension of a spring: add masses in equal steps and read the pointer each time.
Plot force (the weight added) against extension.
How to answer each type of question
Calculate using F = k e
2 to 3 marksGrade 5
Work out the extension (new length − original length).
Convert it to metres.
Substitute into F = k e (or rearrange for k or e).
Example. A spring has a spring constant of 25 N/m. Its original length is 12.0 cm. A force stretches it to a length of 18.0 cm. The limit of proportionality is not exceeded. Calculate the force.
Show the model answerHide the model answer
extension = 18.0 − 12.0 = 6.0 cm = 0.060 m (1) F = 25 × 0.060 (1) F = 1.5 N (1)
Don’t lose marks
Using the stretched length instead of the extension.
Forgetting to convert cm or mm to metres.
Using Ee = ½ k e2 beyond the limit of proportionality.
Plotting extension on the y-axis and calling the gradient k. With extension on the y-axis, the gradient is 1 ÷ k.
Squaring k × e instead of squaring only the extension.
More tips
Memory tricks
Extension, not length: always subtract the original length first.
cm to m: divide by 100, so 6.0 cm = 0.060 m.
Stiff spring = steep force–extension line = big k.
For ½ k e2, square the extension first, then multiply by k, then halve.
Exam technique
F = k e must be recalled; Ee = ½ k e2 is on the equations sheet.
Before using a graph, check which quantity is on each axis.
In method questions, name the instrument (metre rule), what you measure (length), what you calculate (extension) and what you plot.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 3
Explain why more than one force is neededTo stretch, bend or compress an object, forces must act on it in different directions.
Grade 4
Distinguish elastic and inelastic deformationAn elastically deformed object returns to its original shape when the forces are removed; an inelastically deformed one does not.
Grade 5
Calculate force or extension with F = keFor example, k = 40 N/m and e = 0.15 m give F = 6.0 N.
Grade 5
Describe the spring extension required practicalHang known weights on a spring, measure its length each time, calculate the extension and plot force against extension.
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
A spring has a spring constant of 40 N/m. Calculate the force needed to stretch the spring by 0.15 m. Use the equation: force = spring constant × extension
6.0 N
Complete the sentence. Work done in stretching a spring is stored as ............ energy, as long as the spring is not permanently stretched.
Elastic potential.
Name the type of deformation in which the spring stays permanently stretched.
Inelastic deformation.
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy6 marks
(a) A spring hangs from a clamp. A weight is hung from the bottom of the spring and the spring stretches. Why must more than one force act on the spring to stretch it? Tick (✓) one box.[1]
A single force would make the spring move instead of changing its shape.
A single force is always too small to stretch a spring.
Two forces are needed to double the extension.
The weight of the spring must be balanced first.
(b) Describe the difference between elastic deformation and inelastic deformation.[2]
(c) A spring has a spring constant of 40 N/m. Calculate the force needed to stretch the spring by 0.15 m. Use the equation: force = spring constant × extension[2]
(d) A diver stands on the end of a diving board and the board changes shape. Name the type of change of shape that happens to the diving board.[1]
Show the answer and mark scheme
(a)Answer: A single force would make the spring move instead of changing its shape.
(b)Answer: Elastic: returns to its original shape when the force is removed. Inelastic: does not return to its original shape.
elastic deformation: the object returns to its original shape / length when the force is removed
inelastic deformation: the object does not return to its original shape / length when the force is removed
(c)Answer: 6.0 N
F = 40 × 0.15
6.0 (N)
(d)Answer: Bending.
bending
Question 2Medium4 marks
An archer pulls back a bowstring, storing elastic potential energy in the bow.
(a) Describe the energy transfer that occurs from the moment the archer releases the bowstring to the moment just after the arrow leaves the bow.[2]
(b) Explain why the archer must apply a bigger force to pull the bowstring back further.[2]
Show the answer and mark scheme
(a)Answer: From the bow’s elastic potential energy store mainly to the arrow’s kinetic energy store; some is dissipated to the surroundings by heating and as sound.
energy is transferred from the elastic potential energy store of the bow mainly to the kinetic energy store of the arrow
some energy is dissipated to the surroundings: to thermal energy stores (because of friction and vibrations) and as sound
(b)Answer: A bigger extension of the bow needs a bigger force (like a spring, F = k e).
pulling the string back further gives the bow a greater extension (deformation)
the force needed increases with extension (like a spring, F = k e, if the bow stays within its limit of proportionality)