F.2 Forces and Hooke's Law
Investigating Newton's laws of motion, contact vs non-contact forces, friction, and the elastic stretching of springs.
Questions to explore
- ? Why do objects change their motion — or refuse to?
- ? How far can we stretch a material before it stops springing back?
💡 Key ideas, explained simply
🤝 Contact vs non-contact forces
Contact forces need objects to touch: friction, tension in a rope, the normal (support) force, air resistance.
Non-contact forces act across a gap through a *field*: gravity, magnetism, and electrostatic force. A dropped ball falls because Earth pulls it with gravity — nothing has to touch it.
🪢 Balanced vs unbalanced forces
When forces are balanced (resultant = ) an object stays still or keeps moving at constant velocity — that is Newton's first law.
When forces are unbalanced, the object accelerates in the direction of the resultant force, following . Bigger resultant force → bigger acceleration; more mass → smaller acceleration.
🔗 Hooke's law and springs
Pull a spring and it stretches; the extension is proportional to the force — double the force, double the stretch. This is Hooke's law, , where is the spring constant (stiffness).
But only up to the elastic limit. Stretch it too far and it deforms permanently and never returns to its original length.
📖 Key terms
- Force
- A push or pull, measured in newtons (N).
- Resultant force
- The single force equal to all forces added together (with direction).
- Free-body diagram
- A sketch showing every force acting on one object as labelled arrows.
- Spring constant
- How stiff a spring is, in N/m — the gradient of a force–extension graph.
- Elastic limit
- The point beyond which a spring is permanently deformed.
- Friction
- A contact force that opposes motion between surfaces.
1 Key Formulas
✏️ Worked example
Use Hooke's law
A spring has a spring constant . What force is needed to stretch it by ?
- 1
Write the formula
- 2
List the values
, extension .
- 3
Substitute
F = 6 N — and this only holds while the spring is below its elastic limit.
🛏️ Physics around you
Bathroom scales, mattress springs, and the suspension in a car all use Hooke's law. A weighing machine turns the stretch (or squash) of a spring into a reading, because the compression is proportional to your weight.
🎯 Nail it in the exam
Hooke’s Law Investigations & Graphs
Hooke’s law is a core practical. Exam questions often show a force–extension graph and ask you to:
- Determine the spring constant from the gradient.
- Identify the limit of proportionality (point where graph stops being a straight line).
- Explain that beyond the elastic limit the spring is permanently deformed.
Key formula: (when using applied force) – the gradient of a force–extension graph gives .
MYP command terms used:
- *Determine*: Find the value, often from a graph.
- *Explain*: “The spring obeys Hooke’s law until the extension reaches X cm because the graph is a straight line through the origin.”
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Always convert extension to meters.
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When calculating from a graph, select two points far apart on the straight section.
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Many past questions ask: ‘Why does the spring not return to its original length after a large force?’ – Answer: it has exceeded its elastic limit and undergone plastic deformation.
Resultant Forces and Equilibrium
Newton’s First Law: An object remains at rest or in uniform motion unless acted on by a resultant force.
Free‑body diagrams are a frequent exam task. Arrows represent forces; their length indicates magnitude.
If an object is stationary or moving at constant speed, forces are balanced → resultant force = 0.
Calculation: , where is the resultant force. If mass is in kg and acceleration in m/s², force is in newtons (N).
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Draw free‑body diagrams with arrows touching the object, labelled clearly.
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Never include ‘centrifugal force’ – it doesn’t exist in MYP.
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If an object accelerates, the resultant force is in the direction of acceleration.
🧠 Check your understanding
Tap an answer to see if you're right — and why.
Q1. A spring with a constant of 50 N/m is stretched by 0.1 meters. What restoring force is exerted by the spring?
Q2. Which of the following is a non-contact force?
📝 Exam-style questions
Try each one, then reveal the model answer.