Elastic Deformation, Moments and Centre of Gravity

This guide covers the elastic deformation, turning effect and centre of gravity parts of subtopic 1.5 Forces, from Topic 1, Motion, forces and energy, for Cambridge O Level Physics 5054, 2026–2028 series. The balanced/unbalanced forces, friction and circular motion parts of 1.5 are covered separately in Forces and Motion.

Where this fits in 5054

These three ideas share a theme distinct from Forces and Motion: rather than forces changing an object’s velocity, here forces change an object’s shape (elastic deformation), cause rotation about a pivot (moments), or determine whether an object stays upright (centre of gravity). All three are common practical-exam contexts.

Syllabus coverage

CAMBRIDGE O LEVEL PHYSICS 5054

• Know that forces may produce a change in size and shape of an object (1.5)
• Define the spring constant as force per unit extension; recall and use spring constant = force ÷ extension (1.5)
• Sketch, plot and interpret load–extension graphs for an elastic solid, and describe the associated experimental procedures (1.5)
• Define and use the term “limit of proportionality” for a load–extension graph, and identify this point on the graph (an understanding of the elastic limit is not required) (1.5)
• Describe the moment of a force as a measure of its turning effect, and give everyday examples (1.5)
• Define the moment of a force as moment = force × perpendicular distance from the pivot; recall and use this equation (1.5)
• State and use the principle of moments for an object in equilibrium (1.5)
• Describe an experiment to verify the principle of moments (1.5)
• State what is meant by centre of gravity (1.5)
• Describe how to determine the position of the centre of gravity of a plane lamina using a plumb line (1.5)
• Describe, qualitatively, the effect of the position of the centre of gravity on the stability of simple objects (1.5)

5054 is not tiered — every candidate covers all of the above.

Elastic deformation and the spring constant

A force applied to an object can change its size and shape — stretching, compressing or bending it. For a spring (or any elastic object) stretched within its elastic region, the spring constant relates the force applied to the extension it produces:

spring constant = force / extension        k = F / x

Worked example. A spring extends by 0.08 m when a 4 N force is applied. Find its spring constant.

k = F / x = 4 / 0.08 = 50 N/m

The standard experiment hangs increasing loads from a spring, measuring the extension (the increase in length from the spring’s natural length) at each load, and plots a load–extension graph. For an elastic solid, this graph is a straight line through the origin up to the limit of proportionality — the point beyond which extension is no longer proportional to load, identified on the graph as where the line stops being straight. (The related idea of the elastic limit — the point beyond which the spring won’t return to its original length — is a different point on the same graph, but is not required at this level.)

Moments and the principle of moments

The moment of a force is a measure of its turning effect about a pivot — the everyday examples are a spanner turning a nut, a door opening about its hinges, or a see-saw balancing. It’s defined as:

moment = force × perpendicular distance from the pivot

Worked example. A force of 20 N is applied 0.3 m from a pivot, perpendicular to the lever. Find the moment.

moment = 20 × 0.3 = 6 N·m

For an object in equilibrium, two conditions must both hold: there must be no resultant force (the forces in every direction balance), and there must be no resultant moment — the principle of moments — the sum of the clockwise moments about any pivot equals the sum of the anticlockwise moments about the same pivot. An object can satisfy one condition without the other, so both must be checked; the principle of moments alone only guarantees that the object is not rotating, not that it is genuinely in equilibrium. This moment condition is verified experimentally with a metre rule pivoted at its centre, hanging known weights at measured distances on each side, and adjusting until the rule balances — confirming that clockwise and anticlockwise moment totals are equal at that point.

Worked example. A uniform see-saw is pivoted at its centre. A 300 N weight sits 1.2 m from the pivot on one side. How far from the pivot on the other side must a 400 N weight sit, to balance?

clockwise moment = anticlockwise moment
400 × d = 300 × 1.2
d = 360 / 400 = 0.9 m

Centre of gravity and stability

The centre of gravity of an object is the single point through which its entire weight can be considered to act. For a flat, irregularly-shaped object (a plane lamina), its position is found experimentally: suspend the lamina freely from a point, hang a plumb line from the same point, and mark the vertical line it traces; repeat from a second suspension point, and the centre of gravity is where the two lines cross.

The position of the centre of gravity determines how stable an object is. Qualitatively: an object with a low centre of gravity and a wide base is more stable, because it can be tilted further before its centre of gravity moves outside its base and it topples — this is why, for instance, a wide-based, low-set object resists tipping over far more than a tall, narrow one with the same weight.

Common mistakes

• Using extension instead of total length in the spring constant equation. Extension is the increase in length from the natural (unstretched) length, not the total stretched length.
• Confusing the limit of proportionality with the elastic limit. Only the limit of proportionality (where the load–extension graph stops being a straight line) is required — the elastic limit is a related but different point, and understanding it isn’t examined.
• Forgetting “perpendicular distance” in the moment equation — using the distance along the object rather than the perpendicular distance from the line of action of the force to the pivot gives the wrong answer unless the force already acts perpendicular to the object.
• Applying the principle of moments without checking equilibrium. It only holds when the object is not turning — if the sums aren’t equal, the object has a resultant moment and will rotate.
• Forgetting the force condition. Balanced moments alone are not enough for equilibrium — the resultant force must also be zero. A body can have zero resultant moment about a pivot and still accelerate if the forces on it don’t balance.
• Describing stability only in terms of weight, not centre of gravity position. Two objects of equal weight can have very different stability, depending on how low and how central their centre of gravity is relative to their base.

Quick revision checklist

• Spring constant, k = F/x, and reading it from a load–extension graph
• The limit of proportionality: what it means and how to identify it on a graph (elastic limit not required)
• Moment = force × perpendicular distance from the pivot
• Both conditions for equilibrium: no resultant force, and no resultant moment (the principle of moments), and the metre-rule experiment that verifies the moment condition
• Centre of gravity: definition, the plumb-line method for a plane lamina, and its qualitative link to stability

Related resources

• Forces and Motion — the rest of subtopic 1.5
• Kinematics and Motion Graphs — the motion these forces can also cause
• Cambridge O Level Physics subject hub

Written against Cambridge O Level Physics 5054, 2026–2028 series. Always check the current syllabus for your examination year.