Ch 7 · 1.5.3 Elastic Deformation · O Level Physics 5054

Topic 7 of 17 in Motion, Forces and Energy — O Level Physics 5054 — 60 lessons.

Introduction

Squash a tennis ball, stretch a rubber band, bend a ruler: forces can change the size and shape of objects as well as their motion. Springs are the classic example, because up to a point their stretch is perfectly predictable. This lesson covers the spring constant, load–extension graphs and the limit of proportionality. (Syllabus section 1.5.3.)

Key ideas — Forces change shape

A force may stretch, compress, bend or twist an object, changing its size and shape. An object is elastic if it returns to its original shape when the force is removed.

🧑‍🏫 Teacher's explanation

Imagine you are playing with a piece of chewing gum versus a rubber band. When you pull the rubber band, it stretches out, but as soon as you let go, it snaps back to its original size. This is called 'elastic' behavior. If you pull the chewing gum, it stays stretched out and permanently deformed; it has lost its ability to return to its original shape.

📖 Definitions

🔍 Worked example — Easy

A spring has an extension of 0.04 m when a force of 2.0 N is applied. Calculate the spring constant k.

🔍 Worked example — Standard

A load of 15 N is applied to a spring with a spring constant of 25 N/m. Calculate the extension produced.

🔍 Worked example — Exam-style

A student plots a load-extension graph. At 2 N, extension is 1 cm. At 4 N, extension is 2 cm. At 6 N, extension is 3.5 cm. Identify the limit of proportionality based on the trend and calculate the spring constant for the elastic region.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Load and extension

The load is the force stretching the spring (often the weight of hanging masses). The extension is the increase in length:

🧑‍🏫 Teacher's explanation

Imagine you are playing with a stretchy hair tie. When you pull it slightly, it wants to snap back to its original shape immediately. This 'snappiness' is what we call elasticity. If you pull it harder, it stretches more. The amount of force you apply is the 'load', and the extra length it gains is the 'extension'.

📖 Definitions

🔍 Worked example — Easy

A spring has an original length of 50 mm. When a load of 2.0 N is applied, the new length is 75 mm. Calculate the extension and the spring constant k.

🔍 Worked example — Standard

A spring constant is 150 N/m. Calculate the load required to produce an extension of 4.0 cm.

🔍 Worked example — Exam-style

A load-extension graph for a spring shows a straight line passing through the origin. At a load of 12 N, the extension is 3 cm. At a load of 20 N, the extension is 5 cm. Determine the spring constant k.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Spring constant

The spring constant k is the force per unit extension:

🧑‍🏫 Teacher's explanation

Imagine you are playing with a Slinky or a rubber band. When you pull on it, it stretches. If you pull harder, it stretches more. The 'spring constant' is just a number that tells you how 'stubborn' the object is. A very stiff spring, like the suspension in a car, is very stubborn—you need a massive amount of force to move it even a tiny bit. A soft spring, like the one in a cheap ballpoint pen, is very easy to stretch.

📖 Definitions

🔍 Worked example — Easy

A spring is stretched by 2.5 cm when a load of 5.0 N is applied. Calculate the spring constant k in N/cm.

🔍 Worked example — Standard

A spring has a spring constant k = 150 N/m. Calculate the extension x produced by a force of 45 N. Give your answer in cm.

🔍 Worked example — Exam-style

A student plots a load-extension graph for a spring. The graph is a straight line passing through the origin up to a force of 12 N. At 12 N, the extension is 3.0 cm. Beyond 12 N, the graph curves. Calculate the spring constant k in N/m.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Load–extension graphs

Plot extension (or load) on the axes the question asks for. For a spring the graph starts as a straight line through the origin: extension is proportional to load.

🧑‍🏫 Teacher's explanation

Imagine you are stretching a thick rubber band or a metal spring. When you pull it gently, it stretches a certain amount. If you pull it twice as hard, it stretches twice as much. This predictable, 'fair' relationship is what we call proportionality. On a graph, this looks like a perfectly straight line starting from zero.

📖 Definitions

🔍 Worked example — Easy

A spring is stretched by 2.5 cm when a load of 5.0 N is applied. Calculate the spring constant k.

🔍 Worked example — Standard

A spring has a spring constant of 150 N/m. Calculate the extension x produced by a load of 4.5 N.

🔍 Worked example — Exam-style

A load-extension graph for a spring shows a straight line through the origin. At a load of 12 N, the extension is 3 cm. At 15 N, the extension is 4 cm. Determine the spring constant k in N/m.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Load (N): 0, 2.0, 4.0, 6.0, 8.0, 10.0 Extension (cm): 0, 0.5, 1.0, 1.5, 2.0, 3.0 \n(a) Identify the limit of proportionality from the data provided. (b) Calculate the spring constant k for the spring in N/m, using the data from the proportional region. [3 marks]

Key ideas — Limit of proportionality

The limit of proportionality is the point where the graph stops being a straight line. Beyond it, extension is no longer proportional to load and k = F/x no longer applies. On the graph it is the end of the straight section, where the line starts to curve.

🧑‍🏫 Teacher's explanation

Imagine you are stretching a thick rubber band. At first, if you pull it twice as hard, it gets twice as long. This predictable, steady relationship is what we call 'proportionality'. In physics, we represent this with a straight line on a graph. As long as you stay on that straight line, the material is behaving predictably.

📖 Definitions

🔍 Worked example — Easy

A spring has an extension of 0.04 m when a load of 2.0 N is applied. Calculate the spring constant k.

🔍 Worked example — Standard

A spring with a spring constant of 150 N/m is stretched by a force of 4.5 N. Calculate the extension x.

🔍 Worked example — Exam-style

A load-extension graph for a spring shows a straight line passing through the origin (0,0) and the point (0.05 m, 2.5 N). The graph starts to curve at a load of 3.0 N. Calculate the spring constant k in the elastic region and identify the limit of proportionality.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

\n| Load (N) | Extension (m) |

Practical notes

Safety: do not overload the spring, and keep feet clear in case the masses fall.

Worked example

Example 1: spring constant. A spring is 8.0 cm long. With a 3.0 N load it is 14.0 cm long. Find k, and the extension with a 4.5 N load (below the limit of proportionality).

🔍 Worked example — Easy

A spring has an original length of 5.0 cm. When a load of 2.5 N is attached, its length becomes 7.5 cm. Calculate the spring constant k in N/cm.

🔍 Worked example — Standard

A spring has a spring constant k = 150 N/m. Calculate the extension in cm when a force of 4.5 N is applied.

🔍 Worked example — Exam-style

A load-extension graph for a spring shows a straight line passing through the origin. At a load of 12 N, the extension is 4.0 cm. At a load of 18 N, the graph begins to curve. Calculate the spring constant k in N/m and identify the load at the limit of proportionality.

⚠️ Common errors

Common mistakes

Practice

Answers: (1) 2.0/4.0 = 0.50\ N/cm = 50\ N/m. (2) x = 1.2/40 = 0.030\ m = 3.0\ cm. (3) The point beyond which extension is no longer proportional to load; it is where the straight line through the origin starts to curve. (4) Read the rule at eye level (avoid parallax) using a fixed pointer; wait for the spring to stop oscillating; use equal load steps and repeat readings.

Ch 7 · 1.5.3 Elastic Deformation · O Level Physics 5054

All chapters in Motion, Forces and Energy