Hooke's law

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Lesson notes

Hooke's Law

Hooke's law states that the **extension** of a spring is **directly proportional** to the **force** applied to it.
This means doubling the force doubles the extension, provided the **limit of proportionality** is not exceeded.
The law applies to both **extension** (stretching) and **compression** (squeezing) of a spring.

Key Equation

The equation is: **Force = Spring constant × Extension** or **F = k × e**.
**F** is force in **newtons (N)**.
**k** is the **spring constant** in **newtons per metre (N/m)**.
**e** is **extension** in **metres (m)**.

Spring Constant

The **spring constant** measures how **stiff** the spring is.
A **higher** spring constant means **more force** is needed to stretch the spring by the same amount.
A **lower** spring constant means the spring is easier to stretch.

Calculations

To find force: **F = k × e**.
To find extension: **e = F ÷ k**.
To find spring constant: **k = F ÷ e**.
Always use consistent units: N, N/m, m.

Example Calculation

A spring with **k = 4 N/m** is extended by **0.1 m**. Force = 4 × 0.1 = **0.4 N**.
A spring with **k = 200 N/m** is compressed by **0.04 m**. Force = 200 × 0.04 = **8 N**.
A rubber band with **k = 60 N/m** is pulled with **15 N**. Extension = 15 ÷ 60 = **0.25 m**.

Graph of Force vs Extension

A graph of **force** against **extension** is a **straight line** through the origin.
The **gradient** of the line equals the **spring constant**.
If the force is too large, the line **curves** (the spring is permanently deformed).

Graph showing force directly proportional to extension for a spring obeying Hooke's law.

Slides

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Practice questions

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1.What is the unit of force?
Easy
- ANewton (N)
- BMetre (m)
- CNewton per metre (N/m)
- DJoule (J)
2.What is the unit of the spring constant?
Easy
- ANewton (N)
- BMetre (m)
- CNewton per metre (N/m)
- DMetre per newton (m/N)
3.What is the unit of extension?
Easy
- ANewton (N)
- BMetre (m)
- CNewton per metre (N/m)
- DCentimetre (cm)
4.According to Hooke's law, how is the extension of a spring related to the force applied to it?
Medium
- AExtension is inversely proportional to force
- BExtension is directly proportional to force
- CExtension is equal to force
- DExtension is independent of force
5.A spring with a spring constant of 4 N/m is extended by 0.1 m. What force is applied?
Medium
- A0.4 N
- B4 N
- C40 N
- D0.04 N
6.A rubber band with a spring constant of 10 N/m is extended by 0.2 m. What force is applied?
Medium
- A2 N
- B0.5 N
- C50 N
- D20 N
7.A spring with a spring constant of 20 N/m is compressed by 0.05 m. What force is applied?
Medium
- A1 N
- B4 N
- C0.25 N
- D400 N
8.The same force is applied to two springs. Spring X has a high spring constant, Spring Y a low spring constant. Which spring has the larger extension?
Medium
- ASpring X
- BSpring Y
- CBoth have same extension
- DCannot tell

More questions

9.A rubber band has a spring constant of 60 N/m and is pulled with a force of 15 N. What is the extension?
Hard
- A0.25 m
- B4 m
- C900 m
- D0.4 m
10.A spring has a spring constant of 200 N/m and is compressed by 0.04 m. What force is applied?
Hard
- A8 N
- B0.5 N
- C5000 N
- D50 N
11.A rubber band has a spring constant of 15 N/m and is pulled with a force of 0.3 N. What is the extension?
Hard
- A0.02 m
- B50 m
- C4.5 m
- D0.2 m
12.What does the spring constant measure?
Medium
- AThe length of the spring
- BThe force needed to extend the spring by one metre
- CThe maximum extension of the spring
- DThe weight of the spring
13.A student hangs a 0.5 kg mass on a spring, causing an extension of 0.1 m. What is the spring constant of the spring? (Take g = 10 N/kg)
Medium
- A50 N/m
- B5 N/m
- C0.5 N/m
- D20 N/m
14.A spring of natural length 20 cm is stretched to a length of 25 cm by a force of 10 N. What is the spring constant?
Medium
- A2 N/cm
- B0.5 N/cm
- C200 N/m
- D0.4 N/cm
15.A spring has a spring constant of 500 N/m. What force is needed to compress it by 3 cm?
Hard
- A15 N
- B1.5 N
- C150 N
- D0.15 N
16.A force of 12 N extends a spring by 0.3 m. What is the spring constant?
Medium
- A40 N/m
- B3.6 N/m
- C0.025 N/m
- D4 N/m
17.A spring extends by 4 cm when a force of 8 N is applied. What extension would a force of 20 N produce?
Hard
- A10 cm
- B1.6 cm
- C0.1 m
- D20 cm
18.A spring is stretched by 0.2 m when a force of 4 N is applied. What force would stretch it by 0.5 m?
Medium
- A10 N
- B1.6 N
- C0.8 N
- D20 N
19.A student plots a graph of force (y-axis) against extension (x-axis) for a spring that obeys Hooke's law. What shape is the graph?
Easy
- AA straight line through the origin
- BA curved line through the origin
- CA horizontal line
- DA straight line not through the origin
20.The graph shows force against extension for two springs, A and B. Which spring has the larger spring constant?
Medium
- ASpring A
- BSpring B
- CBoth have the same spring constant
- DCannot tell from the graph
21.A student investigates Hooke's law using a spring. They add masses one by one and record the extension. Which of the following would indicate that the spring has exceeded its limit of proportionality?
Hard
- AThe graph becomes curved
- BThe graph is a straight line
- CThe spring returns to its original length
- DThe extension is zero
22.A spring is 10 cm long. When a 2 N force is applied, its length becomes 12 cm. What is the extension?
Medium
- A2 cm
- B10 cm
- C12 cm
- D22 cm
23.What does Hooke's law state about the relationship between force and extension?
Easy
- AExtension is directly proportional to force
- BExtension is inversely proportional to force
- CForce is inversely proportional to extension
- DExtension is equal to force
24.A spring has a spring constant of 100 N/m. A force of 5 N is applied. What is the extension in centimetres?
Hard
- A5 cm
- B0.05 cm
- C20 cm
- D0.5 cm
25.A student investigates Hooke's law by hanging masses on a spring and measuring the extension. Which piece of equipment is used to measure the extension?
Easy
- AA metre ruler
- BA newton meter
- CA balance
- DA stopwatch
26.A student adds masses to a spring and records the extension. The results are shown in the table: Force (N) | Extension (cm) 0 | 0 1 | 2 2 | 4 3 | 6 4 | 8 Which conclusion can be drawn from the results?
Medium
- AThe spring obeys Hooke's law because extension is directly proportional to force.
- BThe spring does not obey Hooke's law because extension is not proportional to force.
- CThe spring constant is 0.5 N/cm.
- DThe spring constant is 2 N/cm.
27.A student investigates a spring and plots a graph of force (y-axis) against extension (x-axis). The graph is a straight line through the origin. What does the gradient of this line represent?
Hard
- AThe spring constant
- BThe extension
- CThe force
- DThe elastic limit
28.A student hangs a mass on a spring and measures the extension. They then repeat the experiment with the same spring but add more masses. Which variable is the independent variable?
Medium
- AThe force applied
- BThe extension
- CThe spring constant
- DThe length of the spring
29.A spring has a natural length of 10 cm. When a force of 4 N is applied, its length becomes 14 cm. What is the spring constant?
Hard
- A100 N/m
- B0.25 N/m
- C1 N/m
- D0.4 N/m
30.A student carries out an experiment to determine the spring constant of a spring. Which of the following should be done to ensure accurate results?
Medium
- AUse a micrometer to measure extension
- BTake several readings and calculate an average
- CStart with the largest mass first
- DUse a spring with a high spring constant
31.A spring obeys Hooke's law. A force of 6 N produces an extension of 0.15 m. What force would produce an extension of 0.25 m?
Hard
- A10 N
- B3.6 N
- C15 N
- D0.4 N
32.In a Hooke's law experiment, what is the 'extension' of a spring?
Easy
- AThe increase in length compared to the original length
- BThe total length of the spring
- CThe force applied to the spring
- DThe mass hung from the spring
33.A student adds masses to a spring and records the length. The original length is 5 cm. After adding a 2 N force, the length is 7 cm. After adding another 2 N (total 4 N), the length is 9 cm. What is the spring constant?
Medium
- A1 N/cm
- B0.5 N/cm
- C2 N/cm
- D100 N/m
34.Which of the following is a correct statement about the spring constant?
Medium
- AA high spring constant means the spring is easy to stretch.
- BThe spring constant is the force needed to stretch the spring by one metre.
- CThe spring constant is measured in newtons.
- DThe spring constant is the same for all springs.
35.A student investigates whether a rubber band obeys Hooke's law. They apply increasing forces and measure the extension. The results are not a straight line through the origin. What does this suggest?
Hard
- AThe rubber band does not obey Hooke's law.
- BThe rubber band has a very high spring constant.
- CThe student made a measurement error.
- DThe rubber band obeys Hooke's law only for small forces.
36.A spring of natural length 20 cm is stretched to 25 cm by a force of 10 N. What is the spring constant?
Medium
- A2 N/cm
- B0.5 N/cm
- C200 N/m
- D0.4 N/m
37.A student investigates Hooke's law using a spring. They add masses one by one and record the extension. Which of the following would indicate that the spring has exceeded its elastic limit?
Medium
- AThe spring does not return to its original length when masses are removed
- BThe extension is directly proportional to force
- CThe spring constant increases
- DThe graph is a straight line
38.A student adds masses to a spring and records the extension. The results are shown in the table: Force (N): 0,1,2,3; Extension (cm): 0,2,4,6. What is the spring constant?
Hard
- A0.5 N/cm
- B2 N/cm
- C0.5 N/m
- D2 N/m
39.A student investigates a spring and plots a graph of force (y-axis) against extension (x-axis). The graph is a straight line through the origin. What does the gradient represent?
Medium
- ASpring constant
- BExtension
- CForce
- DElastic limit
40.In a Hooke's law experiment, a student hangs a mass on a spring and measures the extension. She then adds another identical mass and measures the new extension. Which of the following is the independent variable?
Medium
- AThe force applied to the spring
- BThe extension of the spring
- CThe spring constant
- DThe natural length of the spring

Revision notes

## Hooke's Law - **Hooke's law**: The extension of a spring is directly proportional to the force applied to it. - **Equation**: \( F = k \times e \) - \( F \) = force (Newtons, N) - \( k \) = spring constant (Newtons per metre, N/m) - \( e \) = extension (metres, m) - **Spring constant**: A measure of how much force is needed to extend the spring by one metre. A higher spring constant means more force is needed for the same extension. - **Key points**: - Doubling the force doubles the extension (if within elastic limit). - The relationship is linear: force is directly proportional to extension. - The same formula applies for compression (negative extension). - **Rearranged formula**: \( e = \frac{F}{k} \) to find extension.

Hooke's law: The extension of a spring is directly proportional to the force applied to it.
Spring constant: A measure of how much force is needed to extend the spring by one metre. Units: N/m.
Extension: The increase in length of a spring when a force is applied. Units: metres (m).
Force: A push or pull that can cause an object to stretch, compress, or change motion. Units: Newtons (N).

Flashcards

What is Hooke's law?

The extension of a spring is directly proportional to the force applied to it.

What is the equation for Hooke's law?

Force = Spring constant × Extension, or F = k × e.

What is the unit of force?

Newtons (N).

What is the unit of spring constant?

Newtons per metre (N/m).

What is the unit of extension?

Metres (m).

What does the spring constant measure?

It measures how much force is needed to extend the spring by one metre.

If a spring has a high spring constant, what does that mean?

More force is needed to stretch the spring by the same amount compared to a spring with a lower spring constant.

How does the extension change when the force on a spring is doubled?

The extension doubles (if Hooke's law is obeyed).

A spring with spring constant 4 N/m is extended by 0.1 m. Calculate the force.

F = 4 N/m × 0.1 m = 0.4 N.

A rubber band with spring constant 10 N/m is extended by 0.2 m. Calculate the force.

F = 10 N/m × 0.2 m = 2 N.

A spring with spring constant 20 N/m is compressed by 0.05 m. Calculate the force.

F = 20 N/m × 0.05 m = 1 N.

The same force is applied to two springs: Spring X (high k) and Spring Y (low k). Which has larger extension?

Spring Y (low spring constant) will have the larger extension.

A rubber band has spring constant 60 N/m and is pulled with force 15 N. Calculate the extension.

e = F / k = 15 N / 60 N/m = 0.25 m.

A spring has spring constant 200 N/m and is compressed by 0.04 m. Calculate the force.

F = 200 N/m × 0.04 m = 8 N.

A rubber band has spring constant 15 N/m and is pulled with force 0.3 N. Calculate the extension.

e = 0.3 N / 15 N/m = 0.02 m.

What happens to a spring when a force is applied?

It extends (increases in length) or compresses (decreases in length).

In the diagram, what is the extension when one mass is hung?

The extension is x.

In the diagram, what is the extension when two identical masses are hung?

The extension is 2x.

What does the symbol 'k' represent in F = k e?

The spring constant.

What does the symbol 'e' represent in F = k e?

The extension.

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