Physics 9702/13 — October/November 2016

Background Concept

Young modulus $E$ is defined as

$$E = \frac{\text{stress}}{\text{strain}} = \frac{F/A}{\Delta L/L}$$

Stress has unit $\text{Pa}$ and strain is dimensionless, so $E$ has unit $\text{Pa}$. A large Young modulus means a material is stiff: it requires a large stress to produce a small strain.

Metals are generally very stiff materials. Typical values are:

• metals: $E \sim 10^{11}\ \text{Pa}$
• plastics: $E \sim 10^{9}\ \text{Pa}$
• rubber: $E \sim 10^{6}$ to $10^{7}\ \text{Pa}$

Understanding the Question

The question asks for the order of magnitude of the Young modulus for a metal such as copper. You are not expected to know an exact value for copper; you only need to choose the closest power of ten from the options given.

Approach

Use the known typical scale of Young modulus values for common classes of materials. Since copper is a metal, its Young modulus should be around $10^{11}\ \text{Pa}$. Then match that to the option list.

Step-by-Step Reasoning

1. Recognise copper as a metal and recall that metals have $E$ around $10^{11}\ \text{Pa}$.
2. Compare with options:
   • $10^{-11}\ \text{Pa}$ and $10^{-4}\ \text{Pa}$ are absurdly small (softer than gases/fluids; solids cannot have such tiny stiffness).
   • $10^{4}\ \text{Pa}$ is still extremely small (similar to pressure changes you might measure in air, not stiffness of a solid metal).
   • $10^{11}\ \text{Pa}$ matches the expected value for metals.

Therefore the correct option is D.

Key Takeaways

• Young modulus is a measure of stiffness: metals have very large $E$ values.
• For A-level purposes, remembering typical orders of magnitude helps with MCQs.
• Metals: $E$ is usually around $10^{11}\ \text{Pa}$.

Common Mistakes

• Choosing a value with the wrong sign in the exponent (e.g. $10^{-11}$ instead of $10^{11}$).
• Confusing Young modulus with pressure values encountered in everyday contexts (kPa) and picking $10^{4}\ \text{Pa}$.

Things to Be Careful About

• The question asks for order of magnitude, so you should look for the nearest power of ten, not an exact material constant.
• Ensure you keep track that Young modulus for stiff solids is very large in pascals because strain is typically very small for a given stress.