For a wire, define stress.
For a wire, define strain.
A school experiment is carried out on a metal wire to find the Young modulus of the metal. A force is applied to one end of the wire while the other end is fixed. Fig. 4.1 shows how the force $F$ varies with extension $x$ of the wire. The greatest force applied to the wire is $F_1$. The gradient of the graph line in Fig. 4.1 is $G$. The wire has initial length $L$ and cross-sectional area $A$. Determine an expression, in terms of $A$, $G$ and $L$, for the Young modulus $E$ of the metal.
A student repeats the experiment in $\text{b(i)}$ with a new wire whose diameter is twice that of the first wire. The wire’s initial length and the metal it is made from stay the same. On Fig. 4.1, draw the graph line for the new wire as the force increases from $F = 0$ to $F = F_1$.
Another student repeats the original experiment in $\text{b(i)}$, increasing the force beyond $F_1$ to a new maximum force $F_2$. The graph obtained from this is shown in Fig. 4.2. On Fig. 4.2, shade an area that shows the work done in extending the wire when the force increases from $F_1$ to $F_2$.
Explain how the student can check that the elastic limit of the wire was not exceeded when force $F_2$ was applied.
Each student in the class carries out the experiment in $\text{b(i)}$. The teacher describes the students’ calculated values of the Young modulus as showing high accuracy and low precision. Explain what is meant by low precision.