Figure 5 shows a tool for driving nails into wood - AQA - A-Level Physics - Question 4 - 2021 - Paper 6

To determine the correct nail, we need to calculate the work done by the gas expanding in the combustion chamber. The work done (W) can be approximated using the formula:

$W = p imes riangle V$

where

• $p$ is the pressure (in Pascals)
• $riangle V$ is the change in volume.

We can derive the average pressure from the graph given in Figure 6. First, we note the volumes:

• Volume of combustion chamber = $20 imes 10^{-6} ext{ m}^3$
• Volume moved by piston = $60 imes 10^{-6} ext{ m}^3$

Therefore, the total volume change is:

$riangle V = 60 imes 10^{-6} ext{ m}^3 - 20 imes 10^{-6} ext{ m}^3 = 40 imes 10^{-6} ext{ m}^3$

Next, we use the graph to estimate the pressure corresponding to this volume. From Figure 6, when $V$ is around $40 imes 10^{-6} ext{ m}^3$, the pressure $p$ is roughly between $6.0$ and $7.0 imes 10^5 ext{ Pa}$. Calculating the work done:

Using an average pressure of about $6.5 imes 10^5 ext{ Pa}$:

$W ext{ (average)} = 6.5 imes 10^5 ext{ Pa} imes 40 imes 10^{-6} ext{ m}^3 = 26.0 ext{ J}$

Now we compare this energy to the energy required to drive each nail in Table 2:

• Nail A: 250 N x 0.032 m = 8.0 J
• Nail B: 320 N x 0.038 m = 12.16 J
• Nail C: 370 N x 0.045 m = 16.65 J
• Nail D: 420 N x 0.050 m = 21.0 J
• Nail E: 560 N x 0.063 m = 35.28 J

The work done (26.0 J) closely matches the energy required for Nail D (21 J), which is the closest without exceeding. Therefore, the correct nail to use in the tool is Nail D.