A student plots a graph of extension x against force F and draws a best-fit line
Measurements & Uncertainties - OCR A-Level Physics
- A student plots a graph of extension x against force F and draws a best-fit line.
- Best-fit $gradient = 0.0125 m N^-1$.
- Steepest acceptable line $gradient = 0.0138 m N^-1$.
- Shallowest acceptable line $gradient = 0.0112 m N^-1$.
- Find the percentage uncertainty in the gradient.
$$\begin{aligned}
\text{Uncertainty in gradient} &= \frac{0.0138 - 0.0112}{2} \\
&= 0.0013 \text{ m N}^{-1}
\end{aligned}$$
$$\begin{aligned}
\text{Percentage uncertainty} &= \frac{0.0013}{0.0125} \times 100\% \\
&= 10.4\%
\end{aligned}$$
- The gradient represents 1/k (the reciprocal of the spring constantThe force per unit extension of a spring. A measure of the stiffness of the spring. Measured in N m⁻¹.).
- So $k = 1 / 0.0125 = 80 N m^-1$, with a percentage uncertainty of 10.4%.
- Absolute uncertaintyThe uncertainty expressed in the same units as the measurement. Written as +/- a value after the reading. in $k = 10.4 / 100 x 80 = 8.3 N m^-1$.
- Report: $k = 80 +/- 8 N m^-1$.