A student measures the mass m = 0
Measurements & Uncertainties - OCR A-Level Physics
- A student measures the mass $m = 0.250 +/- 0.001 kg$ and speed $v = 3.0 +/- 0.2 m s^-1$.
- Calculate the kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. and its absolute uncertaintyThe uncertainty expressed in the same units as the measurement. Written as +/- a value after the reading..
$$\begin{aligned}
E_k &= \frac{1}{2}mv^2 \\
&= \frac{1}{2} \times 0.250 \times 3.\(0^{2}\) \\
&= 1.125 \text{ J}
\end{aligned}$$
- Step 1: Find percentage uncertainty in m.
- % uncertainty in $m = (0.001 / 0.250) x 100% = 0.4%$.
- Step 2: Find percentage uncertainty in v. Since v is squared, multiply by 2.
- % uncertainty in v = (0.2 / 3.0) x 100% = 6.7%. For \(v^{2}\): 2 x 6.7% = 13.3%.
- Step 3: Total percentage $uncertainty = 0.4% + 13.3% = 13.7%$.
- Step 4: Convert back to absolute uncertaintyThe uncertainty expressed in the same units as the measurement. Written as +/- a value after the reading..
- Absolute $uncertainty = 13.7 / 100 x 1.125 = 0.15 J$.
$$E_k = 1.1 \pm 0.2 \text{ J}$$
Examiner Tips and Tricks
- Notice how the uncertainty in v dominates (13.3% vs 0.4% for m).
- This tells the student that measuring speed more precisely would improve the result far more than a better balance.
- Examiners love asking 'Which measurement contributes most to the uncertainty?'