Quick answer: Homogeneity means every term of an equation has the same base units, which lets you test formulae. This Physics 11-12 lab on uncertainty and vectors gives the aim, the equipment, the safety points, a step-by-step method, sample results and 8 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
Many physics results are only as good as their weakest measurement. In this lab you find the density of a wooden dowel from three measurements and work out which of them limits the accuracy of the answer. You need only a ruler and a kitchen scale.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: A Level 1, IB A
Aim
To find the density of a wooden dowel and to decide which measurement contributes most to the uncertainty in the result.
Equipment
- Wooden dowel or broom handle, about 12 cm long, with square-cut ends
- 30 cm ruler (±0.1 cm) or vernier callipers
- Kitchen scale reading to 0.1 g
- Calculator
Safety
Cut the dowel with adult help and sand any splinters. Keep the dowel away from the edge of the bench so that it cannot roll off and drop on a foot.
Method
- Place the dowel on the scale and record its mass m.
- Lay the dowel against the ruler and measure its length l, reading both ends carefully.
- Measure the diameter d at five different places, turning the dowel between readings.
- Calculate the mean diameter and use half the range as its uncertainty.
- Calculate the volume V = πd²l ÷ 4 and the density ρ = m ÷ V.
Results
Sample measurements:
| Measurement | Value | Absolute uncertainty |
|---|---|---|
| Mass m | 62.4 g | ±0.1 g |
| Length l | 12.0 cm | ±0.1 cm |
| Diameter d, reading 1 | 3.20 cm | – |
| Diameter d, reading 2 | 3.18 cm | – |
| Diameter d, reading 3 | 3.22 cm | – |
| Diameter d, reading 4 | 3.19 cm | – |
| Diameter d, reading 5 | 3.21 cm | – |
Analysis questions
Question 1 Mean diameter
Calculate the mean diameter and its absolute uncertainty using half the range.Question 2 Percentage uncertainties
Calculate the percentage uncertainty in m, l and d.Question 3 Volume
Calculate the volume of the dowel.Question 4 Density and uncertainty
Calculate the density and its percentage and absolute uncertainty.Question 5 Largest contribution
Identify the measurement that contributes most to the uncertainty and explain your choice.Question 6 Float or sink
Water has a density of 1000 kg/m³. Decide whether the dowel floats and estimate the fraction submerged.Question 7 Unit check
Show that kg m⁻³ is the correct base unit for density and convert your result.Question 8 Improvement
Suggest one improvement that would reduce the uncertainty most.
