Practise converting instrument or spread estimates into absolute, fractional and percentage uncertainties, propagating them and quoting a defensible final result.
A group of students uses pressurized air to move a piston that forces a nail into a block of wood. A gauge is used to measure the pressure P of compressed air above atmospheric pressure. The nail enters the wood perpendicular to its surface.
The students use a ruler to measure the length of the nail which remains above the surface of the wood as shown. The depth of the nail inside the wood is d. All necessary length measurements are recorded using a ruler with uncertainty .
The students systematically increase the pressure and calculate d.
State the absolute uncertainty of d.
The students suggest the following relationship between d and P :
where k is a constant.
To verify the relationship, the variation of d with is plotted.
One data point is missing.
The percentage uncertainty in P is . Determine the uncertainty for when and draw the uncertainty bar for this data point on the graph.