IB Physics SL 6.3.4 Uncertainties Question Bank

Practise IB Physics SL/HL 6.3.4 by applying uncertainties concepts to exam-style physics questions.

[Maximum number: 4]

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.

Figure for Question S1.3.4—Uncertainties question 1 — IB Physics SL

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 $\pm 1 \mathrm{~mm}$ .

(a)

The students systematically increase the pressure and calculate d.

[ 1 ]

(i)

State the absolute uncertainty of d.

[ 1 ]

«Addition of absolute uncertainties $\pm$ » 2 mm

Accept 0.002

(b)

The students suggest the following relationship between d and P :

d=k \sqrt{P}

where k is a constant.
To verify the relationship, the variation of d with $\sqrt{P}$ is plotted.
One data point is missing.

[ 3 ]

(i)

The percentage uncertainty in P is $\pm 8 \%$ . Determine the uncertainty for $\sqrt{P}$ when $d=33 \mathrm{~mm}$ and draw the uncertainty bar for this data point on the graph.

[ 3 ]

Alternative 1

«Uncertainty in $\sqrt{P}$ is» $\frac{1}{2} \times 0.08= \pm 4 \%$ $\pm 4 \% \times 500= \pm 20$

Uncertainty bar plotted correctly

Alternative 2
$\frac{0.08 \times 250000=20000 \quad }{\sqrt{250000+20000}-\sqrt{250000-20000}}= \pm 20$

Uncertainty bar plotted correctly

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S1.3.4—Uncertainties question 1

Question (a)

Question (i)

Question (b)

Question (i)