IB Physics SL S1.3.3 Units and Numerical Values Questions

Use SL SI units, prefixes and numerical conversions correctly when calculating momentum, energy and other physical quantities.

Exam points

identify correct SI units for derived quantities such as momentum and distinguish common unit distractors
convert between SI prefixes and electronvolts or joules when interpreting numerical physics data
check numerical answers for unit consistency, powers of ten, significant figures and appropriate scale

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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 IB Physics SL S1.3.3 Units and Numerical Values Questions 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 $\pm 1 \mathrm{~mm}$ .

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.

The SI units of k can be expressed as $\mathrm{kg}^{-\frac{1}{2}} \mathrm{~m}^{x} \mathrm{~s}^{y}$ . Determine the values of x and y.

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IB Physics SL S1.3.3 Units and Numerical Values Questions question 1