Practical Investigation — practice questions

State the two things a conclusion must contain for this standard at Achieved level.

A student's conclusion reads: "My experimental value of $g$ was $9.5$ m s⁻², which is close to the accepted value of $9.81$ m s⁻², so the theory is supported."

Explain why this does not meet the Merit criterion, and rewrite it so that it does. The student's gradient analysis gave $g = 9.5 \pm 0.4$ m s⁻².

A student obtains $g = 9.5 \pm 0.1$ m s⁻² from their pendulum investigation. The accepted value is $9.81$ m s⁻².

Discuss what this result means, and what it tells the student about their investigation.

Theory predicts that the energy stored in a spring $E$ depends on its extension $x$ as $E = \tfrac{1}{2}kx^2$. State the power $n$ this predicts for a log-log plot of $E$ against $x$.

Explain why stating the predicted power $n$ before collecting data is better practice than only working it out afterwards.

An investigation into $T = 2\pi\sqrt{L/g}$ finds a log-log gradient of $0.52 \pm 0.04$ and an experimental $g$ of $9.6 \pm 0.5$ m s⁻². Evaluate whether this data supports the theory.

In an investigation of how the period of a mass on a spring depends on the mass, state two variables that should be controlled.

Describe how you would control the amplitude in an investigation of how the period of a mass on a spring depends on the mass, and explain why it needs controlling.

A student measuring the resistance of a wire against its length uses a digital multimeter, takes three repeats at each length, and reports a very small random uncertainty — but their line has a clear positive intercept.

Evaluate their approach to accuracy and justify two changes.

A length is measured with a ruler marked in millimetres.

State the uncertainty in a single reading, and state the uncertainty in a length measured between two points on the ruler.

A student times five oscillations with a stopwatch that displays to $0.01$ s. Their three repeats are $6.8$ s, $7.2$ s and $6.9$ s.

Determine an appropriate uncertainty in the period of one oscillation, and explain why the stopwatch's resolution is not the appropriate uncertainty here.

In an investigation of how the period of a mass on a spring depends on the mass, a student uses a balance reading to $0.1$ g for masses between $50$ g and $500$ g, and hand-times 10 oscillations with a $\pm 0.2$ s reaction-time uncertainty for periods between $0.5$ s and $1.6$ s.

Analyse which measurement limits the precision of the final result, and justify one change that would most improve it.

A length is measured as $8.0 \pm 0.1$ cm. Calculate its percentage uncertainty.

A calculation uses $z = x^3$, where $x$ has a percentage uncertainty of $2.0\%$. Find the percentage uncertainty in $z$, and explain why raising to a power increases uncertainty so much.

Kinetic energy is calculated as $E_k = \tfrac{1}{2}mv^2$, where $m = 2.00 \pm 0.01$ kg (0.5%) and $v = 3.0 \pm 0.3$ m s⁻¹ (10%). Find the percentage uncertainty in $E_k$ and explain which measurement the student should improve first to make the biggest difference to the final uncertainty.

A student's steepest acceptable line has gradient $2.45$ and their shallowest has gradient $2.05$.

Calculate the uncertainty in the gradient, and state the gradient if the line of best fit gives $2.24$.

A student plots $T$ against $L$ with vertical error bars of $\pm 0.02$ s on periods of about $1.5$ s, then linearises by plotting $T^2$.

Calculate the error bar to use on the $T^2$ axis, and explain why it is not simply $\pm 0.02$.

A student draws error bars, then draws their steepest and shallowest lines by pivoting both about the leftmost data point.

Evaluate this method and explain what effect it has on the uncertainty they obtain.

A theory predicts a linearised graph should pass through the origin.

State what a significant non-zero intercept indicates.

Explain why a systematic error usually changes the intercept of a linearised graph but not its gradient, and explain why this matters for a value calculated from the gradient.

A student measuring the resistance of a wire plots resistance $R$ against length $l$, expecting a line through the origin, and obtains a positive intercept of $0.8 \pm 0.1$ Ω.

Discuss possible causes of this intercept, and evaluate whether it invalidates their conclusion about the relationship between $R$ and $l$.

A student obtains an experimental value of $g = 9.6 \pm 0.5$ m s⁻².

State whether this is consistent with the accepted value of $9.81$ m s⁻², and justify your answer.

A student's linearised graph gives a gradient of $0.041 \pm 0.003$ and the theory predicts $0.045$.

Make a quantitative comparison of the experimental result with the theory, including consideration of uncertainties.

Two students test the same theory. Student A obtains a value within $1\%$ of the accepted value with a quoted uncertainty of $\pm 15\%$. Student B obtains a value $6\%$ from the accepted value with a quoted uncertainty of $\pm 2\%$.

Discuss which investigation provides better evidence about the theory.

State one assumption made by the theory $T = 2\pi\sqrt{L/g}$ that may not hold in a school laboratory.

In an investigation of how the resistance of a wire depends on its length, explain how the heating of the wire by the current could have affected the results, including the direction of the effect.

A student investigating how the period of a pendulum depends on length finds that their points at the shortest lengths sit consistently above the line of best fit on a graph of $T^2$ against $L$.

Discuss this outcome: give a cause, explain how it produces this specific pattern, and evaluate its effect on the validity of the conclusion.