Physics 5054/31 — October/November 2011

Walkthrough

The candidate is given a list of apparatus and asked to assemble it as shown in the diagram. The key feature to achieve is that the string segment BC, which runs over the pulley to the 50 g mass, must be horizontal. This is done by adjusting the position and height of the pulley.

Key Takeaways

Candidates must be able to follow instructions to assemble a practical apparatus and make fine adjustments to achieve a specific geometric condition (a horizontal string).

Common Mistakes

Failing to adjust the pulley height so that BC is truly horizontal, which will introduce errors in the angle $\theta$ and invalidate the equilibrium assumption used in later calculations.

Things to Be Careful About

This is a Paper 3 practical question. The candidate performs the setup themselves. Ensure the string is taut and the mass M hangs freely without touching the stand or bench.

Walkthrough

To ensure BC is horizontal, the candidate must use one of the provided tools (metre rule or set square) to verify the alignment. The most direct method is to measure the vertical distance from the bench to the string BC at two separate points along its length; if the distances are identical, the string is horizontal. Another valid method is to use the set square to check that the angle between the vertical stand (or a vertical line) and the string BC is exactly $90^\circ$.

Key Takeaways

Practical skills involve using simple apparatus (rulers, set squares) to verify geometric conditions required for the experiment to be valid.

Common Mistakes

Saying 'looked along the string' without using an instrument, or suggesting 'aligned with the bench' without explaining how that measurement is made.

Things to Be Careful About

The mark scheme accepts either measuring heights at two points or using a set square. Both must be described as a method of verification, not just 'checking' visually.

Walkthrough

The candidate uses a metre rule to measure three quantities from Fig. 1.1:

• $h_1$: the vertical height from the bench to point A (the split cork).
• $h_2$: the vertical height from the bench to point B (the junction of the strings).
• $l$: the length of the string segment AB.

For the subsequent calculation of $\theta$ to fall in the acceptable range ($50^\circ$ to $70^\circ$), the difference $(h_1 - h_2)$ must be roughly $0.77l$ to $0.94l$. Using $l = 25.0 \text{ cm}$, a suitable difference is $23.0 \text{ cm}$, giving $h_1 = 45.0 \text{ cm}$ and $h_2 = 22.0 \text{ cm}$.

Key Takeaways

Practical measurements must be taken to the precision of the instrument (nearest mm for a metre rule) and always include units. The values must also be physically consistent with the apparatus geometry ($l$ must be greater than the vertical difference $h_1 - h_2$).

Common Mistakes

Forgetting to include units, recording to the wrong precision (e.g. nearest cm instead of mm), or providing values where $l < h_1 - h_2$ (which is geometrically impossible for a right-angled triangle with hypotenuse $l$).

Things to Be Careful About

The metre rule is read to the nearest mm, so a reading like $25.0 \text{ cm}$ (or $250 \text{ mm}$) is correct, but $25 \text{ cm}$ without the trailing zero may be penalised for precision. Ensure $l > h_1 - h_2$ is explicitly checked.

Walkthrough

The candidate substitutes their recorded values from part (c) into the provided equation:

$$\sin\theta = \frac{h_1 - h_2}{l}$$

Using the representative values: $h_1 - h_2 = 45.0 - 22.0 = 23.0 \text{ cm}$, and $l = 25.0 \text{ cm}$.

$$\sin\theta = \frac{23.0}{25.0} = 0.92$$

Then, use the inverse sine function ($\sin^{-1}$ or $\arcsin$) on a calculator to find $\theta$:

$$\theta = \sin^{-1}(0.92) \approx 66.9^\circ$$

The mark scheme requires the candidate to show the calculation of $\sin\theta$ and then the final angle $\theta$ in degrees, with the unit.

Key Takeaways

Candidates must correctly substitute measured values into a trigonometric relationship and use their calculator's inverse trig functions, remembering to include the unit ($^\circ$) in the final answer.

Common Mistakes

Forgetting to use the inverse sine function (e.g. answering $0.92^\circ$ instead of $66.9^\circ$), forgetting the degree symbol in the final answer, or carrying forward an error from part (c) without showing the working for $\sin\theta$.

Things to Be Careful About

Ensure the calculator is in degree mode, not radian mode. The mark scheme awards a method mark (C1) for the correct calculation of $\sin\theta$ and an answer mark (A1) for the final value of $\theta$ in the range $50^\circ$ to $70^\circ$ with the unit. Error carried forward (ecf) from part (c) is allowed if the method is correct.