O Level Physics 5054 Paper 41, Oct/Nov 2024

method 1 (i) The student takes one straw and: • cuts it into 5 pieces that are equal in length • lines up the pieces of straw as shown in Fig. 1.1 • ensures the pieces of straw are touching. Fig. 1.1 is drawn actual size. Measure and record lengths $x$ and $D$ to the nearest $0.1\text{ cm}$. $x=\text{.......................................................... cm}$ $D=\text{.......................................................... cm}$

Use your value of $x$ in (a)(i) to calculate the length $l$ of the straw before it was cut into pieces. $l=\text{.................................................... cm}$

Use your value for $D$ in (a)(i) to calculate the diameter $d$ of one straw. Give your answer to the nearest $0.01\text{ cm}$. $d=\text{.................................................... cm}$

Explain how the student uses a ruler and two set squares to make sure that the measurement of $D$ is as accurate as possible. You may draw a diagram to help your explanation.

The volume $V_1$ of the straw is given by the equation: $$V_1=\frac{3.14d^{2}l}{4}$$ Use your answers from (a)(ii) and (a)(iii) to calculate $V_1$. Give your answer to two significant figures. $V_1={\text{.................................................. cm}}^3$

method 2 The student: • takes the second straw • immerses the straw fully in a container of water as shown in Fig. 1.2 • moves the straw backwards and forwards in the water several times so that the water enters the straw • puts a finger firmly over one end of the straw, and removes the straw from the water • puts the straw above the open end of a $50{\text{ cm}}^3$ measuring cylinder, and then removes the finger so that the water is transferred into the measuring cylinder. The student repeats the process 4 more times for a total of 5 transfers. (i) Fig. 1.3 shows the total volume of water $V_T$ in the measuring cylinder. Write down the reading $V_T$. $V_T={\text{.................................................. cm}}^3$

Calculate the average volume of water $V_2$ in one straw. $V_2={\text{.................................................. cm}}^3$

Suggest two reasons why $V_1$ and $V_2$ are different. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ...................................................................................................................................................

• The student closes the switch. Fig. 2.2 shows the readings $V_X$ on the voltmeter and $I_S$ on the ammeter. Record the readings of $V_X$ and $I_S$. $V_X=\text{............................................................ V}$ $I_S=\text{............................................................. A}$ • The student opens the switch.

The resistance of a resistor can be found using the equation: $$\text{resistance}=\frac{\text{voltage across the resistor}}{\text{current in the resistor}}$$ Calculate $R_X$, the resistance of resistor X. $R_X=\text{...................................................... }\mathrm{\Omega }$

Suggest why the switch is opened after the readings of potential difference and current are recorded.

• The student disconnects the voltmeter and reconnects it across resistor Y. The potential difference $V_Y$ across Y is given by the equation: $$V_Y=3.0-V_X$$ Using this equation and your value of $V_X$ from (a)(i), calculate $V_Y$. Calculate the resistance $R_Y$ of Y. $V_Y=\text{............................................................ V}$ $R_Y=\text{............................................................ }\mathrm{\Omega }$

• The student now connects X and Y in parallel. Complete the circuit diagram in Fig. 2.3 to show the two resistors connected in parallel between points W and Z. Draw the voltmeter connected to measure the potential difference $V_P$ across both resistors.

Theory suggests that, if the two resistors are arranged in parallel, the combined resistance $R_T$ is given by: $$R_T=\frac{R_X{R}_Y}{R_X+R_Y}$$ Use the equation and your values of $R_X$ and $R_Y$ from (a)(ii) and (a)(iv) to calculate $R_T$. $R_T=\text{...................................................... }\mathrm{\Omega }$

The manufacturer suggests that the combined resistance of resistors X and Y when placed in parallel is $2.5\mathrm{\Omega }$. Two quantities can be considered to be equal within the limits of experimental accuracy if their values are within 10% of each other. State whether your value of $R_T$ calculated in (b)(ii) has the same value as that suggested by the manufacturer. Support your statement with a calculation. calculation statement .......................................................................................................................... ........................................................................................................................................... .....................................................................................................................................

A fixed mass is placed on the metre rule at the $5.0\text{ cm}$ mark as shown in Fig. 3.1. The student: • places the pivot below the $25.0\text{ cm}$ mark on the metre rule • places a mass of mass $m=20\text{ g}$ on the metre rule • adjusts the position of the $20\text{ g}$ mass until the rule is as close to balance as possible. (i) The position of the $20\text{ g}$ mass when the rule is as close to balance as possible is shown in Fig. 3.2. Using Fig. 3.2, determine the distance $d$ of the centre of the $20\text{ g}$ mass from the pivot when the metre rule is as close to balance as possible. $d=\text{................................................... cm}$

Describe the technique the student uses to balance the metre rule with the $20\text{ g}$ mass.

• The student repeats the procedure for values of mass $m=30\text{ g},40\text{ g},50\text{ g}$ and $60\text{ g}$. Table 3.1 shows the results. Add your value of $d$ for mass $m=20\text{ g}$ in (a)(i) to Table 3.1. Calculate $1\mathrm{/}d$ for each mass $m$, and record all values in Table 3.1. Give your answers to an appropriate number of significant figures. Table 3.1

Suggest why a value of $d$ cannot be found for mass $m=10\text{ g}$.

Using the grid provided in Fig. 3.3 on page 13, plot a graph of $1\mathrm{/}d$ on the y-axis against $m$ on the x-axis. Start your axes from the origin $(0,0)$. Draw the straight line of best fit.

Calculate the gradient $G$ of your line. Show all your working, and indicate on the graph the values you use. $G=\text{.........................................................}$

The mass $M$ of the metre rule can be calculated using the equation: $$M=160-\frac{0.040}{G}$$ Use your value of $G$ in (b)(ii) to calculate $M$. $M=\text{...................................................... g}$

The student is given a piece of modelling clay. He places it on the metre rule as shown in Fig. 3.4. He finds that the metre rule is balanced when the modelling clay is a distance of $40.0\text{ cm}$ from the pivot. Using your graph in Fig. 3.3 on page 13, find the mass of the piece of modelling clay. Show your working. $\text{mass of piece of modelling clay}=\text{...................................................... g}$