O Level Physics 5054 Paper 42, Oct/Nov 2023

Method 1 The student: • measures the unstretched length of the spring to the nearest $0.1\mathrm{c}\mathrm{m}$. A full-size diagram of the spring is shown in Fig. 1.1. Measure the unstretched length $l_0$ of the spring to the nearest $0.1\mathrm{c}\mathrm{m}$. Do not include the loops at the end of the spring in your measurement. $l_0=$ ................................................... $\mathrm{c}\mathrm{m}$

The student: • attaches the spring to a clamp on a stand • suspends a $300\mathrm{g}$ mass from the spring. The arrangement of apparatus is shown in Fig. 1.2. • The student measures the new length $l_1$ of the spring. $$l_1=17.6\mathrm{c}\mathrm{m}$$ Calculate the extension $e$ of the spring produced by the mass. Use the equation: $$e=l_1-l_0$$ $e=$ ................................................... $\mathrm{c}\mathrm{m}$

Calculate the spring constant $k_1$ of the spring. Use the equation: $$k_1=\frac{300}{e}$$ $k_1=$ ................................................. $\mathrm{N}\mathrm{/}\mathrm{m}$

It is important to avoid line-of-sight (parallax) errors when determining the extension of the spring. Explain what is meant by parallax errors and how to avoid parallax errors. explanation ........................................................................................................................ ........................................................................................................................................... how to avoid parallax errors .............................................................................................. ...........................................................................................................................................

Method 2 The student: • pulls the $300\mathrm{g}$ mass down by a small distance and releases it so that the mass oscillates up and down • measures the time $t_1$ taken for 20 oscillations. The reading on the stop-watch is shown in Fig. 1.3. Record this time $t_1$ in Table 1.1 to one decimal place.

• The student measures the time for 20 oscillations once more and records the time $t_2$ in Table 1.1. Calculate the mean time $t$ for 20 oscillations and record your answer in Table 1.1.

The mean period $T$ of the oscillation is the mean time taken for one oscillation. Calculate the mean period $T$. Calculate the value of $T^2$. Record all your values in Table 1.1.

Use your value of $T^2$ from Table 1.1 to calculate the spring constant $k_2$ of the spring. Use the equation: $$k_2=\frac{11.8}{T^2}$$ $k_2=$ ................................................. $\mathrm{N}\mathrm{/}\mathrm{m}$

Explain why the value for the mean period $T$ obtained by measuring 20 oscillations twice is more accurate than the value obtained by measuring 1 oscillation twice. ................................................................................................................................................... .............................................................................................................................................

The student: • measures the room temperature ${\theta }_R$ as ${\theta }_R=22.5{}^{\circ }\mathrm{C}$ • pours $200{\mathrm{c}\mathrm{m}}^3$ of hot water into a beaker • lowers a thermometer into the beaker until its bulb is just covered by the hot water, as shown in Fig. 2.1 • waits for approximately $30\mathrm{s}$ • starts a stop-watch and reads the thermometer. The temperature on the thermometer at time $t=0$ is shown in Fig. 2.2. Record the temperature reading at time $t=0$ to the nearest $0.5{}^{\circ }\mathrm{C}$ in Table 2.1.

Explain why the student waits for $30\mathrm{s}$ before reading the initial temperature of the hot water. ........................................................................................................................................... .....................................................................................................................................

The student waits for 3 minutes, reads the thermometer and records the new temperature reading in Table 2.1. The student then: • removes the thermometer from the beaker and pours the water away • repeats the procedure in (a), but lowers the thermometer into the beaker, so that the bulb is just above, but not touching the bottom of the beaker, as shown in Fig. 2.3. • records the initial and final temperatures of the water as shown in Table 2.1. Calculate the average rate of cooling $P_T$ of the hot water at the top of the beaker. Use the equation: $$\text{average rate of cooling}=\frac{\text{decrease in temperature of the water}}{\text{time taken}}$$ Give your answer to 2 significant figures and state the unit. $P_T=$ ...................... unit ...................

Use the data in Table 2.1 on page 7 to calculate the average rate of cooling $P_B$ of the hot water at the bottom of the beaker. $P_B=$ .........................................................

Use your answers to (b)(i) and (b)(ii) to suggest why a hot liquid should be stirred before measuring its temperature. ........................................................................................................................................... .....................................................................................................................................

State one way in which the apparatus in this experiment is arranged to make it easy to read the thermometer accurately. ........................................................................................................................................... .....................................................................................................................................

The experiment is repeated to check the results. Suggest one variable that must be kept constant. .............................................................................................................................................

The student leaves the thermometer in the hot water and waits for 30 minutes before reading the thermometer again. Predict a value for the temperature of the water in the beaker. temperature of water = .................................................... ${}^{\circ }\mathrm{C}$

The student closes the switch and observes the reading $V_0$ on the voltmeter. The reading is shown in Fig. 3.2. Record the voltmeter reading $V_0$. $V_0=$ ...................................................... $\mathrm{V}$

The student then: • connects the crocodile clip to the resistance wire at a distance $d=100.0\mathrm{c}\mathrm{m}$ from end X • records the potential difference $V$ across the wire as $V=2.3\mathrm{V}$ • records the current $I$ in the wire • opens the switch. The reading on the ammeter is shown in Fig. 3.3. Record the ammeter reading $I$. $I=$ ...................................................... $\mathrm{A}$

The student: • closes the switch • repeats (b) for values of $d=80.0\mathrm{c}\mathrm{m}$, $60.0\mathrm{c}\mathrm{m}$, $40.0\mathrm{c}\mathrm{m}$ and $20.0\mathrm{c}\mathrm{m}$. The student’s results are shown in Table 3.1. Complete the header of each column. Include the value of $I$ from (b).

On the grid provided in Fig. 3.4, plot a graph of $V$ on the y-axis against $I$ on the x-axis, using the data in Table 3.1. Start both axes from the origin $(0,0)$. Draw the best-fit straight line.

The gradient $m$ of your line is numerically equal to the resistance $r$ of the power supply. Calculate the gradient of your line. Show clearly on the graph the values you chose and show your working. $m=$ .........................................................

The intercept between the y-axis and your line is the electromotive force $V_0$ of the power supply. Extend your best-fit line to meet the y-axis and write down the value of $V_0$. $V_0=$ ...................................................... $\mathrm{V}$

Compare the value of $V_0$ in (a) with the value of $V_0$ you obtained from the graph in (e)(ii). 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 results show that the two values obtained for the electromotive force are the same. Support your statement with a calculation. calculation statement .................................................................................................................. .............................................................................................................................................

Another student decides to connect the crocodile clip in Fig. 3.1 so that there is only a very small length of the resistance wire included in the circuit. The teacher tells the student not to do this. Suggest one practical reason why values of $d$ less than $20.0\mathrm{c}\mathrm{m}$ should not be used. ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................

It is possible to change the potential difference $V$ by using a variable resistor rather than using different lengths of resistance wire. Complete the circuit diagram in Fig. 3.5 to show how the variable resistor is connected.