Physics 5054/42 — October/November 2023

Cambridge O-Level · Alternative to Practical · worked solutions for every part, with the mark scheme

questions

marks

minutes

Topics Experimental Contexts · Observations and Measurements · Use of Techniques, Apparatus and Materials · Analysis, Conclusions and Evaluation · Planning Experiments and Investigations

Q110MObservations and MeasurementsExperimental ContextsUse of Techniques, Apparatus and MaterialsAnalysis, Conclusions and EvaluationFree sample

A student measures the spring constant $k$ of a spring using two different methods.

The spring constant $k$ of a spring is a measure of the stiffness of the spring. The larger the spring constant $k$ , the more difficult the spring is to stretch.

(a)

Method 1

The student:

measures the unstretched length of the spring to the nearest 0.1 cm.

A full-size diagram of the spring is shown in Fig. 1.1.

Fig. 1.1

(i)

Measure the unstretched length $l_0$ of the spring to the nearest 0.1 cm.

Do not include the loops at the end of the spring in your measurement.

$l_0$ = ______ $\text{cm}$

(ii)

The student:

attaches the spring to a clamp on a stand
suspends a 300 g mass from the spring.

The arrangement of apparatus is shown in Fig. 1.2.

Fig. 1.2

The student measures the new length $l_1$ of the spring.

l_1 = 17.6\ \text{cm}

Calculate the extension $e$ of the spring produced by the mass.

Use the equation:

e = l_1 - l_0

$e$ = ______ $\text{cm}$

(iii)

Calculate the spring constant $k_1$ of the spring.

Use the equation:

k_1 = \frac{300}{e}

$k_1$ = ______ $\text{N/m}$

(iv)

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 ______

(b)

Method 2

The student:

pulls the 300 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.

(i)

The reading on the stop-watch is shown in Fig. 1.3.

Fig. 1.3

Record this time $t_1$ in Table 1.1 to one decimal place.

(ii)

Table 1.1

mass $m / \text{g}$	time $t_1$ for 20 oscillations / $\text{s}$	time $t_2$ for 20 oscillations / $\text{s}$	mean time $t$ for 20 oscillations / $\text{s}$	period $T / \text{s}$	$T^2 / \text{s}^2$
300		13.8

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.

(iii)

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.

(iv)

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}

$k_2$ = ______ $\text{N/m}$

(c)

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.

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Q4Planning Experiments and Investigations · Experimental Contexts6M

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