A student in a laboratory investigates how the length $l$ of a spring varies when different loads $L$ are added to it. He sets up a spring in a clamp with a load of $1.0\text{ N}$ attached to its lower end, as shown in Fig. 1.1. (i) Measure the length $l$ of the spring shown in the diagram in Fig. 1.1. Do not include the loops at each end of the spring in your measurement. Record your answer in Table 1.1. (ii) On the diagram in Fig. 1.1, draw a ruler in the correct position…

Physics 5054/42 — October/November 2019

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

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

Q115MExperimental ContextsObservations and MeasurementsUse of Techniques, Apparatus and MaterialsPlanning Experiments and InvestigationsAnalysis, Conclusions and EvaluationFree sample

A student in a laboratory investigates how the length $l$ of a spring varies when different loads $L$ are added to it.

He sets up a spring in a clamp with a load of $1.0\text{ N}$ attached to its lower end, as shown in Fig. 1.1.

Fig. 1.1

(a)

(i)

Measure the length $l$ of the spring shown in the diagram in Fig. 1.1. Do not include the loops at each end of the spring in your measurement.

Record your answer in Table 1.1.

(ii)

On the diagram in Fig. 1.1, draw a ruler in the correct position for the student to measure the length $l$ in the laboratory.

(iii)

The student determines as accurately as possible the reading on the ruler at the bottom of the spring.

On Fig. 1.1, mark with an X the position of the student's eye.

(b)

The student varies the load and takes a series of measurements of $L$ and $l$ . His results are shown in Table 1.1.

Table 1.1

$\text{load } L / \text{N}$	$\text{spring length } l / \text{mm}$
1.0
3.0	130
5.0	198
2.0	100
4.0	163

(i)

State one way to improve the table of results.

______

(ii)

On the grid in Fig. 1.2, plot a graph of $L$ ( $y$ -axis) against $l$ ( $x$ -axis). Start both axes from the origin $(0,0)$ . Draw the best-fit straight line.

Fig. 1.2

(iii)

State whether $l$ is directly proportional to $L$ .

Explain your answer.

______

(iv)

Use your graph to determine the length $l_0$ of the unstretched spring.

Show on your graph how you did this.

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

(c)

(i)

Using your graph in Fig. 1.2, determine the extension $e$ of the spring for a load of $3.6\text{ N}$ .

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

(ii)

On the axes in Fig. 1.3, sketch a graph of $L$ against $e$ .

Fig. 1.3

(d)

The gradient of your graph in Fig. 1.2 measures the force constant of the spring. The greater the force constant, the harder it is to stretch the spring.

A second spring has the same unstretched length but a greater force constant.

Using the same axes, draw on Fig. 1.2 a line to show how the length of this second spring changes as loads are added to it.

Label this line S.

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