Physics 9702/31 — October/November 2016

Cambridge AS Level · Advanced Practical Skills · worked solutions for every part, with the mark scheme

questions

marks

120

minutes

Topics Manipulation, Measurement and Observation · Presentation of Data and Observations · Analysis, Conclusions and Evaluation

Q1Manipulation, Measurement and ObservationPresentation of Data and ObservationsAnalysis, Conclusions and EvaluationFree sample

In this experiment, you will investigate the motion of a mass attached to a system of springs.

(a)

(i)

Set up the apparatus as shown in Fig. 1.1.

Fig. 1.1

Slide the string loop over the rod of a stand and fix it in place near the top of the rod with one of the clips.

Slide the free loop of the spring over the other rod and fix it in place with the other clip.

The string loop in clip A is a height $h$ above the base of the stand and the spring loop in clip B is a height $h_1$ above the base of the stand. Adjust the apparatus until $h$ and $h_1$ are equal.

(ii)

Measure and record $h$ .

$h$ = ______

(b)

Pull the 400 g mass down through a short distance.
Release the mass.

The mass will oscillate.

Determine the period $T$ of these oscillations.

$T$ = ______

(c)

The period $T$ of the oscillation of a mass $m$ attached to a system of springs is given by

T = 2\pi\sqrt{\frac{m}{k}}

where $k$ is the spring constant of the system.

The mass $m$ is 0.400 kg.

Using your answer in (b), calculate the corresponding value of $k$ .
Give your answer to an appropriate number of significant figures.

$k$ = ______ $\text{N m}^{-1}$

(d)

(i)

Slide the spring loop in clip B down by approximately 5 cm as shown in Fig. 1.2.
Do not move clip A.

Fig. 1.2

The spring loop in clip B is a height $h_1$ above the base of the stand.

(ii)

Measure and record $h_1$ .

$h_1$ = ______

(iii)

Calculate $(h - h_1)$ .

$(h - h_1)$ = ______

(iv)

Repeat (b).

$T$ = ______

(e)

Vary $h_1$ and repeat (d)(ii), (d)(iii) and (b) until you have six sets of values of $(h - h_1)$ and $T$ . Do not move clip A.

Include in your table the two sets of values already taken.

(f)

(i)

Plot a graph of $T$ on the $y$ -axis against $(h - h_1)$ on the $x$ -axis.

(ii)

Draw the straight line of best fit.

(iii)

Determine the gradient and $y$ -intercept of this line.

gradient = ______
$y$ -intercept = ______

(g)

It is suggested that the quantities $T$ and $h_1$ are related by the equation

T = P(h - h_1) + Q

where $P$ and $Q$ are constants.

Using your answers in (f)(iii), determine the values of $P$ and $Q$ .
Give appropriate units.

$P$ = ______
$Q$ = ______

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