6

3      A student has been asked to determine the linear acceleration of a toy car as it moves down a slope. He sets up the apparatus as shown in Fig.3.1.

Fig. 3.1

The time t to move from rest through a distance d is found for different values of d. A graph of d (y-axis) is plotted against t² (x-axis) as shown in Fig.3.2.

t ² / s²

Fig.3.2

© UCLES 2004                                                                          9702/02/M/J/04

7

(a)     Theory suggests that the graph is a straight line through the origin.

Name the feature on Fig.3.2 that indicates the presence of (i) random error,

...................................................................................................................................

(ii)     systematic error.

...................................................................................................................................

[2]

(b)    (i)     Determine the gradient of the line of the graph in Fig.3.2.

gradient  =  ........................................... [2]

(ii)     Use your answer to (i) to calculate the acceleration of the toy down the slope. Explain your working.

acceleration  =  ........................................ ms^–2 [3]

© UCLES 2004                                                                          9702/02/M/J/04

Answer all the questions in the spaces provided.

1      (a)    (i)    Define density.

...................................................................................................................................

...................................................................................................................................

                   (ii)    State the base units in which density is measured.

...................................................................................................................................

[2] (b) The speed v of sound in a gas is given by the expression

v            = √ ρ, γp

where p is the pressure of the gas of density ρ. γ is a constant.

Given that p has the base units of kgm⁻¹s⁻², show that the constant γ has no unit.

[3]

2 A student uses a metre rule to measure the length of an elastic band before and after stretching it.

The lengths are recorded as

length of band before stretching, L₀ = 50.0 ± 0.1 cm length of band after stretching, L_S = 51.6 ± 0.1 cm.

Determine

(a)    the change in length (L_S− L₀), quoting your answer with its uncertainty,

(L_S− L₀) = ……………………………………… cm  [1]

9702/2/O/N/02

(L_S− L₀)

(b)    the fractional change in length,      , L0

fractional change = ……………………………….  [1]

(c)    the uncertainty in your answer in (b).

uncertainty = …………………………………  [3]

9702/2/O/N/02

Answer all the questions in the spaces provided.

1 A simple pendulum may be used to determine a value for the acceleration of free fall g. Measurements are made of the length L of the pendulum and the period T of oscillation.

        The values obtained, with their uncertainties, are as shown.

            T = (1.93 ± 0.03) s      L = (92 ± 1) cm

         (a) Calculate the percentage uncertainty in the measurement of

  (i) the period T,  uncertainty =  ............................................ % [1]   (ii) the length L.  uncertainty =  ............................................ % [1]

© UCLES 2009                                                                          9702/22/O/N/09

(b)    The relationship between T, L and g is given by

4²L g = T ₂ .

                Using your answers in (a), calculate the percentage uncertainty in the value of g.

                                                                                uncertainty =  ............................................ % [1]

(c)    The values of L and T are used to calculate a value of g as 9.751 m s^–2.

(i)       By reference to the measurements of L and T, suggest why it would not be correct to quote the value of g as 9.751 m s^–2.

 ..................................................................................................................................

 ............................................................................................................................ [1]

(ii)     Use your answer in (b) to determine the absolute uncertainty in g.

                                   Hence state the value of g, with its uncertainty, to an appropriate number of

significant figures.

                                                                               g =  .......................... ±  ........................ m s^–2 [2]

© UCLES 2009                                                                          9702/22/O/N/09

Answer all the questions in the spaces provided.

1 A student takes readings to measure the mean diameter of a wire using a micrometer screw gauge.

(a)     Make suggestions, one in each case, that the student may adopt in order to (i)            reduce a systematic error in the readings,

...................................................................................................................................

...................................................................................................................................

(ii)       allow for a wire of varying diameter along its length,

...................................................................................................................................

...................................................................................................................................

(iii)     allow for a non-circular cross-section of the wire.

...................................................................................................................................

...................................................................................................................................

[3]

(b)    The mean diameter of the wire is found to be 0.50 ± 0.02mm. Calculate the percentage uncertainty in

(i)       the diameter,

uncertainty  =  ………………………………….  %

(ii)     the area of cross-section of the wire.

uncertainty  =  ………………………………….  %

[2]

           © UCLES 2004                                                              9702/02/O/N/04

For

Examiner’s Use Answer all the questions in the spaces provided.

1       (a) Distinguish between systematic errors and random errors.

systematic errors  .............................................................................................................  .......................................................................................................................................... random errors  ..................................................................................................................

 ..................................................................................................................................... [2]

         (b) A cylinder of length L has a circular cross-section of radius R, as shown in Fig. 1.1.

Fig. 1.1

                The volume V of the cylinder is given by the expression

V  =  πR²L .

                The volume and length of the cylinder are measured as

               V  =  15.0 ± 0.5 cm³

                L  =  20.0 ± 0.1 cm.

  Calculate the radius of the cylinder, with its uncertainty.  radius  =  ........................  ±  ........................ cm  [5]

© UCLES 2007                                                                          9702/02/O/N/07