OCR A-Level Physics: Foundations and Measurement

A student uses a metre rule and a stopwatch to measure the period of a simple pendulum. She repeats the timing several times. When she examines her results she finds that they are closely grouped together, but a later check against a calibrated timer shows that every one of her readings is too large by about the same amount.

Describe and explain the difference between random error and systematic error, and the difference between precision and accuracy. In your answer you should classify the student's results using these terms, and state one practical method by which each type of error could be reduced.

(6 marks)

Three horizontal forces act at the same point on a small ring lying on a smooth table. Each force is measured from the positive x-axis, with angles measured anticlockwise.

Force	Magnitude / N	Direction (from +x-axis)
$F_1$F1​	8.0	$0^{\circ}$0∘
$F_2$F2​	6.0	$90^{\circ}$90∘
$F_3$F3​	5.0	$217^{\circ}$217∘

(a) Resolve each force and show that the resultant x-component is $+4.0 \ \text{N}$+4.0 N and the resultant y-component is $+3.0 \ \text{N}$+3.0 N (to 2 significant figures). (3 marks)

(b) Calculate the magnitude of the resultant force. (2 marks)

(c) Calculate the direction of the resultant force, measured anticlockwise from the positive x-axis. (1 mark)

A student measures the diameter of a steel ball bearing five times using a micrometer screw gauge that reads to the nearest 0.01 mm. The accepted value, marked on the packaging, is 5.00 mm. The readings are:

Reading	1	2	3	4	5
Diameter / mm	4.62	4.65	4.61	4.66	4.61

(a) Calculate the mean diameter. (1 mark)

(b) Using half the range as the absolute uncertainty, find the absolute and the percentage uncertainty in the mean diameter. (2 marks)

(c) With reference to your results, comment on whether the student's measurements are precise and whether they are accurate. (2 marks)

A jeweller checks the density of a small solid metal sphere. She measures its mass and its diameter $d$d, and uses the density formula

$\rho = \frac{6m}{\pi d^{3}}.$ρ=πd36m​.

Her measurements have the following percentage uncertainties:

Quantity	Value	Percentage uncertainty
Mass, $m$m	18.0 g	$1.0\%$1.0%
Diameter, $d$d	16.0 mm	$1.5\%$1.5%

(a) Explain why the percentage uncertainty in $d^{3}$d3 is three times the percentage uncertainty in $d$d, and state its value. (2 marks)

(b) Calculate the total percentage uncertainty in the density $\rho$ρ. (2 marks)

(c) The calculated density is $8.39 \ \text{g cm}^{-3}$8.39 g cm−3. State the absolute uncertainty in this density. (1 mark)

When a sphere of radius $r$r falls slowly through a thick liquid it experiences a viscous drag force given by Stokes' law:

$F = 6\pi\eta r v,$F=6πηrv,

where $\eta$η is the coefficient of viscosity of the liquid and $v$v is the sphere's speed.

(a) By rearranging the equation and substituting the SI base units of each quantity, determine the SI base units of the coefficient of viscosity $\eta$η. (3 marks)

(b) A student claims that viscosity could equally be measured in $\text{Pa s}$Pa s (pascal seconds). Show, using base units, that $\text{Pa s}$Pa s is equivalent to your answer in part (a). (1 mark)

Physicists often work with quantities that span many orders of magnitude, using SI prefixes and standard form.

(a) A capacitor stores a charge of 47 nC. Express this charge in coulombs, in standard form. (1 mark)

(b) A wire has a cross-sectional area of $2.5 \ \text{mm}^{2}$2.5 mm2. Express this area in $\text{m}^{2}$m2, in standard form. (1 mark)

(c) Estimate, to the nearest order of magnitude, the number of seconds in a human lifetime of about 80 years, and briefly justify your estimate. (1 mark)