Edexcel A-Level Physics Assessed Mathematical Skills

Practise Edexcel A-Level Physics AS and A2 mathematical skills by handling uncertainties, units, formula substitutions, speeds and graphs.

Covered syllabus points

C.0 Arithmetic and numerical computation C.1 Handling data C.2 Algebra C.3 Graphs C.4 Geometry and trigonometry

[Maximum number: 2]

A student investigated the flow of water through a horizontal pipe using the apparatus shown.

Figure for Question Assessed mathematical skills and measurement conventions question 1 — Edexcel A-Level Physics A2

The mass M of water leaving the pipe in a time t is given by the formula

M=\frac{\pi \rho P r^{4} t}{8 \eta L}

where
$\rho=$ density of water
P= pressure difference between the ends of the pipe
r= internal radius of the pipe
$\eta=$ viscosity of water
L= distance between digital pressure gauges

Show that the formula gives the unit for $\eta$ as $\mathrm{N\,s\,m^{-2}}$ .

[Maximum number: 2]

A student investigated the properties of a spring using the apparatus shown.

Figure for Question Assessed mathematical skills and measurement conventions question 2 — Edexcel A-Level Physics A2

The student determined the time period T of the oscillations of the mass-spring system.

The student displaced the mass downwards. He released the mass so that the mass oscillated vertically. He used a stopwatch to measure the time for multiple oscillations.

The student recorded the following results.

Table for Question Assessed mathematical skills and measurement conventions question 2 — Edexcel A-Level Physics A2

Calculate the mean value of T.

Mean value of T =

[Maximum number: 4]

An L-shaped steel rod was held horizontally in a stand clamped by its shorter end as shown.

The end of the steel rod was at a height p above the bench. A student attached a mass m to the end of the steel rod causing it to bend towards the bench. The end of the steel rod was then at a height q above the bench.

Figure for Question Assessed mathematical skills and measurement conventions question 3 — Edexcel A-Level Physics A2

(a)

The difference between p and q was recorded as 26 mm ± 1 mm.

Explain why the uncertainty in this value is given as 1 mm.

[ 2 ]

(b)

The shear modulus G is a measure of a material’s resistance to bending, and is given by

G = 32mglx²/(πyd⁴)

where m is the mass attached to the end of the rod and y is the vertical deflection. l and x are the lengths as shown below.

Determine a value of G for steel in N m^-2.

m = 100 g with negligible uncertainty
l = 58.9 cm ± 0.1 cm
x = 10.3 cm ± 0.1 cm
y = 26 mm ± 1 mm

G =

Figure for Question (b) — Edexcel A-Level Physics A2

[ 2 ]

[Maximum number: 3]

A student investigated the damped oscillations of a pendulum using the apparatus shown.

The paper cone acted as a damper.
The student displaced the cone and allowed the pendulum to oscillate.
He measured the amplitude A every 5 oscillations and recorded the value to the nearest 5 mm.

Figure for Question Assessed mathematical skills and measurement conventions question 4 — Edexcel A-Level Physics A2

The relationship between A and the number of oscillations n is

A=A_0 e^- n

where A_0 is the initial amplitude and is a constant.

Determine the value of A_0 from the graph.

A_0=

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Covered syllabus points

Assessed mathematical skills and measurement conventions question 1

Assessed mathematical skills and measurement conventions question 2

Assessed mathematical skills and measurement conventions question 3

Question (a)

Question (b)

Assessed mathematical skills and measurement conventions question 4