CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS: COURSEBOOK
Exam-style questions and sample answers have been written by the authors. In examinations, the way marks are awarded
may be different.
Coursebook answers
Chapter P2
b
Self-assessment questions
1
he dependent variable is resistance and the
T
independent variable is the cross-sectional
area (or possibly the radius or diameter) of
the wire. Variables to be controlled include the
length of the wire, temperature and the type
of material.
2
ith the same readings a graph of RA against
W
l has gradient ρ. Other graphs are possible;
if readings were taken of R against A then
a graph of R against A1 has gradient rl. If
readings were taken of current I at a fixed
value of p.d. V, then a graph of 1I against l
ρ
has gradient AV
3
a
i Independent variable v (or the height
from which the mass falls); dependent
variable d; variables to be controlled
are mass of object that falls, size of
nail, type of wood
iiMeasure the height h of fall and use
v = ( 2gh ) , or find the time t for the
fall and use v = gt. It is also possible
to record the fall with a video camera
and stopwatch, and a rule behind the
mass. Play back frame by frame and,
using the last two frames, record s,
the distance covered, and t, the time
taken, and use v = st
4
iiiValues of d as low as 1 mm may be
measurable. Values over 20 mm are
likely to be difficult to obtain. One
could experiment using different
masses dropped from sensible heights
of 10 cm to 100 cm and using nails of
different thickness and different pieces
of wood.
ivA graph of d is plotted against v2. The
relationship is true if the graph is a
straight line through the origin.
1
5
raw a diagram showing the wood, nail
D
and mass. First measure the length l0
of the nail with calipers. Then hold the
nail so that its sharp end just touches
the wood and drop the mass from a
measured height h onto the flat head of
the nail. Use the calipers to measure the
length l of the nail that is sticking into
the wood. Calculate d = l0 − l. Repeat
the measurement for the same value of
h and average the values of d. For seven
different values of h from 10 cm to
100 cm, repeat the experiment. Each time,
use the same nail or an identical one in
a similar piece of wood. To make sure
that the mass falls squarely on the top of
the nail, you might use a cardboard tube
down which the mass falls vertically as a
guide, so that it always hits the centre of
the nail. Use the largest mass that gives a
good change in the value of d. For safety,
make sure that the mass does not fall
on your fingers by using a long nail and
wearing stiff gloves or having a guard
around your fingers. For each value of h,
calculate v = ( 2gh ) and plot a graph of
the average value of d against v2, which
should be a straight line through the
origin if the relationship is true.
a
1.00
b
2.30
c
2.00
d
0.699
e
10
f
1.65
lg 48 = 1.68
lg 3 + 4 lg 2 = 0.477 + 4 × 0.301 = 1.68
They are the same because lg 48 = lg (3 × 24) =
lg 3 + lg 24 = lg 3 + 4 lg 2
Cambridge International AS & A Level Physics – Sang, Jones, Chadha & Woodside
© Cambridge University Press 2020
CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS: COURSEBOOK
6
a
y2 against x3 has gradient k2; y against
x3/2 has gradient k; ln y against ln x has
gradient 32 and intercept ln k
b
ln y against ln x has gradient q
c
y2 against x has gradient In
against ln x has k =
7
1
2
( mB8 ) ; ln y
8
, intercept = 12 In mB
d
ln y against x has gradient k and intercept
ln y0
e
y against x2 has gradient R and intercept y0
Additional detail: relevant points might
include:
• Discussion of use of motion sensor, e.g.,
light gates, with details
• Use small-amplitude or small-angle
oscillations (to ensure equation is valid)
• Method of securing string to clamp, e.g.
use bulldog clip
Discussion of magnitude of mass:
• Large enough so that air resistance does
not reduce amplitude significantly
• Use of fiducial marker
• Time from the middle of the swing
Defining the problem:
• Vary l or l is the independent variable
• Determine the period T or T is the
dependent variable
8
tandard masses are used for the load. The
S
uncertainties in these are much smaller than
any others in the experiment, so they are
negligible.
9
a
gradient = b, y-intercept = ln a
Methods of data collection:
• Diagram showing the simple pendulum
attached, e.g., retort stand and clamp
• Many oscillations repeated to determine
average T (n ≥ 10 or t ≥ 10 s for stopwatch)
b
• Measure l using metre rule or ruler
• Measure to centre (of gravity) of mass
• Use of vernier calipers or micrometer to
measure the diameter of the bob and hence
the centre of mass
• At least five different values of l chosen
• Range of values of l at least 50 cm
• Appropriate graph plotted, e.g. T2 against l
or ln T against ln l
(if T2 against l) or intercept


of ln T versus ln l graph is ln  2π 
 g
ln (r / mm)
ln (R / Ω)
2.0 ± 0.1
175.0 0.69 ± 0.05 5.16
3.0 ± 0.1
77.8
1.10 ± 0.03 4.35
4.0 ± 0.1
43.8
1.39 ± 0.02 3.78
5.0 ± 0.1
28.0
1.61 ± 0.02 3.33
6.0 ± 0.1
19.4
1.79 ± 0.02 2.97
line of best fit
line of worst fit
5.0
4.5
4.0
3.5
3.0
• Calculation of g from gradient
Safety considerations:
2.5
0.6
• Relevant safety precaution related to the
use of masses, e.g. avoid fast-moving
mass, keep feet away, keep distance from
experiment, use clamp stand to avoid
toppling.
2
R / Ω
5.5
ln (R / Ω)
• Gradient =
r / mm
c, d
Method of analysis:
4π 2
g
0.8
1.0
1.2
1.4
ln (r / mm)
1.6
e
gradient = −2.00 ± 0.07
f
−2.00 ± 0.07
g
taking lnR = 5.3 ± 0.1 when ln r = 0.6
5,3 = lna - 2 × 0.6
lna = 6.5 ± 0.1 and a = 665 ± 70 mm2
1.8
Cambridge International AS & A Level Physics – Sang, Jones, Chadha & Woodside
© Cambridge University Press 2020