PHYC10003
SCHOOL OF PHYSICS
SESSION 1 TUESDAY 9 NOVEMBER 2021
EXAMINATION QUESTION PAPER – Gradescope Section 1
Write your ID on the first page of your solutions
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PHYSICS 1
PHYC10003
3 hours (180 MINS) NOT including reading or uploading time.
Estimate 1 hour (60 MINS) Canvas Quiz, 2 hours (120 MINS) Long Answer
UP TO 30 MINS (15 MINS FOR CANVAS QUIZ, 15 MINS FOR LONG ANSWER)
30 MINS (LONG ANSWER)
150 marks (50 marks Quiz, 100 marks Long Answer). This examination is worth 60
per cent of your total marks for this subject.
32 QUIZ QUESTIONS AND 9 GRADESCOPE QUESTIONS
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Duane Hamacher
Steven Prawer
[This page is included as an example of how the first page of your exam solutions should look]
My student number: 31415967
Subject: PHYC10003 – Exam semester 2 2021
I acknowledge the University of Melbourne rules for this exam
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Question 1
Here is my solution to question 1 ……
PHYC10003 Physics 1 Exam Semester 2, 2021
Gradescope component – 100 marks total
Question 1 - Kinematics and Projectile motion 13 Marks
a) What are the different components of a car that cause acceleration and how do they cause
acceleration?
b) A skateboarder plans to jump a ramp on a level road in front of a ditch measuring 245 cm
across. If the top surface of the ramp is 1.0 m long and stands 59 cm above the level road at
the end of the ramp, what minimum velocity must the skater achieve at the top of the ramp
in order to clear the ditch. Assume that the skater plans to land on a ramp of the same
dimensions on the other side of the ditch. You may ignore air resistance, and model the
skateboarder as a point particle.
c) For how long will the skateboarder be airborne?
[3 + 5 + 5 = 13 marks]
PHYC10003 Physics 1 Exam Semester 2, 2021
Question 2 - Circular Motion, Friction, Energy, and Hooke’s Law 12 Marks
a) After landing, the skater is travelling at a constant speed of 2.0 m/s. The skater then
accelerates at a constant rate of 1.5 m/s2 for 2.0 seconds before turning right on a horizontal,
circular path of radius 12 m. What minimum coefficient of static friction between the
skateboard’s wheels and the ground is required so that the skateboard does not slide off the
path?
b) If the skater continues moving in a circle of 12 m radius at the speed calculated in part (a),
how long will it take the cyclist to complete ¾ of a full circle?
c) In an alternate scenario, the 76 kg skater launches off the ramp with the 5.0 kg skateboard
and tries unsuccessfully to perform a flip trick. Instead, the skateboard flies off and the skater
lands vertically on a platform, under which is a large, heavy spring (see the figure below). The
top of the platform is level with the road surface before the skater lands on it. After landing
on the platform, the skater comes to rest when the spring has compressed by 3.2 cm.
Assuming an elastic collision between the skater and the platform, and that the mechanical
energy of the skateboard is negligible throughout the motion, what is the spring constant, k?
[5 + 2 + 5 = 12 marks]
PHYC10003 Physics 1 Exam Semester 2, 2021
Question 3 - Work, Power, and Torque 12 Marks
(a) A box with a mass of 3.00 kg is at rest. A person lifts the box upwards using a rope of negligible
mass looped over a pulley, so that the rope pulls vertically upwards on the box with a tension
force of 60.0 N. Calculate the work done by the tension force in the first 4.0 seconds after the
box leaves the ground.
(b) At what rate is the tension force doing work on the body at end of those 4.0 seconds?
(c) A merry-go-round (which can be treated as a solid metal disc) has a mass of 100 kg and a
radius of 1.3 m. A 15 kg child sits on the merry-go-round 1.0 m from the centre. Their parent
exerts a force of 300 N at the edge, causing it to spin. Neglecting friction, what is the resulting
angular acceleration, , of the Merry-go-round?
(I(disc) = ½ MR2 and I(child) = MR2)
[5 + 2 + 5 = 12 marks]
PHYC10003 Physics 1 Exam Semester 2, 2021
Question 4 – Collisions, Momentum, and Energy 13 Marks
A moving cue ball on a billiard table strikes another ball which is at rest. Both balls have the same
mass. After the collision, the cue ball has a speed of 3.2 m/s at angle of 28° to its direction of motion
just before the collision. The other ball has a speed of 2.1 m/s after the collision.
(a) Find the angle between the direction of motion of the second ball and the original direction
of motion of the cue ball.
(b) What was the speed of the cue ball before the collision?
(c) Was the collision elastic or inelastic? Justify your answer. Include an appropriate calculation.
[4 + 3 + 6 = 13 marks]
PHYC10003 Physics 1 Exam Semester 2, 2021
Question 5 – Oscillations 11 Marks
(a) A pendulum can be used to measure the local gravitational field, which changes depending
on the composition of the rocks and soil near the pendulum.
The mass on the end of the pendulum is 3.00 kg, the length is varied, and the time taken for
250 oscillations is measured.
The following results are obtained:
Length (m) Time (s)
0.500 354.25
1.000 501.5
1.500 614.5
2.000 708.75
(i) Use these results to provide an estimate for g, the local acceleration due to gravity. Be
sure to quote your answer to an appropriate number of significant figures.
(ii) You can vary the length of the pendulum, the mass on the end, and the angular amplitude
of the swing. What strategies would you use to increase the precision with which you can
measure ‘g’ (e.g. increase the mass, increase the amplitude, etc.)? Justify your choices.
Estimate the highest sensitivity that you think could be achieved.
(b) In class we demonstrated that a glass can shatter when subjected to a particular frequency of
sound. Explain this phenomenon. What is the condition that must be met for the glass to
shatter?
[(5 + 3) + 3 = 11 marks]
PHYC10003 Physics 1 Exam Semester 2, 2021

Question 6 – Interference 12 Marks
Quink’s apparatus consists of a horn loudspeaker which feeds sound into a network of pipes. Sound
can follow either the upper or lower branch of the network. The microphone on the right records the
combined sound from the two branches.

Figure 1 shows a still image from the demonstration in lectures of Quink’s apparatus. On the left-
hand side is a loudspeaker which sends sound waves into the network of pipes. The upper branch of
the rectangular network can be moved up or down using the dial at the centre top of the image. On
the right-hand side is a microphone which is connected to an oscilloscope. The position of the pipe
near the top of the figure can be recorded by reading the scale on the yellow ruler at the top right.
This image shows the pipes in a position that produces a maximum amplitude on the oscilloscope.
In Figure 2, on the next page, Steve has adjusted the dial, moving the upper section of the apparatus
upwards compared to its position in Figure 1. With the pipes in this position, the CRO shows a
minimum amplitude.
(a) As the dial is turned, the upper branch of the pipe arrangement moves up or down. The CRO
shows that as the dial is turned the signal at the microphone goes through maxima and
minima in intensity. Explain this phenomenon.






Figure 1.
microphone
loudspeaker
dial
ruler
oscilloscope
PHYC10003 Physics 1 Exam Semester 2, 2021














Steve can adjust the frequency of the loudspeaker. For each frequency, he can repeat the experiment
and record the positions of the pipe at the top where the sound amplitude is a maximum or a
minimum. He records the following results:

Frequency
(kHz)
position for maximum
(cm)
position for minimum
(cm)
2.00 15.8 19.8
4.00 16.2 18.1
8.00 15.0 16.0

(b) Use this data to determine the velocity of sound in air. (Assume that, at each frequency, no
maxima or minima were observed between the two positions recorded in the table.)

(c) The air in the pipes is replaced by Helium. Briefly explain what you would expect to observe,
regarding the locations of the maximum and minima, compared to the original
measurements. Would the measured velocity of sound change? Why?

[4 + 5 + 3 = 12 marks]




Figure 2.
PHYC10003 Physics 1 Exam Semester 2, 2021

Question 7 – Sound 8 Marks

(a) An alarm system designed detect intruders sends out pulses of ultrasound at 650 kHz. Due
to the Doppler effect, the sound reflected from an intruder moving slowly in the house is
shifted upwards in frequency by 379 Hz. This represents a shift of only 0.05%. How is it
possible to detect such a small shift?

(b) Orchestras ‘tune up’ using the musical note ‘A’ which has a frequency of 440 Hz. Each
instrument in the orchestra uses adjustments so that the pitch of this note on that particular
instrument is 440 Hz. But despite the fact that each instrument is playing ‘A’, even an amateur
can tell the difference between the piano, violin, and clarinet playing this same note. Explain
how we distinguish between different instruments playing the same note.

[4 + 4 = 8 marks]




Question 8 – Optics 8 Marks
(a) Explain how the eye can form a focussed image of an object on the retina. In your answer,
briefly discuss:

(i) Why light is refracted as it passes through the cornea into the eye;
(ii) how the eye is able to focus on objects at different distances.

(b) A person has a near point of 25 cm. The person dives into a swimming pool without goggles.
Even though the water is crystal clear, she then sees an object held at a distance of 25 cm
from her eye as blurry.

(i) Explain why this is the case.
(ii) What kind of corrective lens could be used to bring the object back into sharp focus?
Explain your answer with a diagram.


[(2 + 2) + (2 + 2) = 8 marks]



PHYC10003 Physics 1 Exam Semester 2, 2021

Question 9 – Relativity 11 Marks
(a) Explain the concepts of ‘Time Dilation’ and ‘Length Contraction’. Are these concepts
connected? If so, what is the connection? Your answer should include a discussion of
observers in different inertial reference frames of reference.

(b) A particle is subject to a constant force.

(i) On the same set of axes, sketch its speed as a function of time according to Newtonian
Physics then according to special relativity.
(ii) The force is doing work on the particle. If the particle’s speed cannot increase beyond
the speed of light, what happens to the energy associated with the work done by the
force? Is it lost?

(c) At the European particle accelerator (CERN), two particles are accelerated in opposite
directions and collide head-on in the interaction zone. Each particle reaches a speed of 0.80 c
with respect to the accelerator’s frame of reference. What is the relative speed of one particle
with respect to the other, i.e. what is the speed of the head on collision?


[5 + (2 + 2) + 2 = 11 marks]







End of Exam
Formula Sheet on next page








PHYC10003 Physics 1 Exam Semester 2, 2021

Equation and Data Sheet PHYC10003 (may be printed)

Newtonian constant of gravitation G 6.673 × 10-11 m3 kg-1 s-2
Gravitational acceleration at Earth’s surface g 9.80 m s-2
Radius of Earth RE 6.37 × 106 m
Speed of light in vacuum c 3.00 × 108 m s-1
Speed of sound in air (20 °C, 1atm) vsound 343 m/s
Avogadro constant NA 6.022 × 1023 kg mol-1
Elementary charge
Electron mass
e
me
1.6022 × 10–19 C
9.11 × 10-31 kg
Planck constant h 6.6261 × 10–34 J s
Atomic mass equivalent mu c2 931.5 MeV
Some Mathematical Formulae: sin(−) = −sin() cos(−) = cos()


(sin) = cos

(cos) = −sin
sin ≈ for small cos ≈ 1 for small sin + sin = 2sin 12 ( + )cos 12 ( − )
circle = 2 circle = 2 sphere = 42 sphere = 43 3
Equations:
⃗ = dt ⃗ = ⃗dt ⃗ = ⃗total ⃗ = ⃗ + ⃗ = + � ()dt
= + � 2
1
dt = + ⃗ + 12 ⃗()2 xf2 = xi2 + 2
= ′ + �⃗ ′ = − �⃗ ⃗ = ⃗′ + �⃗ ⃗′ = ⃗ − �⃗ , = ( in radians)
= dt = dt = = �2 + 2
= 2 = dvdt = + + 12()2 = + ()

2 = 2 + 2
PHYC10003 Physics 1 Exam Semester 2, 2021

= ⃗ ⃗ = dt = ,avg =
= 122 = = 12(∆)2
= � ⃗ ⋅ ⃗

= − = dWdt = ⃗ ⋅ ⃗
cm = 1�

cm = 1�

= �


2
= cm + Md2
= × ⃗ �⃗ = × �⃗ = �⃗ �⃗dt = net
net = ⃗ rot = 12 2 Ω =
= Gm122 = − 12 2 = �42GM�3
= 1

= 2 () = cos() spring= − Δ
= �


= �Mgl

= �
(, ) = sin( ± + 0) = ± ∓ = � = �
= ∆ = 1.22 =
=
= � + 12� 1 = 1 + 1′ = −′ = ℎ′ℎ
=

sin = sin = 1/
=

= 1
�1−2
∆ = ∆
�1 − 2 = �1 − 2
2 = 2(∆)2 − (∆)2 ′ = ( − vt)
′ = ( − vx 2⁄ ) = (′ + ′) = (′ + ′ 2⁄ )
′ = − 1 − uv 2⁄
= ′ + 1 + ′ 2⁄
= mu
2 = 02 + (pc)2
0 = mc2 = mc2 = 0 +














































































































































































































































































































































































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