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Canadian International Matriculation Programme
Sunway University College
SPH4U FINAL EXAMINATION
Student’s Full Name: _______________________________________________________
SPH4U
Section#_______
Period#______
Date:
Thursday, November 27th, 2008
Time:
08:30 – 10:30
Place:
Room 311
Length:
120.0 minutes
Lecturer:
Steve Anderson
DO NOT OPEN THIS BOOKLET UNTIL TOLD TO DO SO!
Please read the following instructions carefully before you begin the examination:
1. This exam paper has ten (10), two-sided, printed pages designated one (1) to twenty
(20). When told to start, check that all pages are included, then remove the last nonnumbered page. This extra page, at the back, contains physical constants
information, a “lazy cheat sheet”, and additional room for rough work.
2. This examination is worth 30 percent of your final mark.
3. The examination consists of three parts: Part A, Part B and Part C.
Clearly enter your answers, in this examination booklet, in the space provided!
PARTS
CONTENT
Marks
%
A
B
C
Multiple Choice Question (MCQ)
Calculations
Problem Solving (PS)
Total
17
27
36
80
21.25
33.75
45.00
100.0
Questions
≈ Time
/part/minute
25.5
40.5
54.0
120
/part
17
9
4
30
Put your common, or class name in the place provided on all subsequent pages!
4. Answers must be written in Standard English format for an academic audience and
quantities must have units with the correct significant digits.
5. Students are permitted to have a “cheat sheet”: one A4 sheet of paper with hand
drawn and written information, AND a scientific or a programmable calculator.
6. Constants are provided on the last page of this exam; please detach that last page,
once you have checked that this examination booklet is complete.
For office use only:
Part A
Part B
Part C
1 of 20
Total
PART A: Multiple Choice Questions
Place your answer to the questions in the answer section on the LEFT side
of the page!
Choose the BEST answer for each question.
Answer
Section
↓
1.
1.
A) Torque
2.
2.
The dimensional representation for Planck’s constant is identical to that of;
C) Power
D) Angular
Momentum
Which of the following unit is different from the others? (i.e. doesn’t belong)
A) kilogram
3.
B) Linear
Momentum
B) second
C) volt
D) kelvin
The string of a pendulum having a “bob” of weight mg is kept horizontal.
When it is released, the tension in the string at the lowest position is;
Figure MCQ 3
Horizontal position
mg
Lowest position
3.
A) mg
B) 3mg
C) 2mg
D) 6mg
Figure MCQ 4
M+m
m
v1
h
M
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SPH4U
Physics
4.
Student_____________________________
A bullet of mass m, moving with initial velocity v1, strikes a suspended
wooden block of mass M and gets imbedded in it (see Figure MCQ 4). If the
block rises to a height h, then v1 is equal to; (g is acceleration due to gravity)
4.
A)
5.
2 gh
B)
m
2 gh
M +m
C)
M +m
2 gh
m
D)
M −m
2 gh
M +m
The trajectory of a projectile moving near the earth’s surface is shown in the
diagram below. Consider the air resistance to be negligible; the force acting
on the projectile when it is at point p is;
Figure MCQ 5
p
5.
A) Directed to the
right
6.
B) Directed along a
tangent to the
path
C) Directed
vertically
downwards
D) directed toward
the centre of
the arch
The diagram below shows two masses hanging on a string, which passes
over a massless, frictionless pulley. Given that; m2 > m1 , the acceleration of
the masses is a, and the earth’s gravitational field strength is g; what is the
tension in the massless, non-stretchable string?
Figure MCQ 6
T
T
m2
m1
6.
A) m1g
B) (m1+m2)g
C) m2g
D) m2(g-a)
E) (m1-m2)g
SPH4U – Final Exam - page 3 of 20 – Semester Two, 2008
7.
Two pucks move with negligible friction across a horizontal plane surface.
The momentum vectors of the two pucks before they collide are shown in
Figure MCQ 7.1. After colliding, the pucks stick together. Which one of the
vectors shown in Figure MCQ 7.2 best represents the total final momentum
of the joined pucks after the collision? Note; figures are to scale.
7.
A)
A
B)
B
C)
C
D)
D
Figure MCQ 7.1
B
D
C
A
Figure MCQ 7.2
8.
A 1000 kg roller coaster, with passengers, starts from rest at point A on a
frictionless track as show in the figure below. What is the maximum speed of
the roller coaster?
Figure MCQ 8
8.
A) 13 m/s
B) 10 m/s
C) 14 m/s
4 of 20
D) 19 m/s
SPH4U
Physics
9.
Student_____________________________
Two charges of +10 µC and -10 µC are placed at a distance of 10 cm. The
electric potential at a point M exactly in the middle is;
9.
A)
0.8 V
B)
-10 V
C)
10 V
D)
zero
10.
An object moves without friction under the influence of a force, which varies
as shown in Graph MCQ 1. If the object had a mass of 2 kg, what would be
the change in velocity (∆v) between 4 s and 6 s?
10
.
A)
10 m/s
B)
15 m/s
C)
20 m/s
D)
40 m/s
Graph MCQ 1
10
force
/N
4
Mass of object is
2 kg
0
1
2
3
4
5
time
/s
Not to scale
11
.
6
11.
r
Using Graph MCQ 1, what was the ∆p between t = 0 s and t = 6.0 s?
A)
38 N ⋅ s
B)
16 N ⋅ s
C)
12 N ⋅ s
D)
SPH4U – Final Exam - page 5 of 20 – Semester Two, 2008
24 N ⋅ s
12.
A charged particle with a charge-to-mass ratio of 5.7(108) C/kg travels in a
magnetic field of strength 0.75 T in a circular path that’s perpendicular to the
magnetic field.
What is the period of revolution for this particle in nanoseconds (ns)?
12
.
B)
1.5
C)
15
D)
1.5(101)
A)
0.150
13.
How is the interference pattern affected in Young’s double-slit experiment if it
was performed in still water rather than in air?
13
.
14
.
15
.
A) fringes will be
narrower
B) fringes will be
broader
C) fewer fringes
will be visible
D) no fringes will
be observed
14.
The alpha-particles emitted during various radioactive processes have same;
A)
speed
15.
In
A)
92
235
16.
At what speed should a body move so that its relativistic mass is twice the
92
B)
momentum
C) kinetic energy
D) specific charge
U 235 nucleus, the ratio of number of nucleons to the number of protons;
B)
235
92
C)
235
143
D)
143
92
value of its rest mass? Take c as the velocity of light.
16
.
17
.
A)
8.67c
B)
17.
Hadrons are subatomic particles that are made up of;
A)
bosons
B)
8.76c
leptons
C)
C)
6 of 20
0.867c
quarks
D)
8.87c
D)
gluons
SPH4U
Physics
Student_____________________________
PART B: Calculations with Answers Only
You will be marked on 9 (nine) of the following 12 (twelve) questions
Only the ANSWERS will be graded and are worth 3 marks each
o One mark for the right answer
o One mark for the correct units
o And another mark for what should now be seen as
significant
Overleaf of the Constants Page can be used for rough calculations
Write your answers, for each question, in the box provide.
1) A baseball player makes perfect contact with the ball, striking it at 45° above the
horizontal at a point 1.3 m above the ground. His home-run hit just clears the
3.0 m wall, 130 m from home plate. Hint: Velocity components can be
considered independently, but the ∆t for the flight is the same.
With what velocity does the ball leave the baseball bat?
Answer
Box
1
2) Determine the acceleration of the system in Figure B.2? Assume the pulley is
frictionless and massless and that the surface of the inclined plane has a
coefficient of static friction, µ=0.15.
Figure B.2
m1=20 kg
m2=25 kg
µ=0.15
Θ=25°
2
SPH4U – Final Exam - page 7 of 20 – Semester Two, 2008
3) A clock’s pendulum is 60 cm long with a bob at the end of mass 500g.
Determine the maximum tension in the pendulum rod when the bob is swinging
at a speed of 2.4 m/s.
3
4) A 10.0 kg flowerpot is suspended from the end of a horizontal strut by a cable
attached at 30° above the horizontal, as shown in Figure B.4.
If the strut has no mass, find the tension in the cable.
Cable
Figure B.4
30°
Strut
10.0 kg
4
8 of 20
SPH4U
Physics
Student_____________________________
5) What is the magnitude of a test charge that experiences a force of 3.71 N in a
field of strength 170 N/C?
5
6) How far from a long conductor passing a current of 12.5 A is the magnetic field
of strength 3.1(10-5) T?
6
7) Figure B.7 shows conductors of length L = 0.65 m and current I = 12.0 A lying in
a plane that’s perpendicular to a magnetic field B = 0.20 T. What is the force on
the wire?
r
B
Figure B.7
r
I
7
SPH4U – Final Exam - page 9 of 20 – Semester Two, 2008
8) Given that the refractive index of water is 1.33, how long does it take light to
travel from one shore of a lake to the opposite shore, if the lake is 12 km long?
8
9) At what angle should two polarizing filters be positioned to reduce the intensity
of light, incident on the polarizer, by 60 %?
9
10) What is the distance to the second-order maximum for a diffraction grating with
230 mm-1, if the screen is 0.95 m away and orange light of wavelength 610 nm
is used?
10
10 of 20
SPH4U
Physics
Student_____________________________
11) An electric stove produces many infrared photons. If the peak wavelength of
the radiation coming from a stove element is 10 µm; what is the momentum of
the released photons?
11
12) In a head-on collision of a 5.3 MeV alpha particle
uranium,
(
4
2
He
)
2+
with a nucleus of
232
92
U , determine the closest distance of the alpha particle before it is
deflected back from the uranium nucleus.
12
SPH4U – Final Exam - page 11 of 20 – Semester Two, 2008
PART C: Problem Solving
You will be marked on the solution you placed in the solution
sections, which are on the facing page, for each set of problems.
Out of a total of twelve (12) problems, you must do four (4).
This section’s solutions must have perfect form for full marks.
To move a 45 kg wooden crate across a wooden floor (µ=0.20), you tie a rope
1
onto the crate and pull on the rope. While you are pulling the rope with a force
of 115 N, it makes an angle 15° with the horizontal.
a) How much time elapses between the time at which the crate just starts to
move and the time at which you are pulling it with a velocity of 1.4 m/s?
b) What is the total work done?
c) Find the best angle to pull the crate and explain or prove it is the best angle?
2
Analyze the system in Figure C.2;
a) Determine the acceleration on the system if µ≡0,
b) What coefficient of friction is required to prevent the system from moving?
c) What effect would a non-ideal pulley have on your solutions? Why?
m1 = 5.87 g
massless, frictionless pulley
m2 = 6.27 g
Figure C.2
In an experiment a 4.987 kg standard brass mass was used to compress a
3
spring. The data is in Table C.3.
a) Show that the spring’s constant is
k = 315.6 N/m
b) If a bowling ball of m = 1.57 kg fell from a height
of 3.25 m, on to the spring, how far would the
Table C.3
Trial /# ∆x /(10-1)m
1
1.526
2
1.624
3
1.585
4
1.465
spring compress?
c) What assumptions, if any, where made in your calculation? Why?
12 of 20
SPH4U
Physics
Student_____________________________
Givens
½
Since
Logical Flow/Calculation
therefore
b) logical flow, therefore
c) logical flow, therefore
SPH4U – Final Exam - page 13 of 20 – Semester Two, 2008
Canadian Indy 500 racing car driver Paul Tracy set the speed record for time
4
trials at the Michigan International Speedway (MIS) in the year 2000. Tracy
averaged 378.11 km/h in the time trials. The ends of the 3 km oval track at MIS
are banded at 18.0° and the radius of curvature is 382 m.
a) At what speed can the cars round the curves without needing to rely on
friction to provide a centripetal force?
b) Prove whether or not Tracey relied on friction for some of his required
centripetal force AND draw a Free Body Diagram (FBD) of Tracey’s car on
the ramp.
Two charged pith balls (q)are in static equilibrium, as represented in Figure C.5.
5
a)
What is the charge q on the pith
balls?
b)
Θ = 24.5°
d = 18.3 cm
If the charges on the pith balls were
doubled; draw a new figure with all
the dimensions labeled and a FBD
for at least one of the pith balls.
m1 = m2 =2.53 g
Figure C.5
A student practices her tennis volleys by hitting a tennis ball against the wall.
6
a) If the 60.0 g ball travels at 48.0 m/s just before hitting the wall and then
bounces directly backward of the wall at 35 .0 m/s, what is the impulse of
the interaction?
b) If the duration of the interaction is 25.0 ms, what is the average force
exerted on the ball by the wall? AND draw a FBD of the tennis ball at the
moment it leaves the wall.
c) Describe why or why not it is believable that the ball bounced directly
backward from the wall.
14 of 20
SPH4U
Physics
Student_____________________________
Givens
½
Since
Logical Flow/Calculation
therefore
b) Validity
c) FBD
SPH4U – Final Exam - page 15 of 20 – Semester Two, 2008
A billiard ball of mass 0.155 kg is rolled down an inclined ramp with a height of
7
62.4 cm directly away from you (consider friction negligible). It collides with a
stationary golf ball of mass 0.052 kg. The billiard ball rolls off at an angle of 15°
clockwise from its original direction with a velocity of 3.1 m/s.
a) What is the final velocity of the golf ball?
b) What is the work done on the billiard ball?
c) What is the answer to a) if this problem was done on the moon?
Hint: the moon’s field strength is
1
g
6
A glass puck of mass 0.155 kg is placed on ice (consider friction negligible) in
8
an electric field of strength 9.81 N/C. The charge on the puck is 0.155 C and
the electric field is turned off after the puck has been accelerated for 0.624 m
due east. Directly in the path of the puck is another, neutrally charged, glass
puck of mass 0.052 kg at rest. The heavier glass puck slides off at an angle of
E15°N with a velocity of 3.1 m/s.
a) What is the final velocity of the lighter puck?
b) What is the work done on the heavy glass puck?
c) What sort of apparatus must have generated the required electric field flux?
A puck, which acts like a bar magnetic, of mass 0.155 kg is placed on a
9
frictionless surface in a magnetic field and accelerated, due north, for a distance
62.4 cm, until the puck’s speed is 3.5 m/s, when the magnetic field is turned off.
Directly in the path of the puck is another, non-magnetic, puck of mass 0.052 kg
at rest. The magnetic puck slides off at an angle of N15°W with a velocity of 3.1
m/s.
a) What is the final velocity of the non-magnetic puck?
b) What is the work done on the magnetic puck?
c) What is the magnetic field strength of the applied magnetic field, in N/T, if
the magnetized puck has field strength of 1 Tesla?
16 of 20
SPH4U
Physics
Student_____________________________
Givens
½
Since
Logical Flow/Calculation
therefore
b) Calculation
c) Proof
SPH4U – Final Exam - page 17 of 20 – Semester Two, 2008
You have a 160.0 µg sample of polonium-218 that has a half-life of 3.0 minutes.
10
a) How much will remain after 7.0 min?
b) How long will it take to decrease the mass of the polonium-218 to 8.0
micrograms?
c) If this isotope of polonium decays by an Alpha Decay process, draw the
COMPLETE yield formula for the transmutation of polonium-218 to its
“daughter” nucleus.
11
An experimenter wants to hit the target below, with an Alpha particle;
a) Show that the r = 1.92(10-2) m in the experimenter’s calculation is reasonable.
b) Why does the experiment not work and what should r be set at?
c) If the particle accelerator cannot be adjusted and the target is too rusted to
move, what else could be adjusted to compensate for the error? & qualify the
value.
Target
Radius of Curvature
Alpha Particle 24 He 2 +
v = 2.07(10 8 ) m
B = 2.25(10 2 )T
s
r
The star Alpha Centauri is 4.2 light-years away (a light year is the distance light
12
travels in one year: 365.25 days).
a) If you traveled in a spaceship at a speed of 2.0(108) m/s, how long would
this distance appear to be?
b) How long would a one-way trip take you?
c) How much time would pass for someone back on earth, for your one way trip
to Alpha Centauri?
18 of 20
SPH4U
Physics
Student_____________________________
Givens
½
Since
Logical Flow/Calculation
therefore
Calculation
Proof
SPH4U – Final Exam - page 19 of 20 – Semester Two, 2008
20 of 20