UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 1
SECTION A
A1.
SHORT QUESTIONS (203 marks)
ANSWER ALL QUESTIONS
ALL QUESTIONS HAVE EQUAL MARKS
A motorist makes a trip of 600 km from Durban (D) to Johannesburg (J). For the first 180 km
she drives at a constant speed of v1 = 120 km/h in a time t1 . Calculate the time t 2 required to
drive the remaining distance (420 km) at a constant speed v2 so that her average speed for the
total trip is to be 100 km/h.
180 km
420 km
D
J
t1
A2.
60 MARKS
t2
The figure shows an acceleration-versus-force graph for three objects pulled by rubber bands.
The mass of object 2 is 36 kg. You may assume that F  ma . Estimate the mass of object 3.
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 2
A3.
A projectile is fired at time t  0 s, from the edge of a vertical cliff with initial velocity
components of v 0 x  30 m/s and v 0 y  40 m/s. The projectile rises and then falls into the sea
at a point P. The time of flight of the projectile is 15 s. Calculate the height of the cliff and the
range of the projectile.
P
A4.
Two blocks are connected by a string that goes over a frictionless pulley as shown in the figure.
Block A has a mass of 5.00 kg and can slide over a smooth frictionless plane inclined 30.0° to
the horizontal. Block B has a mass of 3 kg. Calculate the acceleration of the blocks.
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 3
A5.
A ball weighing 72 N is attached to the ceiling by a 3.0 m rope. The ball is pulled to one side
and released; it then swings back and forth as a pendulum. As the ball swings through point B,
its speed is 4.0 m/s. Calculate the tension in the rope at point B.
C
3.0 m
A
h
B
A6.
A 5.0 m radius playground merry-go-round with a moment of inertia of 2000 kg·m2 is rotating
freely with an angular speed of 2.0 rad/s. One person of mass of 60 kg is standing right outside
the edge of the merry-go-round and steps on it with negligible speed. Calculate the new angular
speed of the merry-go-round right after the person has stepped on it. Assume the person can be
approximated as a point mass with moment of inertia MR 2 .
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 4
A7.
In the figure below, a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal
surface. The crate weighs 930 N, and its center of gravity is at its geometric center. A
horizontal force F is applied at a distance h above the floor.
(i)
If h  0.61 m, calculate the minimum value of F required to make the crate start to tipover. Start to “tip over” means that the crate begins to lose contact with the ground
except for the left hand of the edge of the crate in this case. Assume that the static
friction is large enough that the crate does not start to slide.
(ii)
Deduce the value of the normal force when the crate is just about to tip over.
A8.
A steel guitar string with a diameter of 0.300 mm and a length of 70.0 cm is stretched by 0.500
mm while being tuned. Calculate the force is needed to stretch the string by this amount. The
Stress
Young's modulus for steel is 2.0  1011 N/m2. Assume Modulus 
.
Strain
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CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
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A9.
In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density
1000 kg/m3) that is 3.0 m thick, as shown. Calculate the thickness of the oil layer if the gauge
pressure at the bottom of the tank is 5.0  104 N/m2. The density of the oil is 510 kg/m3.
Assume that the pressure at a given depth h in a fluid is given by gh .
A10.
An astronaut is standing on the surface of a planetary satellite that has a radius of
rs  1.74  106 m and a mass of M S  7.35  1022 kg. An experiment is planned where a
projectile of mass m p needs to be launched straight up from the surface. Calculate the
minimum initial speed of the projectile so that it will reach a height of rf  2.55  106 m above
this satellite’s surface. Hints: Use energy conservation and assume the gravitational potential
GM S m p
energy is U ( r )  
.
r
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
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A11.
A mass m is attached to an ideal massless spring. When this system is set in motion with
amplitude A , it has period T . The system is brought to rest. It is then set into motion again
with an amplitude equal to 2 A . What is the new period? Explain your answer.
A12.
The angle that a swinging simple pendulum makes with the vertical obeys the equation
 (t )  (0.150 rad) cos[(2.85 rad/s)t  1.66 rad].
What is the length of the pendulum?
A13.
Four travelling waves are described by the following equations,
(i)
(ii)
(iii)
(iv)
y  0.12 cos(3x  2t )
y  0.15 sin(6 x  3t )
y  0.23 cos(3x  6t )
y  0.29 sin(1.5x  t )
where all quantities are measured in SI units and y represents the displacement of the medium.
Which of these waves have the same speed?
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CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 7
A14.
A jet plane at take-off can produce sound of intensity 10.0 W/m2 at a distance of 30 m away.
You, however, prefer the tranquil sound of normal conversation, which is 1.0 µW/m2. Assume
that the plane behaves like a point source of sound and ignore absorption losses. What is the
closest distance you should live from the airport runway to preserve your peace of mind?
A15.
A standing wave of the seventh harmonic is induced in a stopped pipe, 1.2 m long. The speed
of sound is 340 m/s. Determine the number of antinodes in the standing wave pattern.
A16.
The Kelvin temperature scale uses the triple point of water for its definition. Define what is
meant by this point and list the physical conditions necessary for its existence.
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 8
A17.
The surface of the Sun has a temperature of 5800 K. The radius of the sun is 6.96  108 m.
Calculate the total energy radiated by the Sun each second. Assume that the emissivity is
0.986.
A18.
Prove that, for a fixed amount of ideal gas undergoing an isobaric expansion, the coefficient of
volume expansion is equal to the reciprocal of the absolute temperature.
A19.
Air at 20.0 C and a pressure of one atmosphere ( 1.01  105 Pa) is compressed adiabatically to
0.0900 times its original volume. By treating the air as an ideal gas with  = 1.4, find the
temperature at the end of the adiabatic compression.
A20.
Molecular oxygen has a molar mass of 32 g/mol. Calculate the root-mean-square speed for
oxygen at a temperature of 300 K.
[60]
END OF SECTION A
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 9
SECTION B
MECHANICS
60 MARKS
ANSWER ALL QUESTIONS
ALL QUESTIONS HAVE EQUAL MARKS
QUESTION B1
The graph in the figure below shows the velocity of a motorcyclist plotted as a function of time.
v (m/s)
60
20
t (s)
0
0
40
80
120
160
200
(a) Find the instantaneous acceleration at t  80 s and t  140 s .
(3)
(b) Draw the acceleration-time graph of the motorcyclist during the first 200 s.
(3)
2
a (m/s )
1.0
0.5
0
-0.5
t (s)
-1.0
0
40
80
120
160
200
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 10
QUESTION B1 (CONTINUED)
(c) Calculate the average speed of the motorcyclist during the first 200 s.
(3)
(d) Sketch the position-time graph of the motorcyclist during the first 200 s.
(3)
x (m)
5000
4000
3000
2000
1000
t (s)
0
0
40
80
120
160
200
[12]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 11
QUESTION B2
In a truck loading station at a post office a small 0.200 kg package is released from rest at a point A on
a track that is one quarter of a circle with radius 1.60 m. The size of the package is much less than 1.60
m, so that the package can be treated as a point mass. It slides down the track and reaches point B with
a speed of 4.0 m s1. From point B it slides on level surface a distance of 3.00 m to point C where it
comes to rest.
1.60 m
A
1.60 m
B
C
(a) What is the coefficient of kinetic friction on the horizontal surface?
(4)
(b) How much work is done one the package by friction as it slides down the circular arc from A to B?
(4)
(c) Deduce the average friction force on the package from A to B.
(4)
[12]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 12
QUESTION B3

A man is dragging a 30 kg box up a loading a ramp at constant velocity ( a  0 ). The ramp has a slope
of 20 and the man pulls on the box with a rope at an angle of 30 with respect to the ramp. The
coefficient of kinetic friction between the ramp and the box is 0.25.
(a) Show and label appropriately all the forces
acting on the box resolved into components
perpendicular and parallel to the ramp.
(2)
30
20
(b) Hence calculate the magnitude of the tension in the rope.
(10)
[12]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 13
QUESTION B4
A 5 gram bullet is fired horizontally into a 1.5 kg wooden block resting on a horizontal surface. The
coefficient of kinetic friction between the block and surface is 0.30. The bullet remains embedded in
the block, which is observed to slide 0.25 m along the surface before stopping.
(a) Calculate the velocity of the bullet and the block just after collision.
(6)
(b) Deduce the initial speed of the bullet.
(4)
(c) State if the collision between the bullet and the block is elastic or inelastic? Justify your answer.
(2)
[12]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 14
QUESTION B5
A block weighing 240 N is suspended at the end of a uniform beam AB which is hinged
to the wall at A as shown in the diagram below. The weight of beam AB is 60 N.
C
1.2 m
A
B
1.6 m
240 N
(a) Show all the force acting on the beam resolved into horizontal and vertical components.
(2)
(b) Calculate the tension in cable BC.
(4)
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 15
QUESTION B5 (CONTINUED)
(c) Calculate the horizontal force exerted by the hinge on the beam.
(2)
(d) Calculate the vertical force exerted by the hinge on the beam.
(2)
(e) Hence deduce the direction of the force exerted by the hinge on the beam.
(2)
[12]
END OF SECTION B
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 16
SECTION C
OSCILLATIONS AND WAVES
ANSWER ALL QUESTIONS
30 MARKS
QUESTION C1
An object is undergoing simple harmonic motion with period 1.210 s and amplitude 0.610 m. At t  0
the object is at x  0 . How far is the object from the equilibrium position when t  0.485 s?
(8)
[8]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 17
QUESTION C2
A standing wave with a frequency of 1100 Hz in a column of methane (CH4 ) gas at 20.0 C produces
nodes that are 0.200 m apart. The molar mass of methane is 16.0 g/mol. Calculate the value of  for
methane.
(9)
[9]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 18
QUESTION C3
A string with a linear mass density of 1.6  10 3 kg/m has one end attached to a wall. The other end is
draped over a pulley and is attached to a hanging object with a mass of 4.00 kg (see diagram below). If
the distance between the wall and the pulley is 5 m, find the fundamental frequency of vibration of the
string.
(6)
[6]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 19
QUESTION C4
Two train whistles, A and B, each have a frequency of 392 Hz. A is stationary and B is moving toward
the right (away from A) at a speed of 35.0 m/s. A listener is between the two whistles and is moving
toward the right with a speed of 15.0 m/s (see diagram below). No wind is blowing. Calculate the beat
frequency detected by the listener.
(7)
[7]
END OF SECTION C
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 20
SECTION D
THERMAL PHYSICS
ANSWER ALL QUESTIONS
30 MARKS
QUESTION D1
At an absolute temperature T0 , the volume of an object is V0 and its density is  0 . The object is made
of a material with coefficient of volume expansion  .
(a) Show that if the temperature changes to T0  T , the change in density of the object,      0 ,
can be written, approximately, as
     0 T .
Hint: You may use the approximation (1  x)  1   x , valid if x  1 , without proof.
(6)
(b) Explain the origin of the minus sign in the above formula. Give an example of a material for which
an increase in temperature would produce an increase in density, including temperature range if
necessary.
(3)
[9]
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CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
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QUESTION D2
A copper calorimeter can with mass 0.450 kg contains 0.160 kg of water and 0.0950 kg of ice in
thermal equilibrium at atmospheric pressure. A cube of iron at a temperature of 355 C is dropped into
the calorimeter can. When equilibrium is established the final temperature is found to be 35.0 C.
Calculate the mass of the iron cube that was added to the calorimeter. Assume that no heat is lost to the
surroundings.
(10)
[10]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 22
QUESTION D3
A sample of an ideal gas is taken through the process abc indicated by the solid lines in the figure.
The curved line between a and c is an isotherm.
(a)
Determine the change in internal energy of the gas in going from state a to state c .
Explain your reasoning.
(2)
(b)
Calculate the pressure of the gas in state a .
(2)
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 23
QUESTION D3 CONTINUED
(c) Calculate the total heat, Qabc , exchanged by the gas with its surroundings during the process abc .
Hint: Consider the first law for process abc .
(6)
(d) Does the gas absorb heat or release heat during this process? Explain.
(1)
[11]
END OF SECTION D
END OF EXAMINATION
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: MAIN EXAMINATION JUNE 2015
CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 24
DATA AND FORMULAE SHEET: PHYS110
k  1.38  1023 J K1
G  6.67  10 N m kg
g  9.80 m/s 2
R  8.314 J mol 1 K 1
c  3.00  108 m s 1
N A  6.023  1023 mol 1
I 0  1012 W m2
M E  5.98  10 24 kg
RE  6.38  10 6 m
1 cal  4.19 J
  5.67  108 W m2 K 4
1 atm  1.013  105 Pa
 water  1.00  103 kg m 3
0 K  273.15 o C
1 u  1.66  1027 kg
11
v x  v0x  axt
  0   t
v  r
v AC  v AB  v BC
KE  12 mv 2
2
2
x  x0  v 0xt  12 a x t 2
 2  02  2 (   0 )
aT  r
 dp
F
 i  dt

W  F  s  Fs cos 
2
v 2x  v 0x
 2a x ( x  x0 )
x  x0  12 ( v 0x  v x )t
   0  12 (0  )t
   0  0t  12  t 2
  s/r
aC  v 2 / r   2 r


F
 i  ma
f  N


p  mv
L  r p
P  ddWt  F  v
L  I
I   mi ri2

GM E m
r
PF/A
U grav  mgh
PABS  PG  PATM
F / A stress

L / L strain
PG   g h
Fx  kx
tan    v 0x /  x0
2
A  x02  v 0x
/ 2
dp
dV
1
U  2 kx2
K  U  12 kA2
  g/L
T  2 L / g
x(t )  A cos(t   )
y( x, t )  A cos(kx  t )
v y ( x, t )  A sin(kx  t )
v  F /
Pmax  2 Pav
I1 I 2  r22 r12
I  P 4 r 2
Pav  12 F  2 A2
y( x, t )  Asw sin kx sin t
f n  nv/2 L
pmax  BkA
v  B/
v  RT / M
I  12 BkA2
I

F t   p  J
  Fr sin 
F
GMm
 mg
r2
  m /V
FB   f V f g
I
2
pmax
2 v
U (r)  
B  V
  (10 dB) log
I
I0
L   L0 T
i
 I
fn  n
v
4L
1 dL
L dT
1 dQ
c
m dt
Q  mL
C
1 dV
V dT
Q  mc(T2  T1 )
p1V1 T1  p2V2 T2
v rms  3kT m  3RT M
H  Ae T 4
dW  pdV

1 dQ
n dt
H  A(TH  TC ) L

  rF
KErot  12 I 2
Y 
B  2 A2
1
2
 v  vL 
 f S
f L  
 v  vS 
V  V0 T
Q  nC (T2  T1 )
pV  nRT  NkT
V2
W   pdV
V1
W  p(V2  V1 )
U 2  U1  Q  W
C p  CV  R
TV  1  const.
W  nCV (T1  T2 )
W
U  23 NkT
T ( K)  T ( o C)  273.15
n  N NA  m / M
1
( p V  p2V2 )
 1 1 1
  CP / CV
V 
W  nRT ln  2 
 V1 
R  kN A
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CAMPUS: WESTVILLE MODULE AND CODE: MECHANICS, WAVES AND THERMAL PHYSICS (PHYS110)
Page 25
THERMODYNAMICS DATA
Table 1: Approximate specific heats and molar heat capacities (constant pressure).
Substance
c (J kg 1 K 1 )
C (J mol 1 K 1 )
Aluminium
Beryllium
Copper
Ice (near 0 C)
Iron
Lead
Mercury
Silver
Water (liquid)
Water (steam, 1 atm)
910
1970
390
2100
470
130
138
234
4190
2027
24.6
17.7
24.8
37.8
26.3
26.9
27.7
25.3
75.4
…
Table 2: Heats of fusion L f and Lv vaporization.
Substance
L f (J/kg)
Lv (J/kg)
Water
334  103
2256  103