# Physics 1A June 200320112421247

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```					                 UNIVERSITY OF KWAZULU-NATAL

HOWARD COLLEGE CAMPUS

EXAMINATIONS : JUNE 2006

SUBJECT, COURSE AND CODE:
ENGINEERING PHYSICS 1A (PHYS151)

DURATION: 3 HOURS                                                   TOTAL MARKS: 180

Examiners :      Internal:    Prof. J.P.S. Rash      Mr T. Mathe
Prof. J.D. Hey         Dr K. Naidoo

External:    Prof. N. Chetty

INSTRUCTIONS:

1. Answer ALL questions ON the question paper.
2. Rough work may be done on the back of each page. If you use the back of a page for work
which you wish to be marked, please indicate this clearly.
3. Marks have been allocated in such a way that 1 mark corresponds roughly to one minute of
time. Candidates are advised not to spend a disproportionate amount of time on any one
question.
4. Check that this paper contains 19 numbered pages (excluding the cover page) plus a sheet of
graph paper (after page 17) and a formula sheet.
5. The use of calculators (including programmables) is permitted.
6. If there is any word in this examination paper which you do not understand, please ask an
7. You may use g = 10 m.s-2 unless otherwise indicated.
8. Where angles of 37° or 53° are given, you may use the approximations
sin 37° = cos 53° = 0.6 and cos 37° = sin 53° = 0.8

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UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 2

SECTION A                                 MECHANICS           75 MARKS

QUESTION A 1 :
Given two vectors     A = 4.00 i + 3.00 j
and    B = 5.00 i – 2.00 j
find the scalar product of these two vectors.
(3)

[3]

QUESTION A 2 :
(a) Figure (a) alongside shows a particle moving in a
circle, radius R, with constant speed. Its velocity vector
is v1 at point P1 and v2 at point P2 a time interval ∆t
later. Figure (b) is a vector diagram showing the vector
difference ∆v = v2 – v1 . Use these diagrams to derive
the expression for the centripetal acceleration in
uniform circular motion. State your reasoning clearly.

(5)
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 3

(b) The Earth has a radius of 6380 km. If the radial acceleration at the equator was greater
than g, objects would fly off the Earth's surface into space. What would the period of the
Earth's rotation have to be for this just to occur?
(3)

[8]

QUESTION A 3 :
(a) An airplane pilot is practicing to fight forest fires by dropping a canister of water onto
a target on the ground in front of and below his plane. If the plane is flying in a horizontal
path 90 m above the ground with a speed of 64 m/s, at what horizontal distance from the
target should the pilot release the canister in order to hit the target?
(Ignore air resistance.)
(4)
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 4

(b) Another pilot sets off in her airplane from A in the direction of B which is due East of A.
The plane’s airspeed (i.e. magnitude of the velocity of the plane relative to the air) is 420 km/hr.
However there is a wind of 200 km/hr blowing due South.
(i) What is the velocity of the plane relative to the Earth (magnitude and direction)?
(3)

(ii) If B is 800 km East of A, how much time will it take the plane to reach a point with the
same longitude as B (i.e. somewhere due North or South of B)?
(2)

(iii) How far North or South of B will the plane be at this time?
(1)

[10]

QUESTION A 4 :
(a) Which of Newton’s Laws is also known as the “Law of Inertia”?
(1)

(b) State, in words, Newton's Third Law, without using the terms "action" and "reaction".

(2)

[3]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 5

QUESTION A 5 :
Block A, of mass 5.0 kg, slides on a plane inclined at 37° to the
horizontal. It is connected to block B, of mass 7.0 kg and hanging
vertically, by a light inextensible string passing over a frictionless
pulley (see figure). The coefficient of kinetic friction between
block A and the surface of the inclined plane is 0.30.

(a)   Draw a free body diagram for block A
using clearly labelled arrows:
(2)

A

(b)   Show that the magnitude of the frictional force on A is approximately 12 N.
(3)

(c)   Calculate the acceleration of the blocks.
(5)

(d)   Find the tension in the string.
(2)

[12]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 6

QUESTION A 6 :
(a) Using the kinematic equations and Newton's Laws, 'derive' the basic form (i.e.
excluding potential energy) of the Work-Energy Theorem for the case of a constant force
F acting over a displacement s. Define clearly any quantities which are introduced in the
course of the derivation.
(5)

(b) A car is travelling on a level road with speed v0 when the brakes lock, so that the tyres
slide (“skid”) rather than roll over the road surface.
(i) Use the Work-Energy Theorem to derive an expression for the stopping distance of the car
in terms of v0 , g and the coefficient of kinetic friction µk between the tyres and the road.
(4)

(ii) The car stops in a distance of 51 m if v0 = 60 km/h. What will be the stopping distance
if v0 = 80 km/h?
(2)

[11]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 7

QUESTION A 7 :
(a) State two properties of the work done by a conservative force.
(2)

(b) A 2.00 kg block is pushed against a
spring with negligible mass and spring
constant k = 400 N/m, compressing it
0.220 m. When the block is released it
moves along a frictionless horizontal
surface, and then up a frictionless incline
with slope 37°, as shown in the figure
alongside.
(i) What is the speed of the block as it slides along the horizontal surface after
having left the spring?
(3)

(ii) How far does the block travel up the inclined surface before starting to slide back down?
(3)

[8]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 8

QUESTION A 8 :
(a) State the Principle of Conservation of Momentum (including the conditions under
which it applies).
(2)

(b) A car of mass 1400 kg travelling east on East
Street at 35 km/h collides with a truck of mass 2800
kg that is travelling north on North Road at 50 km/h.
The two vehicles stick together after the collision.
Calculate the magnitude and direction of the velocity
of the vehicles after the collision.
[Assume that friction forces between the vehicles and
the road during the collision can be neglected as the

(6)

[8]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 9

QUESTION A 9 :
When drilling a 12 mm diameter hole in wood, plastic or aluminium, a workshop manual
recommends a drill rotation speed of 1250 rev/min.
For a 12 mm diameter drill bit turning at a constant 1250 rev/min, find
(i) the maximum linear speed of any part of the bit
(3)

(ii) the maximum radial acceleration of any part of the bit.
(2)

[5]

QUESTION A 10 :
Calculate the net torque about point O for the two forces applied as in the figure below.
The rod and both forces are in the plane of the page.
(6)

[6]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 10

SECTION B                               WAVES & HEAT                           65 MARKS

QUESTION B 1 :
(a) A body acted upon by a force undergoes simple harmonic motion (SHM).
(i) What physical requirements must be met to ensure that the motion is in fact SHM?
(Use words and symbols.)
(3)

(ii) Define 3 of the physical parameters associated with SHM.
(3)
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
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(b) A 100 g object, attached to the end of a horizontal ideal spring with force constant 40 N/m,
undergoes SHM. Its speed when it is displaced from the equilibrium position by half its
amplitude is 3 m/s. Determine:
(i) the amplitude of the SHM
(4)

(ii) the maximum speed of the object
(1)

(iii) the acceleration when its displacement x = –3.0 cm
(1)

(iv) the potential energy when the object’s speed is 1.0 m/s.
(4)

[16]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 12

QUESTION B 2 :
(a) A uniform wire of mass m and length L is fully extended and under tension F.
The one end of the wire is plucked, and a pulse travels along the wire.
mL
Show that time taken for the pulse to travel from one end of the wire to the other end is ∆t =      .
F
Is the pulse longitudinal or transverse?
(4)

(b) The wire is used in the space programme for an experiment on the Moon. It is mounted
vertically on the Moon's surface by an astronaut, and put under tension by attaching a mass M,
which is much greater than the mass of the wire. The transit time for a pulse to travel from the
upper to the lower end of the wire is measured by the astronaut, and found to be ∆t = 36.1 ms .
Other numerical data: M = 3.00 kg, m = 4.00 g, L = 1.60 m.
From the data, calculate the gravitational acceleration on the Moon, g Moon .
What would one expect for the corresponding value of ∆t on Earth?
(6)

[10]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 13

QUESTION B 3 :
(a) Assuming a value B = γ p0 for the bulk modulus of a gas in terms of the equilibrium
pressure, show how the following expression is obtained for the speed of sound in the gas:
γ RT
v=          , where M is the molar mass and the gas is assumed to be ideal.
M
(3)

(b) Sketch the first three standing-wave modes in a hollow tube closed at one end and open
to the atmosphere at the other. With each sketch, relate the wavelength of the normal mode
to the length of the tube.
(3)

(c) A long tube contains air at a temperature of 77 °C and a pressure of 1 atmosphere.
The tube is open at one end, and closed at the other end by a movable piston. A tuning fork
near the open end is vibrating at a frequency of 500 Hz. Resonance is produced when the
piston is measured to be at distances of 18.0 cm, 55.5 cm and 93.0 cm from the end of the
tube. From the average value of the wavelength of the sound from these data, determine
the speed of sound in the air at the given temperature and pressure.
(3)
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 14

(d) Using the information above, obtain a value of γ for the air, assuming M = 28.8 kg/mol.
From this result, which types of energy do most molecules in air have?
(4)

[13]

QUESTION B 4 :
(a) One end of an insulated metal rod is maintained at 100 °C, and the other end is
maintained at 0 °C by an ice-water mixture. The rod is 60.0 cm long and has a cross-
sectional area of 1.25 cm2. The heat conducted by the rod melts 8.50 g of the ice in 10.0
min. Find the thermal conductivity k of the metal.
[ Lf (water) = 334 kJ/kg]
(5)
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 15

(b) The original insulated rod in (a) is now replaced by a copper rod of length 30.0 cm joined onto a
brass rod of 30.0 cm, to make a combined rod of 60.0 cm length and the same cross-sectional area
as previously. The copper end of the new rod is maintained at 100 °C, while the brass end is kept in
the ice-water mixture. If the rate at which the ice melts remains as before, what is the temperature at
the copper-brass junction in the middle of the new rod?
[ k (copper) = 400 W/m °C, k (brass) = 100 W/m °C ]
(5)

[10]

QUESTION B 5 :
(a) List six assumptions made in the kinetic-molecular model of the ideal gas.
(6)
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 16

(b) From the result             ( )
p V = N m v 2 Av
x
show that the mean translational kinetic energy per molecule is 3 k T .
2
Clarify any assumptions made in obtaining this result.
(6)

(c) The speed required for any particle to escape from the Earth's surface is given in terms
of the gravitational constant G, Earth's radius RE and Earth's mass ME by
2G M E
v esc =          .
RE

Use this result to formulate an 'escape temperature', at which a gas (molecular mass m)
would be hot enough to escape from the Earth's atmosphere. By comparing the result for a
light gas (e.g. hydrogen) with that for a heavier gas (e.g. oxygen), can you explain the
practical absence of light gases from the earth's atmosphere?
(4)

[16]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 17

SECTION C                                EXPERIMENTAL                                 40 MARKS

QUESTION C 1 :
A Mechanical Engineering student set out to measure the elastic properties of the steel used in
hacksaw blades. She clamped one end of a hacksaw blade horizontally, attached a series of masses
m to the other end, and set the blade oscillating, measuring the time t for 20 oscillations in each
case, so that she could determine the period of oscillation T as recorded in the table below.

Mass m          Time t for 20        Period T
(g)           oscillations (s)         (s)
50               17.6               0.88

100               21.4               1.07

150               25.0               1.25

200               28.0               1.40

250               30.6               1.53

The student suspected she could not use the relationship between the period of oscillation
and the mass which holds for the spiral spring, but she was sure that the relationship
between T and m should be a power law of the form
T=amn
Plot a suitable straight line graph to show that the student's supposition was correct, and
from the graph determine the values of a and n in the above equation.

[You should use the empty columns of the above table for any values deduced from those in the
table which you wish to plot. Note that marks are allocated for: sensible choice of scales,
labelling of axes, clear and accurate plotting of points, showing how values are found from the
graph, as well as consistency with significant figures and inclusion of units where appropriate.]

(20)

[20]
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 18

QUESTION C 2 :
(a)    What instrument would you use to measure the mass of the following?

(i)    a suitcase full of clothes (which should be around 30 kg to be allowed on your
plane flight) to the nearest 1 kg

(ii)   an empty polystyrene cup (into which you plan to pour a small amount of
liquid), to the nearest 0.01 g

(iii) a physics text book (which you have to carry around the campus), to the
nearest 1 g
(3)

(b)    (i)    In measuring the period of the simple pendulum, why does it improve the
accuracy of the result if you measure the total time for a number of oscillations
(10, say) and divide by that number, rather than timing one oscillation?
(3)

(ii)   Why is the length of the simple pendulum measured to the centre of the bob, rather than the
point of attachment of the string to the bob? How could you measure the position of the centre
more accurately than by estimating with a metre stick?
(3)
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2006
CAMPUS: HOWARD COLLEGE SUBJECT, COURSE AND CODE: ENG. PHYSICS 1A (PHYS151)
Page 19

(c)   In the Spiral Spring experiment, where a mass is hung from the end of the spring and
the extension measured ('static experiment') and then the time of oscillations measured
('dynamic experiment'), does the mass of the 'holder' (onto which 50 g brass mass
pieces are added) need to be included in the measurements in both cases?
Explain what errors would arise if it was not.
(5)

[14]

QUESTION C 3 :
The "Method of Mixtures" is used to determine the specific heat capacity of copper in the
experiment SHC, after the specific heat capacity of water has been determined. What is meant
by the "Method of Mixtures"? Explain briefly the principles of the method. (You do not need
to give a detailed description of the experimental procedure, but you may wish to mention
some precautions taken to ensure that the assumptions made in the procedure are valid.)
(6)

[6]

END

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