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MCS702S- MECHANICS - JAN 2020 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: BACHELOR OF SCIENCE : APPLIED MATHEMATICS AND STATISTICS
QUALIFICATION CODE: 07BAMS.
LEVEL: 7
COURSE: MECHANICS
COURSE CODE: MCS702S.
SESSION: JANUARY 2020
PAPER: THEORY
DURATION: 180 Minutes
MARKS: 100
SUPPLEMENTARY/SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER:
Dr IKO AJIBOLA
MODERATOR:
Prof D. MAKINDE
INSTRUCTIONS
1. Answer all the questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written works must be done in blue or black ink and sketches in pencils
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Excluding this front page)
ATTACHMENTS
None
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QUESTION 1 (20 marks)
1.1 If A=1607+10%+2sin5rk.
s,s
“A
1.1.1 Find the vector — at t=3
[3]
;
,
dA
1.1.2 Determine the magnitude of We at f=3
[2]
t
1.1.3 Fi, nd the unit. vector along vector dA7 at t=3 i. n terms of
the unit vectors i,j andk
[3]
dA
1.1.4 What is the magnitude of the unit vector of - at t=3
[2]
t
1.2
If Rand S are 3-dimensional vectors. Define:
1.2.1 the scalar product of the vectors
[2]
1.2.2 the vector or cross product of the vectors.
[3]
1.2.3. Find the magnitude and direction cosines of the product vector of
P =5i+3j—aknd O=2i-ji+n t4hatkor,der.
[5]
QUESTION 2(20 marks)
2.1 If R=10ri - 61j -9tk and S=16i++°k
position vectors.
are two
Determine £ (5 oR) at t=2.50
[6]
dt
2.2 Fi. nd —l—d;(s5=xR)= at t =3.0
[6]
7 dt
2.3
Find the definite integral {(S> R hat
[3]
0
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QUESTION 3 (19 marks)
3.1
3.1.1 Define the average velocity v,,, ofa particle in a straight line motion
between two points A and B.
[3]
3.1.2 Using your result in (3.1.1) obtain the instantaneous velocity v,
of the straight line motion.
[3]
3.2 Suppose at any time t, the velocity v of a car is given by the equation
V. = 60m/s+(0.500m/s*)?
3.2.1 Find the change in velocity of the car in time interval between ¢, =1.00s
and t, =3.00s
[5]
3.2.2 Find the average acceleration in this time interval
[3]
3.2.3. Estimate the instantaneous acceleration at ¢, =1.00s taking
At =0.10s
[5]
QUESTION 4 (17 marks)
4.1 Derive an expression for the work done by a constant force F’ of magnitude F
of an object that undergoes a displacement sz along a straight line, when
F makes an angle ¢ with S when acting on the object.
[4]
4.2 The acceleration of a point in rectilinear motion is given by a=—9.8
It is observed that the velocity v is zero, and displacement x is +25 when ¢ =0
Determine the equation of the displacement.
[6]
4.3.1 Using SF = ma state Newton’s second law of motion in its component
forms.
[3]
4.3.2 A Railway station attendant with spikes on his shoes pulls with a constant
horizontal force of magnitude 35N on a box with mass 50kg resting on a flat,
frictionless surface.
Determine the acceleration of the box.
[4]
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QUESTION 5 (24 marks)
5.1
Obtain the formula FtoStal = mv; 2 31 2 of a partic° le of mass m movin° g
with velocity V in relationship with the work- kinetic energy
theorem W= K,-K,=AK.
[6]
5.2
If total momentum vector P, has three components derive the
three components in the x, y, z axis
[3]
53 Explain clearly with examples what you understand by conservation
of momentum
[5]
5.4 A small compact car with mass 1500kg traveling due North, with a
speed of 25m/s, collides at an intersection with an Intercampus bus of mass
7500kg traveling due West at 13.5m/s. treating each vehicle as a particle,
find the total momentum just before collision.
[10]
END OF EXAMINATION