Reg. No……………………
KIGALI INSTITUTE OF SCIENCE AND TECHNOLOGY
INSTITUT DES SCIENCES ET TECHNOLOGIE DE KIGALI
Avenue de l’Armée, B.P. 3900 Kigali, Rwanda
INSTITUTE EXAMINATIONS -ACADEMIC YEAR 2012
FACULTY OF ENGINEERING
END OF SEMESTER EXAMINATION (MAIN)
MECHANICAL ENGINEERING
FIRST YEAR SEMESTRE II (FULL TIME)
MEE 3122 – ENGINEERING MECHANICS-STATICS
DATE:
/
/ 2013
TIME: 2hours
MAXIMUM MARKS = 60
INSTRUCTIONS
1.
This paper has FOUR (4) questions in sections A and B.
2.
QUESTION ONE is COMPULSORY
3.
Attempt any other TWO QUESTIONS
4.
All questions carry equal marks.
5.
Do not forget to write your Registration Number.
6.
Write all your answers in the booklet provided.
7.
Do not write any answers on this questions paper.
8.
You need a scientific calculator for this examination.
9.
For some questions please see appendix for formulas.
QUESTION I- COMPULSORY
(a) How can you evaluate the reaction of support of a frame?
(b)
9marks
Determine the reaction and the forces in each member of a simple triangle truss
supporting two loads as shown in below with the method of joints (21marks)
ATTEMPT ANY TWO QUESTIONS
QUESTION II
(a)
Four forces of magnitude P, 2P, 5P and 4P are acting at a point. Angles made
by these forces with x-axis are 0°, 75°, 150° and 225° respectively. Find the
magnitude and direction of resultant force.
8marks
(b)
A body on contact with a surface is being pulled along it with force
increasing from zero. How does the state of motion of a body change with
force? Draw a graph and explain. /6marks
(c) Locate the centred of the shaded area. (dimensions in inches) /6marks
QUESTION III
(a)
Four coplanar forces are acting at a point. Three forces have magnitude of 20,
50 and 20N at angles of 45°, 200° and 270° respectively. Fourth force is
unknown. Resultant force has magnitude of 50N and acts along x-axis.
Determine the unknown force and its direction from x-axis.
8marks
(b)
A wooden block of weight 50N rests on a horizontal plane. Determine the
force required which is acted at an angle of 150 to just (1) Pull it, and (2)
Push it. Take coefficient friction = 0.4 between the mating surfaces.
6marks
(c)
Approximate the x-coordinate of the volume centroid of a body whose length is
1 m and whose cross-sectional area varies with x as shown in the figure.
6marks
N.B:
 Computer areas by interval (e.g. [0, 0.2], [0.2, 0.4], [0.4, 0.6], [0.6, 0.8], [0.8, 1.0])
 For any interval, the considered area is the average of the upper and the lower bound
of that interval (use approximation whenever necessary)

is computed for the x –axis and for rectangle intervals.
QUESTION IV
(a)
A horizontal line PQRS is 12 m long, where PQ = QR = RS = 4m. Forces of
1000, 1500, 1000 and 500 N act at P, Q, R and S respectively with downward
direction. The lines of action of these make angle of 90º, 60º, 45º and 30º
respectively with PS. Find the magnitude, direction and position of the resultant
force.
8marks
(b)
Determine the range of values which the mass
mo may have so that the 100-kg block shown in
the figure will neither start moving up the plane
nor slip down the plane. The coefficient of
static friction for the contact surfaces is 0.30.
6marks
(c)
Locate the center of mass of the bracket-and- shaft combination in mm (for yaxis ad z-axis). The vertical face is made from sheet metal which has a mass of
25 kg/m2. The material of the horizontal base has a mass of 40 kg/m2, and the
steel shaft has a density of 78.3 kg/m3
6marks
Appendix: Formulas you may need.