Engineering Mechanics Statics (EMS 520S)
Examination 1 — Date: 15 September 2022
Duration: 2 hours and 30 minutes — Total marks: 66
Examiner: Mr. A. Zulu
Moderator: Prof. V. Kamara
Important Notices
Write neatly and legibly, as illegible work will not be considered for marks.
Use free-body diagrams, illustrative diagrams and reference (Cartesian) axes where possible or applicable.
Pay attention to units and show the relevant unit in each calculated answer.
No marks will be awarded for answers only. Calculations must contain a minimum number of logically
sequenced steps followed by an answer. In cases where two or more different - and undeleted answers
are given for the same item, the right answer will not be considered for marks.
Do not write your name or sign anywhere on the answer scripts. A 5% penalty is applicable if you
identify yourself other than the student number alone.
Cellular phones and programmable calculators are not permitted.
Use, where applicable, gravitational acceleration g = 9.81 m/s2 .
Answer all questions!
Question 1
~ B
~ and C
~ are given as: A
~ = 4î + 2ĵ + 3k̂; B
~ = 3î − 2ĵ + 5k̂; C
~ = 6î + 8k̂. Determine:
Vectors A,
~
~
(a) the dot product of vectors A and B [2.5]
~ and B
~ [4.5]
(b) the angle between vectors A
~
~ [2]
(c) the scalar projection of vector A on vector B
~
~
~
(d) A × B · C [5].
Question 2
For the force system shown in Figure Q2, if P = 120 N; and the resultants of P and Q is directed
horizontally to the right, determine Q and the magnitude of the resultant [8].
Figure Q2.
Question 3
Determine which of the following systems in Figures Q3(b) through (f) are equivalent to the forcecouple system in Figure Q3(a) [Hint: Calculate resultant forces and moments about a chosen point
for all systems and compare with the first one in (a)][18].
Figure Q3.
Question 4
A force of 6 kN and a moment of 3 kN.m act on the frame as shown in Figure Q4. The angle between
the frame and the cable at B is 60◦ . Determine the forces acting on the beam at B and C [10].
Figure Q4.
Question 5
The centers of gravity of the 50-kg trolley and the 120-kg box are at G1 and G2 , respectively. The
trolley must be able to negotiate the 5-mm step when the pushing force P is 600 N. Calculate the
smallest allowable radius of the wheel at A [16].
Figure Q5.
Visual hint: reaction at A.
The End!
0
