Mid-term quiz for MECH2413 –Engineering Mechanics (2024/25)
Name: ___________________
UID: ___________________
There are X multiple choice questions in total.
Please attempt all questions and write down your answer clearly.
Part A – Statics
A1. The degree of statical indeterminacy of the beam given below is
A. Statically determinate
B. One degree of static indeterminacy
C. Two degrees of static indeterminacy
D. More information is required to conclude
A2. For homogenous rigid body under uniform and parallel gravitational field, which of the
following statement is true?
I. The center of gravity coincides with the center of mass
II. The center of gravity coincides with the center of the volume
III. The center of gravity is the ratio of system moments to system forces
A. None of these
B. (I) and (II) only
C. (I) and (III) only
D. All of these.
A3. Which of the following statement is false?
A. Changes in slope of vertical force exist
B. Changes in slope of moment exist
C. Discontinuity in vertical force exists
D. Discontinuity in moment exists
A4. Which of the following statement is NOT correct?
A. Young’s modulus measures the resistance of strain to linear stress.
B. Young’s modulus is the slope of the stress-strain diagram in the linear elastic region.
C. Young’s modulus is expressed in Newton meter (N m).
D. The coefficient of proportionality in Hooke’s law is Young’s modulus.
A5. Which information you can NOT have from Mohr’s circle?
A. Principal strain
B. Principal stress
C. Principal angle
D. Maximum shear stress
A6. Find the accurate second moments of area for the beam below.
A. Iy=6500 m4
B. Iz=2440 m4
C. Iyz=10 m4
D. Ip=8940 m4
A7. Which of the following vertical force and the moment of the beam below is accurate?
A. Minimum value of Vertical force is −20 N.
B. Minimum value of Moment is 10 N.
C. Maximum value of Vertical force is 20 N.
D. Maximum value of Moment is 20 N m.
A8. For the stress state (in MPa) shown, calculate the principal stresses and principal stress
angles.
A. Maximum principal stress of 51.4 MPa at 82.03 clockwise.
B. Maximum principal stress of 51.4 MPa at 15.95 clockwise.
C. Minimum principal stress of -21.4 MPa at 15.95 counterclockwise.
D. Minimum principal stress of -21.4 MPa at 82.03 counterclockwise.
A9. Determine which systems are statically determined.
A. (a) and (b)
B. (b) and (c)
C. (a), (b) and (c)
D. (b)
Part B – Dynamics
B1: A boat is moving at 50 m/s when its engine is shut down. Due to hydrodynamic drag, its
acceleration is a = -0.1 v2 m/s2 (where v is the boat’s velocity in m/s). Determine the boat’s
velocity 2 seconds later.
a) 3.05 m/s
b) 3.55 m/s
c) 4.05 m/s
d) 4.55 m/s
B2: Determine the distance travelled by the boat described in Q8 in the 2 seconds after its
engine has shutdown.
a) 22.0 m
b) 23.0 m
c) 24.0 m
d) 25.0 m
B3: A rigid bar AB rotates around a fixed point A. The horizontal (unit vector i) and vertical
(unit vector j) distance between the two points is Rx and Ry, respectively. Which of the
following is true? (vB is the velocity of B and is the angular velocity of the bar).
a) vB = Rx i + Ry j
b) vB = Ry i – Rx j
c) vB = –Ry i + Rx j
d) vB = –Rx i + Ry j
B4: As shown in figure below, Points B and C of a robot arm are free to move in the x-y
plane, while point A is fixed. The angular velocity vectors of the arms AB and BC are B/A =
(0, 0, -0.2) rad/s and C/B = (0, 0, 0.4) rad/s. What is the velocity of point C?
a) 0.282 i – 0.102 j
b) 0.282 i + 0.102 j
c) 0.282 i – 0.202 j
d) 0.282 i + 0.202 j
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Answers:
A1. B
A2. D
A3. D
A4. C
A5. A
A6. B
A7. A
A8. A
A9. D
B1: D
B2: C
B3: C
B4: D
