GNG 1105Y Engineering Mechanics
Assignment 2 – Equilibrium of Rigid Bodies and Centroids
DUE: Friday, July 15th, 2022
Let Ω represent the last 3 numbers of your student number. For example if your student number
is 400000123, then Ω=123.
Question 1:
In this following diagram, M=Ωkg. The rod BCD is attached to the wall with a frictionless pin at B
and is supported by a cable attached to a frictionless pin at C. The cable holding the mass M goes
around a frictionless pulley of negligible diameter at D.
(a) Draw a free body diagram of rod BCD with all reactions/forces in the correct directions.
(b) Determine the magnitude of the tension in the cables and the reaction at B.
Solve this question with the methodology shown in class for full marks.
Question 2:
In this set up, the homogeneous density and uniform diameter pole ABC is supported by a
frictionless ball-and-socket joint at point A and by the cable BD which is attached to the midpoint
B of the pole. At point C, the pole leans against a frictionless wall. The pole has a mass of Ωkg
(which can be assumed to be applied at the midpoint B).
(a) Draw the free body diagram of the pole ABC.
(b) Define all vectors found on the free body diagram in component form (𝑖̂, ̂,
𝑗 𝑘̂), including
any reactions, the weight, and the tension in the cable.
(c) Determine the magnitude of the tension in the cable and determine the reactions A and
C.
Solve this question with the methodology shown in class for full marks.
Question 3:
Assume to be uniform thickness and homogeneous density.
(a) Separate the complex shape above into a series of simple shapes.
(b) For each of these simple shapes, determine the location of the centroid relative to the axis and
determine the area of each simple shape.
(c) Determine the location of the centroid of entire shape.
Solve this question with the methodology (the chart) shown in class for full marks. You must keep
the axis shown on the diagram for full marks.