Worksheet 1
On Chapter 1: Introduction to Mechanics & Chapter 2: 2-D and 3-D Force Systems
Part I: Theoretical Questions
1.
2.
3.
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6.
What is engineering mechanics?
Explain the distinction between statics and dynamics using Newton’s Laws.
What is a rigid body?
Distinguish between free, sliding and fixed vectors.
Describe Newton’s Law of Gravitation.
In mechanics, only the gravitational attraction of the earth is considered. Explain why it is
not important to consider the gravitational attraction between human-scale objects (cars,
mechanical machines, trains, buildings, bridges etc). [Hint: consider the relationship
between the parameters in Newton’s Law of Gravitation.]
7. In mechanics, it is safe to approximate the acceleration due to gravitational attraction of
the earth as 9.81 meters per squared second when using the International System of Units
(SI). However, there are variations in this acceleration over the surface of the earth.
Explain why this variation exists. [Hint: consider the relationship between the parameters
in Newton’s Law of Gravitation at, say, the equator and the earth poles.]
8. Explain the effect of the earth’s rotation on the acceleration due to earth’s gravity. [Hint:
consider the concept of apparent weight.]
9. Explain the Principle of Transmissibility.
10. Distinguish between forces distributed over a volume, over an area, and along a line.
11. Describe Varignon’s Theorem.
12. What is moment?
13. How is a force-couple system created?
14. Describe the three ways to specify a 3-D force.
15. How do you find the angle between two vectors?
16. How do you find moment about an arbitrary axis? [Hint: consider the concept of triple
scalar product.]
17. It is clear that a moment vector is oriented perpendicular to the plane resting the moment
arm and the force. However, there is such a thing as wrench resultant where a resultant
moment is aligned perfectly on the line of action of the resultant of the forces involved in
a system. Clarify this apparent contradiction. [Hint: consider the basic definition of
wrench resultant.]
Part II: Numerical Analysis
Note: Here, vector quantities are represented in bold-face letters whereas their scalar
counterparts are represented by normal-face letters
1. A steel tank is to be positioned in an excavation. Knowing that α = 20°, determine by
trigonometry (a) the required magnitude of the force P if the resultant R of the two forces
applied at A is to be vertical, (b) the corresponding magnitude of R.
Answer: a) P = 392 lb
b) R = 346 lb
2. Determine the x and y components of the three forces shown below.
3. Replace the three forces which act on the bent bar by a force-coupe system at the support
point A. Then determine the x-intercept of the line of action of the stand-alone resultant
force R.
Answer: R = 400i – 3010j
N; MA = 18190 N.m CW; x
= 6.05 m
N
4m
N
N
3m
4. Determine the resultant R of the three forces acting on the simple truss. Specify the
points on the x- and y-axes through which R must pass.
Answer: R = -15i – 47.3j
kN; x = 7.42m; y = -23.4 m
5. The end of the coaxial cable AE is attached to the pole AB, which is strengthened by the
guy wires AC and AD. Knowing that the tension in AC is 150 N and that the resultant of
the forces exerted at A by wires AC and AD must be contained in the xy plane, determine
(a) the tension in AD, (b) the magnitude and direction of the resultant of the two forces.
Answer: TAD = 65.2 N; R =
208 N; θx =61.6o; θy = 151.6o;
θz = 90.0o
6. A rigid pole and cross-arm assembly is shown here. Express T as a vector. Determine the
vector expression for the moment of the 1.2-kN tension (a) about point O and (b) about
the pole z-axis. Find each moment in two different ways. Does it make any difference in
the result which coordinate system is used?
Answer:
T = -0.321i + 0.641j – 0.962k kN
Mo = -2.89i – 0.967k kN.m
Mz = -0.962k kN.m