ENGINEERING MECHANICS Statics
Introduction
Mechanics is a branch of
physics that deals primarily on objects in rest or in motion that has action of
force applied on it.
Statics is the branch of mechanics that is concerned with the analysis
of loads (force and torque, or "moment") on physical systems in static
equilibrium, that is, in a state where the relative positions of subsystems do
not vary over time, or where components and structures are at a constant
velocity. When in static equilibrium, the system is either at rest, or
its centre of mass moves at constant velocity.
Scalars is any positive or negative physical quantity that can be completely specified by its magnitude. Scalar quantities examples are length, mass, time.
Vector is any physical quantity that has magnitude and a direction. Examples of vector quantities are force, position, and moment.
“Force System” is the forces and their locations that act on a body. Resultant Force is the equivalent of all forces acting on a body and resolved into one force and in one direction. Combining all forces or the force system acting on a certain body is what we call the Resultant force.
Two forces acting in a rectangular object both in an opposite direction. Combining the two forces makes an equation of “Resultant R”. The standard of writing down the equation should be “all forces going to the right is positive, and all forces going to the left is negative”.
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Example#1
What is the resultant force in the diagram XY1 if F=800Newton?
diagram: XY1
Resultant Force = 800N ---Ans.
Since there is only one force acting in the body
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Example#2
In diagram XY2, while steadily pushing the machine up an incline, a person exerts a 180-N force P as shown. Determine the components of P which are parallel and perpendicular to the incline.
diagram: XY2
Create a free body diagram as shown in fbd1, we can easily identify the force P and each components along x and y.
get the components of P applying the Rectangular Components rule:
Px = ?, Py = ?
a = 250, P = 180N
solution:
Py = 76.1 N ---Ans.
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Finding the Resultant force using Pythagorean Theorem.
Pythagorean Theorem, is referring to a right angle where the square of the hypotenuse is equal to the sum of the square of the sides.
h2 = a2 + b2
It is recommended to use or apply pythagorean theorem to get the resultant force in a system. For better understanding, try to analyse the example below.
Example#3
A 5 Newton force is applied to the steel ball with a weight of 100 Newton, as shown in the diagram XY4.
Find the Resultant Force.
solution:
Resultant Force = F
F2 = 1002 + 52
F2 = 10,025 --- get the square root
F = 100.13 Newton ---Ans.
angle from vertical = arctan (5/100)
angle from vertical = 3 degrees
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EXAMPLE#4
Determine the magnitude of the resultant force acting on the screw eye and its direction measured clockwise from the x-axis.
diagram: XY5
solution:
R = 6798 Newton --- answer
A = 17.730
B = 1800 -
600 - 17.730 – 450
B = 57.270
Angle from horizontal = B + 450
Angle from horizontal = 102.250
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