Transcript 2 forces in equilibrium

NATIONAL CERTIFICATE/NATIONAL DIPLOMA
ENGINEERING
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This handout covers the following topics:
 SCALAR AND VECTOR QUANTITIES
 TYPES OF FORCES
 FORCES IN EQUILIBRIUM
 TRIANGLE/PARALELLOGRAM OF FORCES
 RESOLUTION OF CO-PLANAR FORCES
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SCALAR QUANTITIES
Quantities which possess a size or magnitude only. Some examples of scalar quantities are
given below:
TIME
MASS
LENGTH
VECTOR QUANTITIES
Quantities which possess both a magnitude AND a direction. Some examples of vector
quantities are given below:
VELOCITY
ACCELERATION
MOMENTUM
Force is a_____________ quantity.
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3 TYPES OF DIRECT FORCES
1. TENSILE
2. COMPRESSIVE
3. SHEAR
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2 FORCES IN EQUILIBRIUM
If two or more forces act on an object it remains at rest, then the forces are
said to be in equilibrium. For two forces to be in equilibrium they have to:
1. Be equal in size
2. Have lines of action which pass through the same point (concurrent)
3. Act in exactly opposite directions
10KN
10KN
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RESOLUTION OF FORCES
A 400-N force is exerted at a 60-degree angle (a direction of 300 degrees) to
move a railroad car along a railroad track. A top view of the situation is
depicted in the diagram. The force applied to the car has both a vertical
(southward) and a horizontal component (eastward).
To calculate, or RESOLVE the forces Fx and Fy, there are 3 different
methods which can be used
1.
2.
3.
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RESOLUTION OF FORCES USING TRIGONOMETRY
Going back to the previous railroad car scenario, the horizontal and vertical
components (Fx and Fy) of the applied force can be calculated using
trigonometry.
Rules of trigonometry
Sin θ = Opposite
Hypotenuse
Cos θ = Adjacent
Hypotenuse
Tan θ = Opposite
Adjacent
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RESOLUTION OF FORCES USING TRIGONOMETRY
F = Hypotenuse
Fx = Adjecent
Fy = Opposite
Finding Fx
Finding Fy
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Worked Example 3:
F2
F1 = 100N
F2 = 300N
F1
20°
40°
F3
F3 = 200N
1. Resolve each of the three forces into their individual horizontal and vertical
components:
F2H
F1H
F1V
20°
F2V
40°
Note: F3 acts 100% in the
horizontal direction and has
no vertical component
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Worked Example 3 Continued:
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Worked Example 3 Continued:
2. Now, calculate the magnitude and direction of resultant force.
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Question 3:
Calculate the magnitude and direction of the resultant of the three co-planar
forces shown in the diagram below using trigonometry.
F1
F3
10°
35°
F2
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