2.9 Equilibrium
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Transcript of 2.9 Equilibrium
8/8/2019 2.9 Equilibrium
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2.9 FORCES IN EQUILIBRIUM
Learning Outcome
Describe the situationswhere forces are in
equilibrium
State what a resultant
force is
Add two forces to
determine the
resultant force.
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Newton¶s Law of Motion
First Law:
In a sate of equilibrium , a stationaryobject will continue to remain stationary
and an object in motion will continue to
move at a uniform velocity
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Newton¶s Law of Motion
Second Law:
The rate of change of momentum of amoving body is proportional to and in
the same direction as the net force
acting on it.
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Newton¶s Law of Motion
Third Law:
To every action there is an equal but
opposite reaction.
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EQUILIBRIUM
R
Object resting on the
table is in equilibrium.
The forces that act on
them are balanced.
The forces cancel
each other so that the
resultant force is zeroWeight = Normal reaction
W = R
Stationary object
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Force + Weight = Normal
reaction
R = 26 N
F + W = R
F = R ± W
= 26 ± 15
= 11 N
Equilibrium with pushing force
F
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Equilibrium with tension in a rope
W = R + T
W = T
R
T=11N
W = 15N
R = W ± T
= 15-11
= 4N
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Pushing
force, F
Frictional
force, f
Weight, W
Normal
reaction , R
F = f
Object Moving with
constant velocity is inequilibrium.
The forces that act on
them are balanced.
The forces cancel
each other so that the
resultant force is zero
EQUILIBRIUM
R = W
Objects in motion with
constant velocity
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Box resting on an
inclined plane
Weight of box
Normal
reactionFriction
The box is in
equilibrium.
How do
these forces
cancel each
other ?
EQUILIBRIUM
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ADDITION OF TWO FORCESParallelogram method
1. The two forces are drawn from
the same point.
2. Complete a parallelogram using r uler,
protractor and compasses.
3. Resultant force is represented by thediagonal from the common point
80o
1 cm : 20 N
80o
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ADDITION OF TWO FORCESTriangle method
1. The two forces are drawn after one
another
2. Complete a triangle.
3. Resultant force is represented by
the third line jointing the startingpoint to the ending point.
80o
1 cm : 20 N
80o
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Refer information given in workedexample (pg 55)
Using a scale of 1 cm to represent 10 kN, draw a
parallelogram of forces .
Determine(a) the magnitude of the resultant force on
the oil rig.
(b) the angle the resultant force made with the100 kN force
Repeat using the triangle method.
Activity
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Home work
Masterypractice 2.9 pg 57
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2.9 FORCES IN EQUILIBRIUMLearning Outcome
Resolve a force into the
effective componentforces.
Solve problems involving
forces in equilibrium.
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RESOLUTION OF FORCES
To break up or resolve a single force into two
components. (Usually perpendicular)
One force
F
U
Two effective components
F1
F2F1
F= sin U
F2
F= cos U
F1 = F sin U F2 = F cos U
F
U
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RESOLVE WEIGH
T ON INCLINED
P
LA
NE
Weight of box50o
W1
W2
W
50o
Component of
weight along plane ,
W1
W= sin 50o
W1 = W sin 50o
Component of weightperpendicular to plane ,
W2
W= cos 50o
W2 = W cos 50o
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ANALYSING FORCES IN EQUILIBRIUM
The addition
and resolutionof forces can
help us analyse
forces in
equilibrium.Weight, W
Normal
reaction,R Friction,F
U
The box is at rest
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Weight, W
Normal
reaction,R Friction,F
U
U
W1
W2
The box is at rest
Resultant force=0
F = W1
= W sin U
R = W2
= W cos U
Resolve forces along & perpendicular
to plane
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By drawing a triangle of forces
The box is at rest
Resultant force=0
Alternative
Weight, W
Normal
reaction,R Friction,F
U
UW
R
F
U
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Worked Example 1pg 56
Fx
120
120 N
40o
Fy
Fx
= cos 40o
Fx = 120 cos 40o
= 91.9 N
Fy
120 = sin 40o
Fx = 120 sin 40o
= 77.1 N
Fx pushes the roller forward.
Fy helps to press the roller
onto the ground.
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Worked Example 2
A lorry is moving with a
constant velocity up a
slope. The frictional force
between lorry and slopeis 500 N . what is the
thrust exerted by the
engine?
Solution
20000 N
R
F
T
Free body diagram
Component of weight
down the slope = W sin U
The lorry is in equilibrium, so
T = F + W sin U
= 500 + 20000 sin 10o
= 500 + 3473 N
= 3973 N
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Worked Example 3
The ring is at rest. The
weight of the engine is
3150 N. Draw a vector
diagram to scale todetermine T1 and T2
Scale : 1 cm : 500 N
6.3 cm
80o
10o
A
B
C
T1= AC
T2= BC
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2.9 FORCES IN EQUILIBRIUMLearning Outcome
Resolve a force into the
effective componentforces.
Solve problems involving
forces in equilibrium.
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