Discover PHYSICS
for GCE ‘O’ Level
Unit 5: Turning Effect of Forces
10 March 2016
Background: Walking the tightrope pg 82
Unit 5.1 Moments
Learning Outcomes:
In this section, you’ll be able to:
• describe the moment of a force and relate this
to everyday examples
• define and apply moment of a force = force x
perpendicular distance from the pivot
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Unit 5.1: Moments
Fig 5.1 Why does the boy require more
effort to pull the doorknob when the
doorknob is near the hinge than when it
is near the edge of the door?
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Unit 5.1: Moments
Definition:
The moment of a force (or torque) is the product
of the force and the perpendicular distance from
the pivot to the line of action of the force.
Fig 5.2 A simple diagram that show the effect of pulling a door open.
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Unit 5.1: Moments
Moment of a force = F x d
where F = force (in N)
d = perpendicular distance from pivot (in m)
• The SI unit of the moment is the newton metre (N m)
• It is a vector and thus has both magnitude and
direction.
• Its direction is either clockwise or anti-clockwise.
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Unit 5.1: Moments
Fig 5.4 The moment of a force can be clockwise or anticlockwise.
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Unit 5.1 Moments
Worked Example 5.1
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Unit 5.1 Moments
Key Ideas
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Unit 5.2 Principle of Moments
Learning Outcome
In this section, you’ll be able to:
• state and apply the principle of moments for a
body in equilibrium
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Unit 5.2: Principle of Moments
• Why does a beam balance measure mass?
(Recall Unit 4)
Fig 5.6 A simple diagram showing the forces
acting on an equal-arm beam balance.
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5.2 Principle of Moments
Fig 5.6 A simple diagram showing the forces
acting on an equal-arm beam balance.
Anticlockwise moment = mg x d
Clockwise moment = Sg x d
For the beam to balance, the turning effects of these two
forces must be equal. Hence,
mg x d = Sg x d
Therefore
m = S
Thus, the mass of apple m can be measured by the
standard masses S.
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Unit 5.2: Principle of Moments
What is the Principle of Moments?
The Principle of Moments states:
When a body is in equilibrium, the sum of
clockwise moments about a pivot is equal to
the sum of anticlockwise moments about the
same pivot.
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5.2 Principle of Moments
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5.2 Principle of Moments
Experiment 5.1 (continued)
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5.2 Principle of Moment
What is the conditions for equilibrium?
For an object to be in equilibrium:
• All forces acting on it are balanced. i.e.
the resultant force is zero.
• The resultant moment about the pivot
is zero. i.e. The Principle of Moment
must apply.
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5.2 Principle of Moments
Worked Example 5.3
Figure 5.9
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5.2 Principle of Moments
Levers
Levers are simple machines that make use of
the principle of moments. When apply a force
at one end of the lever, a load may be lifted at
the other end.
Fig 5.14 Simple levers.
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5.2 Principle of Moments
Key Ideas
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5.2: Principle of Moments
Test Yourself 5.2
State the Principle of Moments. Discuss how this
principle may be used to balance a see-saw by
two persons of different weight.
Answer:
When a body is in equilibrium, the sum of
clockwise moments about a pivot is equal to the
sum of anticlockwise moments about the same
pivot.
The heavier person has to sit nearer to the pivot,
while the lighter person has to sit further away
from the pivot. In this way, the moments of the
two persons can be equal and the see-saw can be
balanced.
•
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5.3 Centre of Gravity
Learning Outcome
In this section, you’ll be able to:
• Understand the centre of gravity of a body as
the point through which its weight appears to
act.
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5.2 Centre of Gravity
Try balancing a meter rule with your index
finger. At which mark did you observe the
ruler does the ruler balance?
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5.3 Centre of Gravity
Why does a uniform metre rule balance only at the
50 cm mark?
W
When the pivot is not at the 50 cm
mark, the moment of the weight W
is not zero. This causes the ruler to
turn clockwise about the pivot.
W
When the pivot is at the 50 cm
mark, the ruler is balanced. The
moment of the weight is zero.
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5.3 Centre of Gravity
What is centre of gravity?
The centre of gravity of an object is
defined as the point through which its
whole weight appears to act for any
orientation of the object.
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5.3 Centre of Gravity
Centre of Gravity of some regular shaped objects.
Fig 5.18 Centre of gravity of regular-shaped objects.
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5.3 Centre of Gravity
How to find the centre of gravity of an object?
Fig 5.19 A piece of thin lamina that is suspended at various positions will
come to rest with its weight acting directly downward as indicated by a
plumb line. Where do you think the centre of gravity is?
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Unit 5.3: Centre of Gravity
How to find the centre of gravity of an object?
Fig 5.20. Locating the centre of gravity of a lamina by the plumb line
method. Note that two lines are sufficient. The third line serves as a check.
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5.2 Centre of Gravity
Experiment 5.2
Fig 5.22
Fig 5.23
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5.4 Stability
Learning Outcome
In this section, you’ll be able to:
• Describe the stability of an object in terms of
the position of its centre of gravity
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Unit 5.4: Stability
Definition:
Stability refers to the ability of an object to
return to its original position after it has been
tilted slightly.
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5.4 Stability
Stable Equilibrium
• The centre of gravity
rises and then falls
back again.
• The line of action of
its weight W lies
inside the base area
of the cone.
• The anticlockwise
moment of its
weight W about the
point of contact C
cause the cone to
return to its original
position.
Fig 5.27(a). Stable Equilibrium.
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5.4 Stability
Unstable Equilibrium
• The centre of gravity
falls and continues to
fall further.
• The line of action of
its weight W lies
outside the base area
of the cone.
• The clockwise
moment of its weight
W about the point of
contact C causes the
toppling.
Fig 5.27(b). Unstable Equilibrium.
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5.4 Stability
Neutral Equilibrium
• The centre of gravity
neither rises nor falls;
it remains at the same
level above the surface
supporting it.
• The lines of action of
the two forces always
coincide.
• There is no moment
provided but its weight
W about the point of
contact C to turn the
paper cone.
Fig 5.27(c). Neutral Equilibrium.
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5.4 Stability
Hence, to increase stability of object,
• Centre of gravity is as low as
possible.
• The area of its base is as wide as
possible.
Fig 5.28. The more stable a car, the faster it can go round turns without overturning.
Hence, all racing cars have a very low wide base and a low centre of gravity.
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Worked Example 5.5
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Worked Example 5.7
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5.3 – 5.4 Centre of Gravity and
Stability
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5.3-5.4 Centre of Gravity and Stability
Test Yourself 5.3-5.4
2.
Flat-dwellers in Singapore usually hang their laundry out on
bamboo poles. These bamboo poles have to be lifted out of
the window and stuck into specially build holes. With wet
laundry on it, a lot of effort may be needed to lift the pole up
at one end. What advice can you give to reduce the required
effort? You may wish to consider
a) The turning effects of the weight of the pole and the wet
laundry.
b) How the distribution of the weight of the wet garments
affects the position of the centre of gravity of the pole and
wet laundry system.
Answer:
Some possible advices:
1. Use a light bamboo pole.
2. Use shorter bamboo poles.
3. Place the heavier clothes nearer the end of the pole where
the hand is.
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