1. 1. Motion, Forces and Energy
Physical quantities and measurement techniques, Motion, Mass and
weight, Density, Forces (Effects of forces, Turning effect of forces,
Centre of gravity), Momentum, Energy, work and power (Energy, Work,
Energy resources, Power), Pressure
1
Copyright by Joyous ACE
3. 3
Newton’s Apple Tree
The descendant of the
tree that grew in Sir Isaac
Newton’s garden at
Woolsthorpe Manor in
Linconshire, England.
It is reputed to have
inspired his Law of
Universal Gravitation
4. Forces
• A force is a or acting upon an object as a result of its
interaction with another object.
• A force can….
a stationary object
a moving object
• change the / of an object
• change the / of an object
• Force is a quantity .
• The S.I. unit for force is or newton,
4
5. Type of Forces
5
– the upward
force from a liquid (or
gas) that makes some
things float
– force with which the earth,
moon, or other massively large object
attracts another object towards itself
6. 6
– force which is transmitted
through a string, rope, cable or wire
when it is pulled tight by forces acting
from opposite ends
– force exerted by a surface as
an object moves across it or makes an
effort to move across it
7. 7
– the forward force
from an aircraft engine
– a special
type of frictional force which
acts upon objects as they travel
through the air.
10. Newton’s Third Law of Motion
10
• When you sit in your chair, your body exerts a downward force on the
chair and the chair exerts an upward force on your body.
• There are two forces resulting from this interaction — a force on the
chair and a force on your body.
• These two forces are called and forces and are the
subject of Newton's third law of motion.
• Formally stated, Newton's third law is:
"For every action, there is an and reaction."
11. Describe the effect of balanced and
unbalanced forces on a body
11
Balanced and
Unbalance Force
12. Balanced Forces
12
• When two forces acting on an object is , the object can either be
or at .
• Two forces are balanced when their is the but they act in
.
14. 14
• An object that is suspended by a rope.
Weight
Tension
15. 15
• An airplane flying at a constant velocity.
Upthrust
Weight
Thrust Drag
16. 16
• A trolley being pushed at a constant velocity
Weight
Reaction
Pushing
Force
Friction
17. Unbalanced Forces
17
• When the forces acting on an object is , the object’s
will be .
• The resultant of two unbalanced forces can be found by considering
their .
• Example: When the driving force on a car is 100 N to the left but the
friction force is 50 N to the right, then the resultant force is 50 N to
the left
18. 18
• An airplane is slowing down at constant height.
Up thrust
Weight
Thrust
Drag
Resultant
Force
19. 19
• An airplane descending at a constant velocity.
Up thrust
Weight
Thrust
Drag
Resultant
Force
26. Mass, Force and Acceleration
26
• A relationship between these factors is given by the formula
F = ma
where
F = force in newtons
m = mass in kg
a = acceleration in m/s2
27. Problem Solving
27
1. Figure below shows the forces acting on three objects. For each, say
whether the forces are balanced or unbalanced. If the forces are
unbalanced, calculate the resultant force and give its direction.
Unbalance force
Resultant force = 80 – 60
= 20 N
Direction = to the right
30. 30
2. What is the acceleration of the model car below.
31. 31
1. Find the resultant force
2. Use the equation
Resultant force = 18 N − 10 N = 8 N
F = m × a
8 N = 2 kg × a
a = 4 m/𝑠2
32. 32
3. Figure
a. What is the resultant force on the car above?
b. What is the car’s acceleration?
c. If the total frictional force rises to 1500 N, what happens to the car?
33. 33
a) Find the resultant force
b) Find the acceleration
c) No resultant force. Car will move at constant velocity
Resultant force = 1500 N − 500 N = 1000 N
F = m × a
1000 N = 800 kg × a
a = 1.25 m/𝑠2
34. 4 A block of mass 20 kg is pulled along the ground by a force, F of 60 N.
The frictional force is 10 N. Calculate the acceleration of the block.
34
35. 35
4. A block of mass 20 kg is pulled along the ground by a force, F of 60
N. The frictional force is 10 N. Calculate the acceleration of the
block.
Resultant force = 60 N − 10 N = 50 N
F = m × a
50 N = 20 kg × a
a = 2.5 m/𝑠2
36. • A car has a mass of 800 kg. its engine provides a forward force of 400
N. There is a frictional force of 160 N, acting to oppose the car’s
motion. What is the resultant force acting on the car? What is its
acceleration?
36
37. 37
5. A car has a mass of 800 kg. its engine provides a forward force of
400 N. There is a frictional force of 160 N, acting to oppose the car’s
motion. What is the resultant force acting on the car? What is its
acceleration?
Resultant force = 400 N − 160 N = 240 N
F = m × a
240 N = 800 kg × a
a = 0.3 m/𝑠2
38. • What force is needed to give a car of mass 600 kg an acceleration of
2.5 m/s2
38
39. 39
6. What force is needed to give a car of mass 600 kg an acceleration of
2.5 m/s2
F = m × a
F = 600 kg × 2.5 m/𝑠2
F = 1500 N
40. • What acceleration will result when a 12 N resultant force is applied to
a 3 kg object.
40
41. 41
7. What acceleration will result when a 12 N resultant force is applied
to a 3 kg object.
F = m × a
12 = 3 kg × a
a = 4 m/𝑠2
42. 42
8. A resultant force of 16 N causes a mass to accelerate at the rate of 5
m/s2. Determine the mass.
F = m × a
16 = m × 5 m/𝑠2
m = 3.2 kg
43. Dynamics 43
9. A car of mass 1000 kg travelling at 10 ms-1 is brought to rest in 5
seconds. Find
a) the average deceleration,
b) the braking force.
a =
v − u
t
a =
0 − 10
5
= −2 m/s2
F = m × a
F = 1000 kg × 2 m/s2
F = 2000 N
44. 44
10. When a force of 6 N is applied to a block of mass 2 kg. It moves
along a table at constant velocity.
a) What is the force of friction?
11. When the force is increased to 10 N, what is
b) the resultant force?
c) the acceleration?
Force of Friction = 6 N
Resultant force = 10 N − 6 N = 4 N
F = m × a
4 N = 2 kg × a
a = 2 m/𝑠2
45. 45
d) the velocity, if it accelerates from rest for 10 seconds?
a =
v − u
t
2 =
v − 0
10
v = 20 m/s
47. 47
1. A newton is a unit of force.
Which quantity is measured in newtons?
A. acceleration
B. density
C. mass
D. weight
48. 48
2. A spring is stretched by hanging a piece of metal from it.
What is the name given to the force that stretches the
spring?
A. friction
B. mass
C. pressure
D. weight
49. 49
3. The diagram shows a bird in flight.
In which direction does the weight of the bird act?
D
50. 50
4. Which property of an object cannot be changed by a force?
A. its mass
B. its motion
C. its shape
D. its size
51. 51
5. A force acts on a moving rubber ball.
How many of the following changes could happen to the ball
because of the force?
• a change in direction
• a change in shape
• a change in mass
• a change in speed
A. 1
B. 2
C. 3
D. 4
52. 52
6. Which is a statement of Newton’s third law of motion?
A. Every force causes a reaction.
B. If there is no resultant force on a body then there is no acceleration.
C. The forces acting on a body are always equal and opposite.
D. To every action there is an equal but opposite reaction.
53. 53
7. Below are four statements about the effects of forces on objects.
Three of the statements are correct.
Which statement is incorrect?
A. A force can change the length of an object.
B. A force can change the mass of an object.
C. A force can change the shape of an object.
D. A force can change the speed of an object.
54. 54
8. In which of these situations is no resultant force needed?
A. a car changing direction
B. a car moving in a straight line at a steady speed
C. a car slowing down
D. a car speeding up
55. 55
9. Two forces act on an object.
In which situation is it impossible for the object to be in
equilibrium?
A. The two forces act in the same direction.
B. The two forces act through the same point.
C. The two forces are of the same type.
D. The two forces are the same size.
56. 56
10. Which statement about a moving object is correct?
A. When an object is accelerating, the resultant force acting on it must equal
zero.
B. When an object is moving at a steady speed, the air resistance acting on it
must equal zero.
C. When an object is moving at a steady speed, the resultant force acting on it
must equal zero.
D. When an object is moving, there must be a resultant force acting on it.
57. 57
11. A person just supports a mass of 20 kg suspended
from a rope.
What is the resultant force acting on the mass?
A. 0 N
B. 10 N
C. 20 N
D. 200 N
58. 58
12. The propeller on a boat pushes water backwards with a force of
2000 N. The boat moves through the water against a total resistive
force of 1800 N.
According to Newton’s third law, what is the forward force on the
propeller due to the water?
B
59. 59
13. An aeroplane is in equilibrium.
The diagram shows the forces acting on the aeroplane.
Which statement about the forces is correct?
A
60. 60
14. A wooden plank rests in equilibrium on two boulders on opposite
sides of a narrow stream. Three forces of size P, Q and R act on the
plank.
How are the sizes of the forces
related?
A. P + Q = R
B. P + R = Q
C. P = Q = R
D. P = Q + R
61. Dynamics 61
15. A girl and a boy are pulling in opposite directions on a
rope. The forces acting on the rope are shown in the
diagram.
Which single force has the same effect as the two forces shown?
A. 50 N acting towards the girl
B. 350 N acting towards the girl
C. 50 N acting towards the boy
D. 350 N acting towards the boy
62. 62
16. An aircraft, flying at a constant height, is gaining speed.
The four forces acting are
What is correct?
C
63. 63
17. A tractor pulls a trailer at a constant speed.
The tractor exerts a forward force of 1600 N on the trailer.
What is the force exerted by the trailer on the tractor?
A. 0 N
B. 1600 N backwards
C. 1600 N forwards
D. 3200 N forwards
64. Dynamics 64
18. When a block of wood of mass 2 kg is pushed along the horizontal
flat surface of a bench, the friction force measured is 4 N.
When the block is pushed along the same bench with a force of 10 N, it
moves with a constant
A. speed of 3 m/s.
B. speed of 5 m/s.
C. acceleration of 3 m/s2.
D. acceleration of 5 m/s2.
65. 65
19. A force of 20 N pushes an object of mass 5.0 kg along a rough
horizontal surface where the frictional force is 5.0 N.
What is the acceleration of the object?
A. 1.0 m/s2
B. 2.0 m/s2
C. 3.0 m/s2
D. 4.0 m/s2
66. 66
20. How is the motion of a body affected by balanced and unbalanced
forces acting on it?
C
67. explain that friction is a force
that impedes motion and
produces heating
67
Friction
68. Friction
68
• Friction is a force that opposes motion between two surfaces that
are in contact.
Motion
69. 69
• The frictional force between two surfaces on a horizontal plane
• Always act against the direction
• Depends on the material on contact.
• Depends on the nature of the surfaces in contact.
• Increases as the speed of the object increases.
73. • discuss the effect of friction on
the motion of a vehicle in the
context of tyre surface, road
conditions
• (including skidding), braking
force, braking distance, thinking
distance and stopping distance
73
Friction
74. 74
A car driver sees a family of ducks
crossing the road in front of her. She
brakes for 1·5 s and took 1·8 s to stop.
76. Stopping Distance
76
• Stopping Distance = Thinking Distance + Braking Distance
• Thinking Distance
• Whilst you are reacting to the hazard, the car is still moving! During your
thinking time, you are not slowing down. We call the distance moved during
this time the thinking distance.
• Braking Distance
• With the brakes applied, the car slows down. The distance that the car
moves whilst braking is called the braking distance.
77. 77
• Stopping is made up of two parts: thinking and braking.
• Thinking distance is the distance travelled during the thinking time.
• Braking distance is the distance travelled during the braking time.
• Stopping distance is the sum of the thinking and braking distances.
• When speed doubles, thinking distances doubles and braking
distance is four time as far
78. 78
Braking Factors -
Brakes
Worn brakes won't work
as well, so you'll need to
brake for longer. Modern
brakes are also better
than old ones - they can
apply bigger forces
without causing skidding.
Dynamics
79. 79
Braking Factors - Tyres
Tread patterns are designed
to push water out from
between the tyre and road.
Good tyres can reduce
braking distance by many
metres! Worn tyres (with little
tread) will have good grip in
the dry but in the wet will
lead to much longer braking
distances...
80. 80
Braking Factors – Road
Surface
Different types of surface
provide different levels of
grip, especially in the wet. If
the road is wet, braking
distance will always be longer.
Oil spills on the road, gravel,
etc. all reduce grip and
increase braking distances.
81. 81
Braking Factors -
aerodynamics
The worse the car's
aerodynamics, the better it
will be at slowing down
during braking! The reason is
that the airflow at and around
the car (drag or air resistance)
is an additional force acting to
slow you.
82. 82
Braking Factors - Mass
The larger the total mass of
the vehicle, passengers and
luggage, the more kinetic
energy it will have at a given
speed. This increases the
braking distance as it is harder
to slow down.
83. 83
1. When a body moves across a rough surface, a frictional force is
produced.
Which statement about this force is always true?
A. It acts in the direction of the motion.
B. It is equal in value to the force producing the
motion.
C. It makes the body recoil in the opposite
direction after stopping it.
D. It opposes the motion across the surface.
84. 84
2. A wooden block is pushed across a table at constant speed.
Which statement is correct?
A. The frictional force increases as the block moves at constant speed.
B. The frictional force is equal and opposite to the pushing force.
C. The frictional force is greater than the pushing force.
D. The frictional force is less than the pushing force.
85. 85
3. The wheel of a moving car is driven by the engine. The car is
accelerating in the direction shown.
In which direction does the frictional force act on the wheel?
B
86. 86
4. Three horizontal forces act on a car that is moving along a straight,
level road.
Which combination of forces would result in the car moving at constant
speed?
C
87. 87
5. A train is travelling along a horizontal track at constant speed. Two
of the forces acting on the train are shown in the diagram.
A force of air resistance is also acting on the train to give it a resultant force of zero.
What is this air resistance force?
A. 40 000 N backwards
B. 80 000 N backwards
C. 40 000 N forwards
D. 80 000 N forwards
88. 88
6. A car is travelling at constant speed along a road and drives over a
large patch of oil. The driver applies the brakes to stop the car.
Compared to braking on a dry road, what may happen?
A. The car slows down more quickly because of the greater friction between
the tyres and the road.
B. The car speeds up at first because of the reduced friction between the tyres
and the road.
C. The car takes longer to slow down because of the reduced friction between
the tyres and the road.
D. The car takes longer to slow down because the thinking distance of the
driver is greater.
89. 89
7. A car travels along a road. The driver stops the car by pushing his
foot down on the brake pedal.
What does not change if he pushes harder on the brake pedal?
A. the braking distance
B. the braking force
C. the stopping distance
D. the thinking distance
90. describe qualitatively motion in a circular path due to a constant perpendicular
force, including
electrostatic forces on an electron in an atom and gravitational forces on a satellite
90
Circular Motion
91. Changing Velocity
91
• Velocity is speed in a particular direction.
• A change in velocity can mean
• change in speed
• change in direction
92. Centripetal Force
92
• When an object is moving in a circle, there must be a force acting on
it to change its direction.
• This force, which always act towards the centre of the circle, is
centripetal force.
It acts perpendicularly to
the direction of motion of
the object at any instant
98. Example 5
98
• A banking aircraft uses the horizontal component of the lift force to
provide the centripetal force for turning.
99. Example 6
99
• A satellite travels round the Earth in a curved path
called orbit.
• Gravitational pull (satellite’s weight) provides the
centripetal force needed.
100. Example 7
100
• In atom, the electrons are in orbit around a positively charged
nucleus.
• The attraction between the opposite charges (electrostatic force)
provides the centripetal force
101. discuss how ideas of circular motion are related to the motion of planets in the
solar system
101
Circular Motion
102. Geocentric Model
102
• This model developed by Greek astronomer Ptolemy assumed that
the Earth is at the centre and all the planets and the sun orbiting
around it.
• This model accounted that each planet moved on an epicycle, that
moved on a larger circle, called a deferent.
103. Geocentric Model
An obsolete concept which held that the
Earth was the centre of the universe and
everything revolved around the Earth.
103
104. Heliocentric Model
104
• Nicolaus Copernicus in 18th Century came up with heliocentric theory that
put the sun at the centre of the universe.
• Johannes Kepler further improve this model;
• The planets move on ellipses around the Sun.
• When planets are near the Sun in their orbit, they move faster than when they are
further away.
105. 105
• The planetary motion is a result of the gravitational attraction of
the Sun at the centre of the Solar System. As the planets are
trying to fly out into deep space, the gravity of the Sun is pulling
them into a curved orbit.
106. 106
1. A body is moving in a circle at a constant speed.
Which of the following statements about the body is true?
A. There is no acceleration.
B. There is a force acting at a tangent to the circle.
C. There is a force acting away from the centre of the circle.
D. There is a force acting towards the centre of the circle.
107. 107
2. A particle P is moving in a horizontal circle about O. It moves at
constant speed V.
Which statement is true?
A. A force of constant size is acting in the
direction of V.
B. A force of constant size is acting
towards O.
C. The force on P varies in size as it moves
around the circle.
D. There are no forces acting on P.
108. 108
3. The diagram shows a cyclist leaning over in order to
cycle around a corner.
Which force is necessary to maintain the motion
around the corner?
A
109. 109
4. The diagram shows an aeroplane turning in a horizontal circle at
constant speed.
In which direction is there a resultant force?
D
110. 110
5. A body P moves in a circle around a point S. A force F
keeps it moving in the circle.
What happens if the force F suddenly disappears?
A. P moves directly towards S.
B. P moves in a circle closer to S.
C. P moves away from S in a curved path.
D. P goes off in a straight line.
111. 111
6. A car moves in a circle at a constant speed.
What is the direction of the resultant force acting on the car?
B
112. 112
7. The diagram represents the Moon in its orbit around the Earth.
8. Which arrow represents the direction of the resultant force acting
on the Moon at the instant shown?
A
113. 113
8. What keeps an electron moving in a circle around the nucleus of an
atom?
A. a gravitational force away from the nucleus
B. a gravitational force towards the nucleus
C. an electrostatic force away from the nucleus
D. an electrostatic force towards the nucleus
114. 114
9. A turntable rotates at constant speed. A coin is placed on the
turntable at P. The friction force between the coin and the turntable
keeps the coin in the same position on the turntable.
In which direction does the friction force act?
A
119. Moment Factors
119
• The moment of a force is bigger if
the force is bigger.
Force
• The moment of a force is bigger if it
acts further from the pivot.
Distance
• The moment of force is greatest if it
acts at 90ᵒ to the object it acts on
Angle
120. Calculating Moment
120
Moment of a Force =
Force × Perpendicular distance from the line of
action of the force to the pivot
= F × d
Make calculations using
moment of a force =
force x perpendicular
distance from the pivot
and the principle of
moments.
122. 2. A mechanic uses a 15 cm long spanner and applies a force of 300 N
at the end of the spanner to undo a nut. What is the moment he
applies?
3. The radius of the wheel of fortune is 1.2 m, and the operator
applies a force of 45 N tangentially to get it spinning. What torque
has he supplied?
4. A 32 kg child sits on a seesaw. If she is 2.2 m from the pivot, what is
the moment that her weight exerts?
5. A force of 40 N is acting at the end of a beam. If the distance of this
force from the pivot is 2.0 m, what is the moment by this force?
122
123. 6. Figure below shows three positions of the pedal on a bicycle which
has a crank 0.20 m long. If the cyclist exerts the same vertically
downward push of 25 N with his foot, in which case A, B and C, is
the turning effect
i. 0,
ii. between 0 and 5 Nm,
iii. 25 0.2 = 5 Nm?
123
125. Balance Beam
• Two forces are causing this see-saw to tip.
• The girl’s weight causes it to tip to the left, while her
father provides a force to tip it to the right.
• He can increase the turning effect of his force by
increasing the force, or by pushing down at a greater
distance from the pivot.
125
weight of girl
father’s
push
126. Principle of Moments
• Moment can be clockwise or anticlockwise.
• When an object is in equilibrium, the sum of clockwise moments about any
point is equal to the sum of anticlockwise moments about the same point.
126
128. Example
128
1. For the beam balance below, work out the unknown weight?
2. Figure below shows three weights on a beam that is
balanced at its centre. Calculate the distance d from the 0.5
N weight to the pivot.
129. 129
4. The diagram shows a uniform rod balance at its centre. Use
the principle of moments to calculate the weight W.
3. A boy weighing 600 N sits on the see-saw at a distance of 1.5
m from the pivot. What is the force F required at the other
end to balance the see-saw?
130. 5. Figure below, someone is trying to balance a plank with stones. The
plank has negligible weight.
130
a. Calculate the moment of the 4 N force about O.
b. Calculate the moment of the 6 N force about O.
c. Will the plank balance? If not which way will it tip?
d. What extra force is needed at point P to balance
the plank?
e. In which direction must the force at P act?
131. 131
6. The board shown is hinged at A and supported by a vertical
rope at B, 3.0 m from A. A boy weighing 600 N stands at the
end D of the board, which is 4.0 m from the hinge. Neglecting
the weight of the board, calculate the force F on the rope.
132. Conditions for equilibrium
• If an object is in equilibrium, the forces on it must balance as well as
their turning effect.
• So:
• The sum of the forces in one direction must equal to the sum of the forces in
the opposite direction.
• The principle of moments must apply.
132
133. 1. Figure below shows a balanced beam. Calculate the unknown
forces X and Y.
133
Y
X 400 N
2.5 m
1.0 m
134. 2. Figure below shows a beam, balanced at its midpoint. The weight of
the beam is 40 N. Calculate the unknown force Z, and the length of
the beam.
134
30 N
Z
0.5 m
20 N
135. 3. Figure below shows a balanced beam. Calculate the unknown
forces X and Y.
135
Y
X
600 N
136. Quiz
1. If a nut and bolt are difficult to undo, it may be easier to turn the
nut by using a longer spanner.
This is because the longer spanner gives
A. a larger turning moment.
B. a smaller turning moment.
C. less friction.
D. more friction.
136
137. 2. A horizontal pole is attached to the side of a building. There is a
pivot P at the wall and a chain is connected from the end of the
pole to a point higher up the wall.
There is a tension force F in the chain.
What is the moment of the force F about the pivot P?
A. F x d
B. F x h
C. F x l
D. F x s
137
138. 3. A plane lamina is freely suspended from point P.
4. The weight of the lamina is 2.0 N and the centre of mass is at C.
5. The lamina is displaced to the position shown. What is the moment that will
cause the lamina to swing?
A. 0.60 N m clockwise
B. 0.80 N m anticlockwise
C. 1.0 N m clockwise
D. 1.0 N m anticlockwise
138
140. Experiment
• Aim: To verify the principle of moments
• Apparatus:
1. Retort stand
2. Metre rule with drill hole at the 50 cm mark.
3. Pivot
4. 10 g slotted mass with hanger labelled W1
5. 100 g slotted mass with hanger labelled W2
140
141. Procedure:
1. Arrange the apparatus as shown
2. Suspend different weights, W1 and W2 at different distances d1 and d2 from the pivot.
3. Carefully adjust the distances d1 and d2 until the rule balances horizontally.
4. Record the values of W1,W2,d1 and d2.
5. Repeat procedure 2, 3 and 4 for different values of W1,W2,d1 and d2.
Results:
• For each set of results, calculate (W1 × d1) and (W2 × d2).
Conclusion:
• For each set of readings, within the limits of experimental accuracy, (W1 × d1) and (W2 × d2)
will be equal for each set of readings.
• Hence clockwise moment equal anticlockwise moment.
141
142. Quiz
1. What are the conditions for equilibrium?
Turning Effect of Forces 142
D
143. 2. A heavy beam is resting on two supports, so that there are three forces acting on it.
The beam is in equilibrium.
Which statement is correct?
A. All the forces are equal in value.
B. The forces are in one direction and their turning effects are in the opposite direction.
C. The resultant force is zero and the resultant turning effect is zero.
D. The total upward force is twice the total downward force.
Turning Effect of Forces 143
144. 3. Two blocks are placed on a beam which balances on a pivot at its
centre. The weight of the beam is negligible.
144
B
1. Which diagram shows the forces
acting on the beam?
2. (The length of each arrow
represents the size of a force.)
145. 4. The weights of four objects, 1 to 4, are compared
using a balance.
Which object is the lightest?
A. object 1
B. object 2
C. object 3
D. object 4
145
146. 5. Three children, X, Y and Z, are using a see-saw to compare their
weights.
6. Which line in the table shows the correct order of the children’s
weights?
146
C
147. 6. Two equal forces F act on each of four planks.
Which plank turns?
147
D
148. 7. The diagrams show a uniform rod with its midpoint on a pivot.
Two equal forces F are applied to the rod, as shown.
Which diagram shows the rod in equilibrium?
148
C
149. 8. Forces are applied to a uniform beam pivoted at its centre.
Which beam is balanced?
149
D
150. 9. The diagram shows a uniform half-metre rule balanced at its mid-
point.
What is the weight of the metal block?
A. 50 N
B. 75 N
C. 100 N
D. 150 N
150
151. 10. The diagram shows a boy of weight 500 N sitting on a see-saw. He
sits 2.0 m from the pivot.
What is the force F needed to balance the see-saw?
151
A 250 N B 750 N C 1000 N D 3000 N
A
152. 11. A beam is pivoted at its centre. Two masses are
suspended at equal distances from the pivot as
shown in the diagram.
Which statement is correct?
A. If X has a mass of exactly 2 kg, it will rise.
B. If X has a mass of less than 2 kg, it will fall.
C. If X has a mass of more than 2 kg, it will fall.
D. If X has a mass of more than 2 kg, it will rise.
152
153. 12. In an experiment, five identical bags of rice are
balanced by a 10 kg mass.
Two bags of rice are added to the other five.
What mass will now balance the bags?
A. 3.5 kg
B. 7.0 kg
C. 10 kg
D. 14 kg
153
154. 13. In an experiment, six identical bags of flour are
balanced by a 9 kg mass.
14. Two bags of flour are removed. What mass will
balance the remaining bags?
A. 3 kg
B. 6 kg
C. 7 kg
D. 9 kg
154
155. 14. A simple balance has two pans suspended from the ends of
arms of equal length. When it is balanced, the pointer is at
0.
15. Four masses (in total) are placed on the pans, with one or
more on pan X and the rest on pan Y.
16. Which combination of masses can be used to balance the
pans?
A. 1 g, 1 g, 5 g, 10 g
B. 1 g, 2 g, 2 g, 5 g
C. 2 g, 5 g, 5 g, 10 g
D. 2 g, 5 g, 10 g, 10 g
155
156. 15. A load is to be moved using a wheelbarrow. The total mass of the load and
wheelbarrow is 60 kg.
The gravitational field strength is 10 N / kg.
What is the size of force F needed just to lift the loaded wheelbarrow?
A. 350 N
B. 430 N
C. 600 N
D. 840 N
156
157. 16. The diagram shows a wheelbarrow and its load,
which have a total weight of 150 N. This is supported
by a vertical force F at the ends of the handles.
What is the value of F?
A. 75 N
B. 150 N
C. 225 N
D. 300 N
157
158. 17. A driver’s foot presses with a steady force of 20 N on
a pedal in a car as shown.
What is the force F pulling on the piston?
A. 2.5 N
B. 10 N
C. 100 N
D. 160 N
158
159. Centre of mass
• Describe how to determine the
position of the centre of mass of
a plane lamina.
159
160. Centre of Mass
• The weight of an object is due to the attraction of the Earth on all
these particles.
• The centre of mass is the point through which the entire weight of
the object appears to act.
160
161. • Above diagram shows the positions of the centre
of gravity for regular-shaped objects with uniform
thickness.
• If the line of action of the weight of an object does
not go through the pivot, then a moment exists
makes the object to turn.
• The object will turn until where it reaches where
there is no moment.
• This fact enable us to find the centre of gravity of
an irregular shaped object.
161
162. Experiment
• Aim: To determine the centre of mass of a plane lamina
• Apparatus:
• Retort stand
• Cork
• Plumb line
• Lamina
162
163. • Procedure:
• On the lamina, make three holes near the edge of the lamina.
• Suspend the lamina through one of the holes.
• Hang the plumb line on the pin.
• When the plumb line is steady, make a dot on the position of the line at the
edge of the lamina
• Repeat steps 2-4 for the other two holes
• Conclusion
• The point where the lines meet is the centre of mass of the body.
163
165. Applying the Principle of Moment
• For a regular object such as uniform metre ruler, the
centre of gravity is at its centre and, when supported
there the object will be balanced
165
166. Applying the Principle of Moment
• If it supported at any other point, it will topple
because there will be a resultant moment about the
point of support.
166
167. Example
1. The illustration in figure below represents a metre scale balancing
on a knife edge at 20 cm mark when a weight of 60 N is suspended
from 10 cm mark. Calculate the weight of the ruler.
167
168. 2. Figure below shows a uniform metre rule weighing 30 N pivoted on
a wedge placed under the 40 cm mark and carrying a weight of 70
N hanging from the 10 cm mark. The ruler is balanced horizontally
by a weight W hanging from the 100 cm mark. Calculate the value
of the weight W.
168
169. 3. Figure below shows a uniform metre rule pivoted off-centre but maintained in
equilibrium by a suspended weight of 2.4 N. The weight is hung 5 cm from one
end of the metre rule. What is the weight of the metre rule?
169
170. 4. Figure below shows a uniform metre rule weighing 3.0 N pivoted on
a wedge placed under the 40 cm mark and carrying a weight of 7.0
N hanging from the 10 cm mark. The rule is kept horizontally by a
weight W hanging from the 100 cm end. Calculate the value of the
weight W.
170
171. 5. Figure below represents a uniform horizontal rod weighing 10 N
and of length 100 cm. The rod is balanced on a knife-edge at C,
when a weight of 8 N is suspended from the point D and a solid S,
of unknown weight is suspended from A. Calculate the weight of
the solid S.
171
172. 6. The beam shown below is 2.0 m long and has a weight of 20 N. It is
pivoted as shown. A force of 10 N acts at one end. What force F
must be applied downwards at the other end to balance the beam?
172
173. 7. Figure below represents a horizontal uniform rod AB
of weight 10 N and length 100 cm, pivoted at A. An
irregular solid X, is suspended 30 cm from the end B.
The end B is supported by a spring balance which
reads 19 N
a) Calculate the weight of the irregular solid X.
b) What is the mass of the solid if g = 10 m s-2
173
175. Stability
• Stability is the measure of a body’s ability to maintain its original
position.
• The degree of stability in an object's position depends on how must
its center of gravity will be changed if it is moved.
• There are three states of equilibrium:
• Stable equilibrium
• Unstable equilibrium
• Neutral equilibrium
175
176. Stable equilibrium
• If the body returns to its original position after being displaced slightly
it is said to be in stable equilibrium.
176
If the book is lifted from one edge and then
allowed to fall, it will come back to its
original position.
Explanation
Reason of stability
When the book is lifted its center of gravity is raised.
The line of action of weight passes through the base of
the book. A moment due to weight of the book brings
it back to the original position.
177. Unstable equilibrium
• If the body continues to move away from its original position after
being displaced, it is said to be in unstable equilibrium.
177
Explanation
If thin rod standing vertically is slightly disturbed
from its position it will not come back to its
original position.
Reason of instability
When the rod is slightly disturbed its center of
gravity is lowered . The line of action of its weight
lies outside the base of rod. The moment due to
weight of the rod toppled it down.
178. Neutral equilibrium
• If an object remains wherever it is after being displaced, it is said to
be in neutral equilibrium.
178
Explanation
If a ball is pushed slightly to roll, it will
neither come back to its original nor it
will roll forward rather it will remain
at rest.
Reason of neutral equilibrium
If the ball is rolled, its center of gravity is neither raised nor
lowered. This means that its center of gravity is at the
same height as before.
179. Designing for Stability
• There are two ways to make a body more stable.
1. Lowering its centre of gravity;
2. Increasing the area of its base.
179
180. Quiz
1. A piece of card has its centre of mass at M.
2. Which diagram shows how it hangs when suspended by a thread?
180
A
181. 2. The diagram shows a flat metal plate that may be hung from a nail
so that it can rotate about any of four holes.
3. What is the smallest number of holes from which the flat metal
plate should be hung in order to find its centre of gravity?
A. 1
B. 2
C. 3
D. 4
181
182. 3. A piece of uniform card is suspended freely from a horizontal pin.
At which of the points shown is its centre of gravity?
182
C
183. 4. A tractor is being used on rough ground.
5. What is the safest position for its centre of mass?
183
D
184. 5. An empty glass is placed on a join between two tables as shown.
The glass remains stable.
Which point is the centre of mass of the glass?
184
C
185. 6. A light aircraft stands at rest on the ground. It stands on three
wheels, one at the front and two further back.
Which point could be its centre of mass?
185
B
186. 7. The diagram shows sections of four objects of equal mass. The
position of the centre of mass of each object has been marked with
a cross.
8. Which object is the most stable?
186
A
187. 8. A student uses a stand and clamp to hold a flask of liquid.
9. Which diagram shows the most stable arrangement?
187
B
188. 9. Some containers are made from thin glass.
10. Which empty container is the most stable?
188
A
189. 10. The diagrams show the cross-sections of different glasses.
11. Which one is the least stable when filled with a liquid?
Turning Effect of Forces 189
B
190. 11. The diagram shows four models of buses placed on different ramps.
How many of these models will fall over?
A. 1
B. 2
C. 3
D. 4
190
191. 12. The diagram shows four objects standing on a flat surface.
The centre of mass of each object is marked M.
Which object will fall over?
191
C
192. 13. A girl uses paper-clips to balance a toy bird on
her finger as shown.
What is the effect of the paper-clips?
A. They help to raise the centre of mass above her
finger.
B. They help to raise the centre of mass to her finger.
C. They help to lower the centre of mass below her
finger.
D. They do not affect the centre of mass but increase
the weight.
192
193. 14.The stability of a bus is tested by tilting it on a ramp.
The diagram shows a bus that is just about to topple
over.
15.Where is the centre of mass of the bus?
193
C
194. 15.Passengers are not allowed to stand on the upper deck of double-
decker buses.
194
1. Why is this?
A. They would cause the bus
to become unstable.
B. They would cause the bus
to slow down.
C. They would increase the
kinetic energy of the bus.
D. They would lower the
centre of mass of the bus.
