Dynamics
– In the previous chapter, we learn about the characteristics of motion.
LESSON OBJECTIVES
• Describe the effect of balanced and unbalanced forces on a body.
• Describe the ways in which a force may change the motion of a body.
• Identify the forces acting on an object and draw free body diagram(s) representing the forces acting on the object (for cases involving forces acting in at most 2 dimensions)
• Recall and apply the relationship resultant force = mass × acceleration to new situations or to solve related problems.
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Force
A force is a push or pull that one object exerts on another.
It produces or tends to produce motion, and stops and tends to stop motion
Force
The SI Unit of force is Newton (N).
Sir Isaac Newton
Adding Forces
• Force always act in a direction, hence force is a vector quantity.
• Unlike adding scalar quantities, when adding two vectors, we must consider for magnitude and direction.
• When we add two vectors, we are finding a
single vector that has the same effect as
the two vectors added together.
Adding Forces
• 2.1 Adding parallel vectors
3 N 4 N
3 N 4 N
7 N
1 N
3 + 4
Adding Forces
2.2 Adding of non-parallel vectors
• Simple steps to add vectors using parallelogram method
• Step 1: Use an appropriate scale (eg, 1 cm:1 N)
• Step 2: Draw both vectors starting from the same origin.
• Step 3: Complete the parallelogram.
• Step 4: The resultant vector is represented by the
Example 1
Two forces act on a mass as shown in the figure below. Determine the resultant force on the
mass.
50
30
140 N
Adding Forces
• Three simple steps to add vectors using tip-to-tail (triangular) method
• Step 1: Use an appropriate scale (eg, 1 cm:1 N)
• Step 2: Start with any vector, then draw the second vector such that the tail of the second
vector joins the tip of the first vector
• Step 3: The resultant force is represented by
joining the tail of the first vector to the tip of the second vector, hence forming a
Example 2
A 5.0 N weight hangs on the end of string,
which is pulled sideway by a horizontal force F. The string makes an angle of 20 with the
vertical, as shown in the figure below. The
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Newton’s 1st Law of Motion
Newton’s 1st Law states that an object will remain at rest or move with constant
velocity, unless it is acted upon by a net or
resultant force.
In other words, if no net or resultant force acts on the object, it will
not move if it is initially at rest or
No net or resultant force on an object
does not mean no force is acting on the object.
It’s simply means that all the forces acting on
the body are BALANCED.
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• Constant velocity
v doesn’t change
a = 0 ms-2
Kinematics Perspective of
Newton’s 1st Law of Motion
t / s v / ms-1
v / ms-1
t / s
• Rest
v = 0 ms-1
Summary of Newton’s 1st Law of Motion
An object at rest or at constant motion
has zero
Balanced Forces
Let’s take a look at the forces acting on the
book.
Balanced Force
Weight of book, W
Force table exerts on book, R
Case II: A toy car being pulled, moving at
constant velocity
Balanced Force
Let’s take a look at the forces acting on the toy car
Rope
Balanced Force
Force rope
exerts on car, P
Frictional Force, R
What’s the acceleration of the car?
Ans: 0 ms-2
Constant velocity
v / ms-1
Example 3
A box is pulled with a force of 20 N and moving at
constant velocity. If the frictional force acting on the box is 20 N, what is the resultant force acting on the box?
Resultant force = 20 – 20 = 0 N
Constant velocity
Balanced Forces
20 N
Example 4
Another box is pulled with a force of 30 N. If the frictional force acting on the box is 20 N, what is the resultant force acting on the box?
Resultant force = 30 – 20 = 10 N
Unbalanced Forces
30 N
Unbalanced
Forces ???
• So what happens when there is a net force acting on the object?
or
Unbalanced Forces
When the forces acting a body is
unbalanced, the net force will:
1. Cause a stationary body to move
2. Cause a moving body to stop
3. Change the speed of a moving body
Unbalanced Forces
In other words, The net force
will cause a body to:
1. accelerate
2. decelerate
Newton’s 2nd Law of Motion…
states that the net force acting on a body is the product of mass and acceleration of the same body; the direction of the force is the same as that of the body’s acceleration.
Mathematically,
F = ma
mass (SI Unit: kg)
acceleration
(SI Unit:ms-2)
Newton’s 2nd Law of Motion
Example 5
What is the acceleration of a 2 kg mass if it is acted upon by a 10 N force?
F = ma
10 = 2(a)
Newton’s 2nd Law of Motion
Example 6
A toy car of mass 300 g, being pulled by a rope, is moving with an acceleration of 1.2 ms-2.
(a)What is the magnitude of the pull, P?
(b) If the magnitude of the pull is doubled, what will be the car’s new acceleration?
Force rope exerts on car, P ?
a = 1.2 ms-2
Mass, m = 300 g = 0.3 kg
Fnet = m a
P = (0.3) (1.2)
P = 0.36 N
(b) Force is doubled, new applied force, P’
= 0.36 x 2 = 0.72 N
Fnet = ma
0.72 = (0.3)(a)
a = 2.4 ms-2
Another toy car of mass 800 g, being pulled by a rope, is moving with an acceleration of 0.8 ms-2. If the frictional force, R is 2 N, what is the magnitude of the pull, P?
Force rope exerts on car, P ?
a = 0.8 ms-2 Frictional
force, R = 2N
Fnet = m a
P – R = (0.8) (0.8) P – 2 = 0.64
P = 2.64 N
Mass, m = 800 g = 0.8 kg
Example 8
A man pushes a box of mass 20 kg across the
floor at a constant speed of 0.5 ms-1 by exerting a force of 60 N.
(a) What is the resultant force on the box?
(b) What is the frictional force acting on the box?
(c) If the man increases his force to 90 N, what will be the new resultant force and the
20 kg
60 N
a = 0 ms-2
R = ??
(a) Fnet = m a
= 20 (0)
= 0 N
(b) F net = m a
60 - R = 20 (0)
20 kg
90 N
a = ?
R = 60N
(c) Fnet = m a
90 - 60 = 20 (a)
a = 30 / 20 a = 1.5 ms-2
Newton’s 3rd Law of Motion
For every action force, there will be anequal and opposite reaction force.
Take Note:
Forces always occur in pairs.
Action and reaction forces are equal in magnitude
Action and reaction forces act in opposite directions
The rifle recoils as you shoot.
Rifle exerts a force on
bullet Bullet exerts a force
on rifle
Let’s look at some examples of Newton’s 3rd
A gravitational pull of earth on an object
Earth pulls object down
with a gravitational force. Object pulls man up with
Free Body Diagrams
- identify the forces.
Contact Force
Pulling Force
Friction Force Resistive Force
Example 9
The diagram shows a horse pulling a carriage via leather strapping, moving at a constant acceleration of 0.05 ms-2. The mass of the carriage is 240 kg while the mass of the horse is 150 kg. There resistive force acting on he object and carriage is 40 N and the resistive force acting on the horse is 25 N.
Example 9
a = 0.05 ms-2
FH, Force exerted by horse.
Leather strapping
(b)
a = 0.05 ms-2FH, Force exerted by the horse
Rh, Resistive force on horse
Horse
C, Contact force
Wh, Weight of horse
(a)
a = 0.05 ms-2T, Tension Force in leather strapping
Rc, Resistive force on carriage
Carriage
C, Contact force
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(c)
Rc, Resistive force on carriage = 40 N
a = 0.05 ms-2
T, Tension Force in leather strapping
Carriage
Fnet = ma
T – Rc = ma
T = Rc + ma
T = 40 + (240)(0.05)
= 52 N
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(d)
Rh, Resistive force on horse = 25 N
a = 0.05 ms-2
FH, Force exerted by the horse
Horse
Fnet = ma
FH – Rh – T = ma
FH = Rh + T + ma
FH = 25 + 52 + (150)(0.05)
= 84.5 N
Force exerted by the horse is 84.5 N
Friction
A force which opposes motion between 2 surfaces in contact
Friction
1. depends on materials in contact.
2. depends on Nature of the surfaces in contact.
3. Proportional to the force pressing the surfaces together.
Effects of friction
Friction has both positive and negative effects in our lives.
Negative effects of friction
• Reduces efficiency of cars by up to 20%.
• Causes wear and tear of moving parts in engines, motors and
Effects of friction
Friction has both positive and negative effects in our lives.
Positive effects of friction
• Needed for walking or holding a pair of chopsticks / pen
• Used in braking pads to slow down cars / bicycles
force of ground pushes the foot forward force of foot
Ways to reduce friction include
• Wheels
• Ball Bearings
• Lubricants and
• Polishing surfaces
• Air cushion
e.g. hovercraft and magnetic levitation in trains
Negative Effects of friction
Utilises rolling action
Smoothens surfaces
