KINETICS – this is the study of the relationship between the motion of bodies and the forces acting
on these bodies.
The forces involved, when solving moving body problems, can be grouped as:
Forces to overcome inertia
Forces to overcome gravity
Forces to overcome friction
In order to fully understand KINETICS it is necessary to consider NEWTON'S LAWS OF MOTION.
1. NEWTON'S LAWS OF MOTION – Sir Isaac Newton was the first to state correctly the basic
laws governing the motion of a body and to demonstrate their validity. These laws are:
Law 1 A body remains in a state of rest, or of uniform motion in a straight line, unless acted on by
an external force.
Law 2 When a body is acted upon by an external force which causes it to accelerate, the
acceleration of the body is proportional to, and in the same direction as, the force. More
exactly the rate of change in momentum of a body is directly proportional to the nett force
acting upon it.
Law 3 For every force there is a reaction which is equal in magnitude and opposite in direction
(i.e. ACTION = REACTION).
The correctness of these laws has been verified by innumerable accurate physical measurements.
Newton’s second law forms the basis for most of the analysis in kinetics and when applied to a
body of constant mass m it may be stated as F = m a.
Newton’s first law contains the principle of the equilibrium of forces, which is the main topic of
concern in statics. Actually this law is a consequence of the second law, since there is no
acceleration when the force is zero, and the body is either at rest or is moving with a constant
velocity. The first law adds nothing new to the description of motion but is included here since it
was a part of Newton’s classical statements.
The third law is basic to our understanding of force. It states that forces always occur in pairs of
"equal and opposite" forces. Therefore the reason for NELSON'S COLUMN remaining at ground
level in TRAFALGAR SQUARE is because the ground on which it stands is pushing upwards with
a force equal to the column's weight (which acts downwards). This principle holds for all forces,
variable or constant, regardless of their source and holds at every instant of time during which the
forces are applied. In analysing bodies under the action of forces it is absolutely necessary to be
clear about which of the pair of forces is being considered. It is necessary first of all to isolate* the
body under consideration and then to consider only the one force of the pair which acts on the
body in question.
*NOTE – this principle is the same as that used in STATICS when drawing free body diagrams.
1
, 2. INERTIA – all bodies, which are at rest or in motion, possess inertia. Inertia is defined as:
the resistance a body has to a change in velocity
The inertia of a body is dependent on its mass, consequently:
bodies with little mass offer little resistance to a change in velocity because they have low
inertia whilst
bodies of large mass have a high resistance to a change in velocity because they have high
inertia.
To overcome the inertia of a body and cause it to change its velocity (i.e. accelerate/decelerate), a
force must be applied. Newton’s laws of motion describe the effects of this force on the motion of
the body.
MOTION
Consider a mass m resting on a frictionless horizontal
surface. A force F is applied to the mass in order to ACC (a)
change its velocity (i.e. cause acceleration). INERTIA
FORCE(F) FORCE (ma)
It has been found experimentally that the force F and m
acceleration a are directly proportional to each other.
Hence F a
or F = constant x a where the constant of proportionality is the mass
F = ma
The product ma is known as inertia force and is a consequence of Newton’s second law.
NOTE - inertia force ma always opposes the acceleration a.
- deceleration in one direction can be considered as acceleration in the opposite direction.
- since friction between the mass and the surface is not considered then the gravity force
(or weight) w = mg which is related to friction force, can also be neglected at this stage.
EXAMPLE 1 – a mass of 100 kg is accelerated at 5 m s -2 along a frictionless horizontal surface by
means of a wire cable attached to the mass. Determine the force required for acceleration (i.e. the
tension in the cable).
………………………………………………………………
MOTION
FORCE (F) ………………………………………………………………
m
………………………………………………………………
EXAMPLE 2 – a mass of 100 kg is decelerated at 5 m s -2 along a frictionless horizontal surface by
pulling on a cable attached to the mass. Determine the force required for deceleration (i.e. the
tension in the cable).
MOTION
………………………………………………………………
FORCE (F)
m ………………………………………………………………
………………………………………………………………
2
on these bodies.
The forces involved, when solving moving body problems, can be grouped as:
Forces to overcome inertia
Forces to overcome gravity
Forces to overcome friction
In order to fully understand KINETICS it is necessary to consider NEWTON'S LAWS OF MOTION.
1. NEWTON'S LAWS OF MOTION – Sir Isaac Newton was the first to state correctly the basic
laws governing the motion of a body and to demonstrate their validity. These laws are:
Law 1 A body remains in a state of rest, or of uniform motion in a straight line, unless acted on by
an external force.
Law 2 When a body is acted upon by an external force which causes it to accelerate, the
acceleration of the body is proportional to, and in the same direction as, the force. More
exactly the rate of change in momentum of a body is directly proportional to the nett force
acting upon it.
Law 3 For every force there is a reaction which is equal in magnitude and opposite in direction
(i.e. ACTION = REACTION).
The correctness of these laws has been verified by innumerable accurate physical measurements.
Newton’s second law forms the basis for most of the analysis in kinetics and when applied to a
body of constant mass m it may be stated as F = m a.
Newton’s first law contains the principle of the equilibrium of forces, which is the main topic of
concern in statics. Actually this law is a consequence of the second law, since there is no
acceleration when the force is zero, and the body is either at rest or is moving with a constant
velocity. The first law adds nothing new to the description of motion but is included here since it
was a part of Newton’s classical statements.
The third law is basic to our understanding of force. It states that forces always occur in pairs of
"equal and opposite" forces. Therefore the reason for NELSON'S COLUMN remaining at ground
level in TRAFALGAR SQUARE is because the ground on which it stands is pushing upwards with
a force equal to the column's weight (which acts downwards). This principle holds for all forces,
variable or constant, regardless of their source and holds at every instant of time during which the
forces are applied. In analysing bodies under the action of forces it is absolutely necessary to be
clear about which of the pair of forces is being considered. It is necessary first of all to isolate* the
body under consideration and then to consider only the one force of the pair which acts on the
body in question.
*NOTE – this principle is the same as that used in STATICS when drawing free body diagrams.
1
, 2. INERTIA – all bodies, which are at rest or in motion, possess inertia. Inertia is defined as:
the resistance a body has to a change in velocity
The inertia of a body is dependent on its mass, consequently:
bodies with little mass offer little resistance to a change in velocity because they have low
inertia whilst
bodies of large mass have a high resistance to a change in velocity because they have high
inertia.
To overcome the inertia of a body and cause it to change its velocity (i.e. accelerate/decelerate), a
force must be applied. Newton’s laws of motion describe the effects of this force on the motion of
the body.
MOTION
Consider a mass m resting on a frictionless horizontal
surface. A force F is applied to the mass in order to ACC (a)
change its velocity (i.e. cause acceleration). INERTIA
FORCE(F) FORCE (ma)
It has been found experimentally that the force F and m
acceleration a are directly proportional to each other.
Hence F a
or F = constant x a where the constant of proportionality is the mass
F = ma
The product ma is known as inertia force and is a consequence of Newton’s second law.
NOTE - inertia force ma always opposes the acceleration a.
- deceleration in one direction can be considered as acceleration in the opposite direction.
- since friction between the mass and the surface is not considered then the gravity force
(or weight) w = mg which is related to friction force, can also be neglected at this stage.
EXAMPLE 1 – a mass of 100 kg is accelerated at 5 m s -2 along a frictionless horizontal surface by
means of a wire cable attached to the mass. Determine the force required for acceleration (i.e. the
tension in the cable).
………………………………………………………………
MOTION
FORCE (F) ………………………………………………………………
m
………………………………………………………………
EXAMPLE 2 – a mass of 100 kg is decelerated at 5 m s -2 along a frictionless horizontal surface by
pulling on a cable attached to the mass. Determine the force required for deceleration (i.e. the
tension in the cable).
MOTION
………………………………………………………………
FORCE (F)
m ………………………………………………………………
………………………………………………………………
2
