Course :- Diploma Engineering
Sub :- Engineering Mechanics
Unit :- V
Laws of Motion
• Concept of momentum
• In classical mechanics, linear momentum or
translational momentum is the product of the mass
and velocity of an object.
• For example, a heavy truck moving fast has a large
momentum—it takes a large and prolonged force to
get the truck up to this speed. If the truck were
lighter, or moving more slowly, then it would have
• Like velocity, linear momentum is a vector quantity,
possessing a direction as well as a magnitude:
• Ρ = mv
Newton’s Laws of Motion
• Newton's First Law of Motion:
• Every object in a state of uniform motion tends to
remain in that state of motion unless an external force is
applied to it.
• Newton's Second Law of Motion:
• The relationship between an object's mass m, its
acceleration a, and the applied force F is F = ma.
• Newton's Third Law of Motion:
• For every action there is an equal and opposite reaction.
• Applications of Newton's First Law
• Blood rushes from your head to your feet while
quickly stopping when riding on a descending
• The head of a hammer can be tightened onto the
wooden handle by banging the bottom of the handle
against a hard surface.
• A brick is painlessly broken over the hand of a
physics teacher by slamming it with a hammer.
• Applications of Newton's Second Law
• An apple falling to the ground must be under the
influence of a force, according to his second law. That
force is gravity, which causes the apple to accelerate
toward Earth's center.
• Applications of Newton's third Law
• Newton reasoned that the moon might be under the
influence of Earth's gravity, as well, but he had to
explain why the moon didn't fall into Earth. Unlike
the falling apple, it moved parallel to Earth's surface.
Derivation Of Force Equation From
Second Law Of Motion
• The second law states that the net force on an
object is equal to the rate of change (that is, the
derivative) of its linear momentum p in an
inertial reference frame:
F = dp / dt
• The second law can also be stated in terms of
an object's acceleration. Since the law is valid
only for constant-mass systems, the mass can
be taken outside the differentiation operator by
the constant factor rule in differentiation.
Piles, Lifts, Bodies Tied with String
• The response of a laterally loaded pile within a group
of closely spaced piles is often substantially different
than a single isolated pile. This difference is
attributed to the following three items:
1. The rotational restraint at the pile cap connection. The
greater the rotational restraint, the smaller the
deflection caused by a given lateral load.
2. The additional lateral resistance provided by the pile
cap. verifying and quantifying the cap resistance is
the primary focus of this research.
• 3. The interference that occurs between adjacent piles
through the supporting soil. Interference between
zones of influence causes a pile within a group to
deflect more than a single isolated pile, as a result of
• Locations of attachment should be:
• Directly over/in alignment with the load's center of gravity
• Above the load's CG.
• Bodies Tied With String
• block of mass 2 kg sits on a frictionless ramp and is tied to the
wall with a string as shown. The string is horizontal and tied to
the center of the block. If the ramp is inclined at 20 degrees,
what is the magnitude of the force from the block on the ramp?
Conservation of Momentum
• The sum of moment of two objects remains same
even after collision.
• In other words, the sum of moments of two objects
before collision and sum of moment of two objects
after collision are equal.
• The force that two colliding bodies exert on one another
acts only for a short time, giving a brief but strong push.
This force is called an impulsive force.
• During the collision, the impulsive force is much stronger
than any other forces that may be present; consequently, the
impulsive force produces a large change in the motion while
the other forces produce only small and insignificant
• For example, during the automobile collision shown in
Figure, the only important force is the push of the wall on
the front end of the automobile; the effects produced by
gravity and by the friction force of the road during the
collision are insignificant.
• Concept of machine
• A machine is a tool that consists of one or more parts,
and uses energy to meet a particular goal.
• Machines are usually powered by mechanical,
chemical, thermal, or electrical means, and are often
motorized. Historically, a power tool also required
moving parts to classify as a machine.
• However, the advent of electronics technology has led
to the development of power tools without moving
parts that are considered machines.
• Mechanical advantage is a measure of the force
amplification achieved by using a tool, mechanical device
or machine system. Ideally, the device preserves the input
power and simply
• trades off forces against movement to obtain a desired
amplification in the output force.
• Machine components designed to manage forces and
movement in this way are called mechanisms.
• An ideal mechanism transmits power without adding to or
subtracting from it. This means the ideal mechanism does
not include a power source, and is frictionless and
constructed from rigid bodies that do not deflect or wear.
• A simple machine has an applied force that works against a
load force. If there are no friction losses, the work done on
the load is equal to the work done by the applied force. This
allows an increase in the output force at the cost of a
proportional decrease in the distance moved by the load.
• The ratio of the output force to the input force is the
mechanical advantage of the machine.
• If the simple machine does not dissipate or absorb energy,
then its mechanical advantage can be calculated from the
Velocity Ratio and Efficiency of A
• Speed ratio
• The requirement for power input to an ideal
mechanism to equal power output provides a simple
way to compute mechanical advantage from the
input-output speed ratio of the system.
• The power input to a gear train with a torque TA
applied to the drive pulley which rotates at an angular
velocity of ωA is
• Mechanical advantage that is computed using the
assumption that no power is lost through deflection,
friction and wear of a machine is the maximum
performance that can be achieved.
• For this reason, it is often called the ideal mechanical
advantage (IMA). In operation deflection, friction and
wear will reduce the mechanical advantage.
• The amount of this reduction from the ideal to the
actual mechanical advantage (AMA) is defined by a
factor called efficiency which is determined by
Law Of Machine
• Machines which are used to lift a load are governed
by the "Law of machines", which states that the effort
to be applied on the machine (p) is related to the
weight (w) which it can lift as –
p = mw + c
• Where m and c are positive constants which are
characteristics of the machine.
• A lever is a machine consisting of a beam or rigid rod
pivoted at a fixed hinge, or fulcrum.
• It is one of the six simple machines identified by
Renaissance scientists. The word comes from the
French lever, "to raise", relevant.
• A lever amplifies an input force to provide a greater
output force, which is said to provide leverage. The
ratio of the output force to the input force is the ideal
mechanical advantage of the lever.
• The law of the lever
• The lever is a movable bar that pivots on a fulcrum
attached to or positioned on or across a fixed point.
The lever operates by applying forces at different
distances from the fulcrum, or pivot.
• Wheel And Axle
• The wheel and axle is one of six simple machines
identified by Renaissance scientists drawing from
Greek texts on technology.
• The wheel and axle is generally considered to be a
wheel attached to an axle so that these two parts
rotate together in which a force is transferred from
one to the other.
• In this configuration a hinge, or bearing, supports the
rotation of the axle.
• A pulley is a wheel on an axle that is designed to
support movement of a cable or belt along its
• Pulleys are used in a variety of ways to lift loads,
apply forces, and to transmit power.
• A pulley is also called a sheave or drum and
may have a groove between two flanges
around its circumference.
• The drive element of a pulley system can be a
rope, cable, belt, or chain that runs over the
pulley inside the groove.
• Jacks Winch Crabs
• Fitted with heavy cast iron wall brackets. The
grooved wheel is of 25 cm diameter and gears are
• This apparatus is used for experiments in efficiency
of mechanical advantage. Weights are not included.