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Simple

Machines

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

less momentum.

• 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 toremain in that state of motion unless an external force isapplied to it.

• Newton's Second Law of Motion:

• The relationship between an object's mass m, itsacceleration 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.

Application

• Applications of Newton's First Law

• Blood rushes from your head to your feet while

quickly stopping when riding on a descending

elevator.

• 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.

Application

• Applications of Newton's Second Law

• An apple falling to the ground must be under theinfluence of a force, according to his second law. Thatforce is gravity, which causes the apple to acceleratetoward Earth's center.

• Applications of Newton's third Law

• Newton reasoned that the moon might be under theinfluence of Earth's gravity, as well, but he had toexplain why the moon didn't fall into Earth. Unlikethe 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 anobject is equal to the rate of change (that is, thederivative) of its linear momentum p in aninertial reference frame:

F = dp / dt

• The second law can also be stated in terms ofan object's acceleration. Since the law is validonly for constant-mass systems, the mass canbe taken outside the differentiation operator bythe constant factor rule in differentiation.

Piles, Lifts, Bodies Tied with String

• Piles

• 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

pile-soil-pile interaction.

• Lifts

Lifting Functions

Attachments:

Chains

Cables

Ropes

Webbing

• Locations of attachment should be:

• Directly over/in alignment with the load's center of gravity(CG).

• Above the load's CG.

• Bodies Tied With String

• block of mass 2 kg sits on a frictionless ramp and is tied to thewall with a string as shown. The string is horizontal and tied tothe 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.

Impulsive Force

• 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

changes.

• 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.

Simple Machine

• 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 oftenmotorized. Historically, a power tool also requiredmoving parts to classify as a machine.

• However, the advent of electronics technology has ledto the development of power tools without movingparts that are considered machines.

Mechanical Advantage

• 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.

Mechanical Advantage

• 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

machine's geometry.

Velocity Ratio and Efficiency of A

Machine

• Speed ratio

• The requirement for power input to an idealmechanism to equal power output provides a simpleway to compute mechanical advantage from theinput-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 angularvelocity of ωA is

P=TAωA

• Efficiency

• Mechanical advantage that is computed using theassumption that no power is lost through deflection,friction and wear of a machine is the maximumperformance that can be achieved.

• For this reason, it is often called the ideal mechanicaladvantage (IMA). In operation deflection, friction andwear will reduce the mechanical advantage.

• The amount of this reduction from the ideal to theactual mechanical advantage (AMA) is defined by afactor called efficiency which is determined byexperimentation.

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.

Simple Machines

• Lever

• 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.

1

• 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.

• Pulleys

• A pulley is a wheel on an axle that is designed to

support movement of a cable or belt along its

circumference.

• Pulleys are used in a variety of ways to lift loads,

apply forces, and to transmit power.

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• 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

machine cut.

• This apparatus is used for experiments in efficiency

of mechanical advantage. Weights are not included.

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IMAGE REFERENCES

Sr. No. Source/Links

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http://upload.wikimedia.org/wikipedia/commons/c/c3/Lever_Principle_3D.png

https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcQR22SzbNS32UkJWWtVyJzwF8-_JL2ljrKPQ8yAeWs5cpe_xUEhAFZkbVRh

http://2.imimg.com/data2/WR/XP/MY-3735131/winch-crab-double-purchase-250x250.jpg

CONTENT REFERENCES

A TEXT BOOK OF ENGINEERING MECHANICS , R.S.KHURMI , S.CHAND & COMPANY PVT. LTD.A TEXT BOOK OF ENGINEERING MECHANICS , Dr. R.K.BANSAL , LAXMI PUBLICATION

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