Physics CH # 9

Definitions:
1. Machine:A machine is a device by means of which useful work can be performed conveniently and it can also transfer one form of energy into another form of energy.
2. Mechanical Advantage:The ratio between the resistance or weight to the power applied in a machine is called the mechanical advantage of that machine. It is denoted by M.A.
M.A. = Weight over-comed by Machine/ Force Applied on the Machine
3. Efficiency:The ratio between the useful work done and the work done on the machine is called efficiency.
M.A = (output/Input) * 100
4. Input:Input is the work done on the machine.
5. Output:Output is useful work done by the machine.
Lever:
DefinitionLever is the simplest machine in the world. It is a rigid bar, which can be rotated about a fixed point.
Principle Of Lever
In the lever the moment P acts opposite to that of work W. It means that force F tends to rotate the lever in one direction which the weight W rotates in opposite direction. If the magnitude of these moments acting in opposite direction is equal, then the lever will be in equilibrium. It means that:
Moment of P = Moment of W


Mechanical Advantage
We know that according to Principle of Lever:
Moment of P = Moment of W
=> Force * Force Arm = Weight * Weight Arm
P * AB = W X BC
AB/BC = W/P
Hence,
M.A = W/P = AB/BC = Weight Arm/ Force Arm
Kinds Of Lever
1. First Kind Of Lever
In the first kind of lever, the fulcrum F is in the between the effort P and Weight W.
Examples
Physical Balance         Handle of Pump           Pair of Scissors            See Saw

2. Second Kind Of Lever:
In the second kind of lever, the weight W is in between the fulcrum F and effort P.

Examples
Door    Nut Cracker     Punching Machine

3. Third Kind Of Lever:
In the third kind of lever, the effort P is in between the fulcrum F and weight W.

Examples
Human forearm           Upper and Lower Jaws in the Mouth.  A Pair of Forceps

Pulley:
A pulley consists of a wheel mounted on an axle that is fixed to the framework called the block. The wheel can rotate freely in the block. The groove in the circumference prevents the string from slipping.
Fixed Pulley:
If the block of the pulley is fixed then it is called a fixed pulley.

Mechanical Advantage of Fixed Pulley:
In a fixed pulley, the force P is the applied force and weight W is lifted. If we neglect the force of friction then:
Load = Effort
In the given case:
Load = W * Load Arm
Load = W * OB
Also,
Effort = P * Effort Arm
Effort = P * OA
So,
W*OB = P*OA
=> W/P = OA/OB
But, OA = OB, then
M.A = W/P = OB/OB
M.A = 1

Moveable Pulley:
In this pulley, one end of the rope that is passing around the pulley is tied to a firm support and effort P is applied from its other end. The load and weight to be lifted is hung from the hook of block. In this system, the pulley can move. Such a pulley is called moveable pulley.

Mechanical Advantage of Moveable Pulley:
In an ideal system of a moveable pulley, the tension in each segment of the rope is equal to the applied effort. As two segments support the weight, the effort acting on the weight W is 2P. Therefore, according to the principle of lever:
W * Radius of the Wheel = 2P * Radius of the Wheel
=> 2P = W
The Mechanical Advantage is given by:
M.A = W/P
M.A = 2P/P
=> M.A = 2
Hence, the mechanical advantage of a moveable pulley is 2.

Inclined Plane:

  Any smooth plane surface which makes an angle q with the horizontal surface is called an “Inclined plane”.
Where 0^o α q α90^o or values of q lies between 0^o and 90^{o .}

Uses OfInclined Plane:

It is a simple machine and is used to raise heavy loads by applying little effort.

Mechanical AdvantageOf Inclined Plane:

  In the figure AB is an inclined plane which makes an angle q with the horizontal plane. A load ‘W’ is being raised from A to B by applying an effort ‘P’. If we neglect the force of friction between load and inclined plane

Output = input
Weight x height = effort x distance
W x h = P x L
W*h/P = L
W/P = L/h
OR
W/P = 1/h/L
in right angled DOAB
Sin θ = OB/AB
Sin θ = h/L
[ perpendicular/hypotenuse = sin θ]
therefore
W/P = 1/sin θ
but [W/P = M.A.]
Thus
M.A. = 1/sin θ

This expression shows that mechanical advantage of an inclined plane depends upon the value of sin θ

Wheel And Axle:

    It is a simple machine and is used to lift heavy loads. It has a wheel of larger radius (R) and an axle of smaller radius (r) fixed on the same shaft. Wheel and axle are free to rotate about its shaft.

Mechanical Advantage Of Wheel And Axle:

  The effort is applied to the rim of the wheel and the load is raised by a rope wound around the axle. In one rotation wheel covers a distance of 2pR In one rotation load is raised by a distance of 2pr If we neglect force of friction,

Output = input
W x 2pr = P x 2pR
W/P = 2pR/2pr
W/P = R/r

Since [W/P = M.A.]

M.A. = R/r
OR
M.A. = radius of wheel / radius of axle

This expression indicates that in order to increase the mechanical advantage
Radius of :wheel must have a large value and Radius of axle must be smaller than that of wheel.

   

Screw:

Screw is one of the most important machines. It is used to hold different parts of machines together. It has waste applications in our daily life plus in industries. It is used in every type of device.

Construction And Working:

It simply consists of a threaded rod with a head known as “Screw head”. It has a number of threads. The perpendicular distance between two adjacent threads is known as pitch of screw. The thread of screw can be regarded as a continuous inclined plane wrapped round a cylinder of radius d .

Mechanical Advantage:

_{If we apply an effort ‘P’ on the head of screw then it turns one revolution and at the same time the screw moves forward in to the wood or wall through a distance equal to its pitch “h”. The effort ‘P’ moves through a distance 2pd. The screw remains in the wood due to frictional forces between the screw and the wood. A large amount of energy changes in to heat energy during the process of screwing.
Let us assume an ideal case when there is no loss of energy then;in this condition}

Output = input
P x _2pd = W x h
W/P = _{2 p d}/h

Hence, the mechanical advantage of the screw will be.

M.A. = _2pd/h

The mechanical advantage of the screw depends upon the following factors.
1.PITCH:
In order to increase mechanical advantage of screw we must use a screw of small pitch.
2. RADIUS OF SCREW:
Larger is the radius of screw head , greater is the mechanical advantage.

Screw Jack:

A screw jack is a simple machine. It is used to lift cars or heavy automobiles. It consists of a long screw rod which passes through a threaded block B and a handle . The distance between two consecutive thread is known as pitch of screw.

Mechanical Advantage:

When an effort is applied to the handle , the effort moves in a circle of radius “d” while “d” is the length of the rod and the block “B” moves up equal to the pitch of the screw jack. If the handle is turned through one complete revolution in a circle of radius “d” the effort moves through a distance 2pd and consequently the load is raised through a height h. Hence, the mechanical advantage is given by:

M.A. = 2pd/h
M.A. = Distance through which the effort is moved/height through which the load is raised

We know that the pitch of the screw is very small as compared to the length of the rod, so the mechanical advantage should be very large. Due to frictional force between the different parts of screw jack, the efficiency is less than one. It is due to the reason that a lot heat energy is used for over coming the frictional forces.
It should be remembered that in case of screw jack friction is a necessary part of operation, because in the absence of friction, it would unwind at once when applied force is removed.