X Physics - Chapter 9 - Machines

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
Definition

Lever 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 wight 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 effortP is in between the fulcrum F and weight W.


Examples

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

Inclined Plane
Definition

A heavy load can be lifted more easily by pulling it along a slope rather than by lifting in vertically. Such a slope is called an Inclined Plane.

Mechanical Advantage

M.A = W/P = l/h = Length of Inclined Plane/Perpendicular Height




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 neclect 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 ffort 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.