Unit-3 | SIMPLE MACHINES | Class-09

Overview: All the tools that make our work easier are machines. Those machines which are simple in construction, and make our work easier and faster are called simple machines. Here, we will discuss Mechanical Advantage, Velocity Ratio, Efficiency of a simple machine, and types of Simple Machines. 




Simple Machine:

The devices which are simple in construction and make our work easier and faster by changing the direction of force are called simple machine(s). 

The Applications  (Advantages) of Simple Machine are:

1. It helps to multiply force.

2. It helps to change the direction of force.

3. It helps to increase the speed of work.

4. It helps to do work safely.

Mechanical Advantage (MA):

Mechanical Advantage of a simple machines is the ratio of load to the effort. Mathematically,MA = Load (L) / Effort (E)

Since, MA is the ratio of two loads, it has no unit.

MA depends on friction and weight of machine.

To increase MA of machines, lubricants and other products can be used to reduce frictional force and other various forces which results in the decrease of MA.

Velocity Ratio (VR):

Velocity Ratio of a simple machines is the ratio of effort distance to the load distance.

Mathematically,

VR = Effort Distance (ED) / Load Distance (LD)

Since, VR is the ratio of two distance, it has no unit. It doesn't depend on friction and weight of machine.




Efficiency of a machine (η):

Efficiency of a machine can be defined as the percentage ratio of output work to the input work of a machine. 

i.e.η  = Output Work ( L x LD) / Input Work (E x ED)  x 100%

or, Î· = MA / VR x 100%

Ideal Machine:

Ideal Machine is not affected by friction. The machine whose efficiency is 100% is called an ideal machine. In this type of machine, the input work is always equal to the output work. This is not a practical machine because no machine is frictionless, in practice. 



Types of Simple Machines:

1. Lever

2. Pulley

3. Wheel and axle

4. Inclined plane

5. Screw

6. Wedge

1. Lever:

Lever is a rigid rod which is free to rotate about a fixed point called fulcrum. A lever has Load, Load arm, Effort, effort arm, and fulcrum.

Lever can be categorized into three types depending on the position of load, fulcrum and effort.

I. First Class Lever (Fulcrum in between)

II. Second Class Lever (Load in between)

III. Third Class Lever (Effort in between)

Principle of Lever:

Load x load arm = Effort x effort arm

2. Pulley:

Pulley is a circular disc having a groove on it's circumference through which a rope can pass. It helps us by changing the direction of Force applied and also by multiplying our force.

There are three types of pulley based on the number of pulleys attached in a system:

I. Single fixed pulley:

In this type of pulley, the pulley is fixed and it doesn't move up and down with load. The MA and VR of a single fixed pulley is always 1. Although, it doesn't multiply our force, it is widely in practice because it uses our own body weight to overcome load and it makes our work easier by changing the direction of Force applied. 

II. Single movable pulley:

In this type of pulley, the pulley move up and down with load. The MA and VR of a single movable pulley is always 2. It is used to overcome heavier load since it multiplies our applied effort by two times.

III. Block and tackle system:

In this type of pulley, two or more pulleys are used in a combined form. The MA and VR of this type of pulley is determined by the number of pulley used. 


3. Wheel and Axle:

Wheel and axle is a system of two co-axial cylinders in which the bigger one is called wheel and the smaller one is called axle.

 Wheel and axle is called a continuous lever because like a lever, it has load, effort and fulcrum. Also, we need to continuously apply effort until the load is overcomed.

Example: door knob, spanner, paddle of a bicycle, etc.

MA = Load / Effort    

VR = Radius of wheel (R) / Radius of axle (r)

Efficiency = MA / VR x 100%



4. Inclined plane:

Inclined plane is a simple machine having a sloping surface. The VR of an inclined plane is always more than one. 

MA = Load / Effort
VR = Length of inclined plane (l) / height of inclined plane (h)
Efficiency= MA / VR x 100%

5. Screw:

Screw is a modified inclined plane with raised spiral line along it's surface. Example: screw nail, Jack screw, driller ,etc.


6. Wedge:

A wedge is a simple machine with two ends, one is a sharp pointed end while the other is a thick end. Example: axe, knife, wedge, etc.



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Moment:

Moment is the turning effect produced by a force. The SI unit of moment is Newton-metre (Nm).

Moment = Force (F) x Moment Arm (r)

Law of moment:

Sum of clockwise moment = Sum of anticlockwise moment

Numerical problems:

1. Calculate the efficiency of a lever if its MA and VR are 3 and 4 respectively.
Solution:
MA = 3
VR = 4
Efficiency= MA /VR x 100%
= 3/4 x 100%
= 75%


2. Calculate the efficiency of a four wheeled pulley system if it is used to lift a load of 500 N by using an effort of 300 N.
Solution:
In a four wheeled pulley system,
VR = 4
Since, Load = 500N , Effort = 300N
MA = Load / Effort = 500/300
MA = 1.67
Now,
Efficiency= MA /VR x 100%
= 1.67/ 4 x 100%
= 41.67%

3. A 20cm long spanner is used to open a rusted nut of a motor cycle by applying an effort of 60N. Calculate the moment produced.
Solution:
Here,
Moment arm (r) = 20 cm
Force (F) = 60 N
Moment = F x r
= 60 x 20
= 1200 Nm

4. A 25cm long spanner is used to open a rusted nut. If the moment produced is 8Nm, calculate the effort applied.
Solution:
Here, Moment = 8Nm
Moment arm (r) = 25cm = 25/100 m = 0.25 m
Now, Effort applied (F) = Moment / r
= 8 / 0.25
= 32 N

5. In a wheel and axle, the radius of the wheel is 50 cm and that of the axle is 20 cm. If a load of 2000N is lifted by applying an effort of 1000N, calculate MA, VR and efficiency.
Solution:
Here,
Load (L) = 2000N
Effort (E) = 1000 N
So, MA = L/E = 2000/1000 =2
And,
Radius of the wheel (R) = 50 cm
Radius of the axle (r) = 20 cm
So, VR = R/r = 50/20 = 2.5

Now, efficiency of the wheel and axle = MA / VR x 100%
= 2/2.5 x 100%
= 80%

6. In an inclined plane, an effort is applied to lift a load of 1000 N. The MA and VR of the incline plane are 2 and 3 respectively. Calculate the efficiency and effort applied.
Solution:
Here, MA = 2
VR = 3
So,
efficiency = MA / VR x 100%
= 2/3 x 100%
= 66.66%

And,
Load (L) = 1000N
We know,
MA = Load / Effort
or, Effort = MA / L
= 1000/2
= 500 N
So, the effort applied is 500 N.





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