We use various tools to perform different types of work in our daily life. The tools or simple devices used for making our work easier, faster and more convenient are simple machines.
Those tools or devices which make our work easier and convenient in the direction of the force is called simple machine.
Purpose of using simple machine
Simple machines are used to make our work easier in the following ways:
Mechanical advantage
The simple machine requires force to do work. The resistive force to be overcome is called load and the force applied to overcome the load is called effort.
The ratio of the load to the effort in a simple machine is called mechanical advantages or actual advantage of the machine.
Therefore,
Mechanical advantage has no unit. It is the simple ratio of two forces and affected by friction.
If a machine overcomes a load ‘L’ and the distance travelled by the load is ‘Ld’. Similarly, the effort applied in the machine is ‘E’ and the distance travelled by effort is ‘Ed’, then
If a machine overcomes a load ‘L’ and the distance travelled by the load is ‘Ld’, the work done by the load is L × Ld. It is also called output work or useful work. Therefore,
Output work = L × Ld
Likewise, the effort applied to overcome the load is E and the distance covered by effort is Ed, the work done by effort is E × Ed. It is also called input work. Therefore,
Input work = E × Ed
The efficiency of a simple machine is defined as the ratio of useful work done by machine (output work) to the total work put into the machine (input work).
We know that,
or,η=\(\frac{L×Ld}{E×Ed}\)×100%
But the mechanical advantages =\(\frac{L}{E}\) and velocity ratio = \(\frac{E_d}{L_d}\)
Thus, the relation shows that efficiency is the ratio of mechanical advantage to velocity ratio in percentage.
The principle of simple machine states that “if there is no friction in a simple machine, work output and work input are found equal in that machine”
Mathematically,
Output work = Input work
Or, L × Ld = E × Ed
Simple machine is a device which is mechanically simple and helps to make our work easier and convenient. They are of six types:
It is defined as the ratio of load to the effort applied.
Mechanical advantage (M.A) =
During calculation, friction is not counted but there is always friction inside a machine. So, actual value of MA is not same as the calculated value of it.
It is defined as the ratio of distance moved by the effort to the distance moved by the load .
Velocity ratio(VR) =
It is because friction is not involved in VR.
Practically, no machine are frictionless. The friction decreases the mechanical advantage and efficiency of a machine whereas the VR of the machine is not affected by friction. So, value of MA is always less than value of VR in a simple machine.
The work done by the machine in overcoming the load is called output work.
i.e. Output work = Load x load distance
The principle of simple machine states that if there is no friction in a simple machine, work output and work input are found to be equal in the machine.
The percentage ratio of the output work to the input work is called efficiency of a simple machine. Mathematically, η = x 100%
A machine having 100% efficiency is called an ideal or a perfect machine.
Efficiency of a simple machine is always less than 100% because friction reduces the input work applied on the machine.
Friction is the main factor which reduces the efficiency of a simple machine. Efficiency of a simple machine can be increased by reducing the friction. But oiling and greasing the machine is a useful way to increase the efficiency of a machine.
The energy input to a machine is greater than its energy output. Source energy is always wasted to overcome the friction and even to move the parts of the machine itself. Hence, no machine is perfect.
We know that, Efficiency(η) = x 100% or, η = x 100% or, η = x 100% or, η = x 100% Hence, proved.
It means that 70% of the input energy is obtained as useful energy. Rest of the 30% is used in overcoming friction.
The grease does not affect the VR of a machine as grease reduces friction and the VR of a machine is not affected by friction.
Given, Load (L) = 300N
Load distance (Ld) = 10cm = 10/100m = 0.1m
Load (L) = 450N
Effort (E) = 150N
Load distance (Ld) = 25cm = 0.25m
Effort distance (Ed) = 1- 0.25 = 0.75m
We know that, Efficiency (η) = x 100% = x 100% = x 100% = 100%
It is a crowbar used as first class lever of the simple machine.
Load (L) = 10N
Load distance (Ld) = 20 cm = 0.2m
Effort distance (E.d) = 70cm = 0.7m
Effort (E) = ?
Now, to balance it,
E x Ed = Ld
or, E x 0.7 = 0.2 x 10
or, E = 2/0.7
or, E = 20/7 N
Now,
Efficiency (η) = x 100% = x 100% = 100%
Suppose unknown weight (W) is load and 40N and 20N act as an effort
To balance lever,
E x E.d = L x L.d
Or, E1 x Ed1 + E2 x Ed2 = W x 25cm
Or, 40 x 5 + 20 (20 +5) = W x 25cm
Or,700 = W x 25
Or, 700/25 = W
Or, 28 = W
Hence, the required weight is 28N.
Given,
Load (L) = 90N
Effort (E) = 60N
It is a single movable pulley, so, VR = 2,
Efficiency (η) = ?
Now,
Mechanical advantage (M.A) = = = 3/2
And,
Efficiency (η) = x 100% = x 100% = 75%
Efficiency (η) = 90%
Load (L) = ?
Effort (E) = 400N
Velocity ratio (VR) = 2
According to formula,
η = x 100% = x 100%
or , 90% = x 100%
or, L = = 720N
Hence, 720 N can be lifted.
Effort (E) = 50N
Load (L) = 150N
Velocity Ratio (VR) = No. of pulley used = 4
Efficiency (η) = ?
We know,
η = x 100% = x 100%
= x 100% = 75%
Hence, the efficiency of the machine is 75%.
Given,
Velocity ratio (VR) = 4
Effort (E) = 36N
Total load (L) = 115 + 5N = 120N
MA = = 120/36 = 3.33
and efficiency(η) = x 100% = x 100% = 83.25%
When load is raised by 5m,
Load distance (L.d) = 5m
And VR = = Or, 4 =
∴E.d = 20m
So, work input = E x E.d = 36 x 20 = 720J
Work output = L x Ld = 120 x 5 = 600J
Total energy lost = Work input – Work output
= 720 – 600 = 120 J
Given,
Given,
Pitch (P) = 1cm = 0.01m
Length of lever = 50cm = 0.5m
Effort (E) = ?
Load (L) = 500N
By using a condition,
MA = VR
or, =
or, =
or, E = = 1.59 N
Now,
MA = = 500/1.59 = 314.46
Hence, MA = 314.46 and E = 1.59N
Here, Load (L) = 600N
Effort (E) = 100 N
Load DIstance (Ld) = 0.20m
Length of Lever (l) = 190 cm = \(\frac{190}{100}\) = 1.9m
Effort DIstance (Ed) = length of lever - load distance = (1.9 - 0.2) = 1.7
Now,according to the formula ,
MA = \(\frac{L}{E}\)
= \(\frac{600}{100}\)
= 6
VR = \(\frac{ED}{LD}\)
= \(\frac{1.7 m}{0.20 m}\) = 8.5
\(\eta \)= \(\frac{MA}{VR}\) \(\times\) 100%
= \(\frac{1.7m}{0.20}\)
= \(\frac{6}{8.5}\)\(\times\) 100%
= 70.5 %
∴MA of the crowbar is 6, VR is 8.5 and \(\eta \) is 70.5 %
Here, Load (L) = 600 N
Load distace (Ld) = 6 cm
Velocity ratio (VR) = 10
Efficiency \(\eta \) = 80%
According to the formula ,
i. \(\eta \) = \(\frac{MA}{VR}\) \(\times\) 100%
80% = \(\frac{MA}{10}\) \(\times\) 100%
or , 100 MA = 80 \(\times\) 10
∴ MA = \(\frac{ 80 \times 10 }{100}\) = 8
ii. MA = \(\frac{L}{E}\)
8 = \(\frac{600 N }{E}\)
or, E = \(\frac{600 N }{8}\)
= 75 N
iii. VR = \(\frac{Distance\;moved\;by\;the\;effort }{Distance\;moved\;by\;the\;load}\)
or, 10 = \(\frac{ ED }{6}\)
∴ Ed = 10 \(\times\) 6 = 60cm = 0.6m
iv. Input work = E \(\times\) Ed = 100 \(\times\) 0.6m = 60J
v. Output Work = L \(\times\) Ld = 600 \(\times\) 0.06m = 36J
Hence, in this lever MA is 8 , effort applied is 75 N , distance moved by the effort moved by the effort is 60cm , input work is 60J and output work is 36J.
Here , Load (L) = 600 N
Load distance (Ld) = 4m
No.of pulleys = 5
Effort (E) = 300N
(i) MA = ?
(ii) VR = ?
(iii) Output Work = ?
(iv) Efficiency = ?
According to the formua ,
i. MA = \(\frac{L}{E}\) = \(\frac{600N}{300N}\) = \(\frac{60}{30}\) = \(\frac{12}{6}\)
ii. VR = No.of pulleys used = 5
iii. Output Work = L \(\times\) Ld = 600N \(\times\) 4m = 2400J
For Effort Distance,
VR = \(\frac{Ed}{Ld}\)
5 = \(\frac{Ed}{4}\)
\(\therefore\) Ed = 20m
iv. Input Work = E \(\times\) Ed = 300N \(\times\) 20m = 6000J
v. \(\eta \) = \(\frac{Output\;work}{Input\;work}\)
= \(\frac{2400J}{6000J}\)
= \(\frac{24}{60}\) \(\times\) 100%
= 40%
Hence, MA is \(\frac{12}{6}\) VR is 5 , work output is 2400J, work input is 6000J and \(\eta \) is 40%
Here,
No.of pulleys = 4
Load (L) = 400N
Mechanical advantage (MA) = 3
i. E= ?
ii. VR=?
iii. \(\eta \)=?
According to the formula,
i. MA = \(\frac{L}{E}\)
or, 3 = \(\frac{400}{E}\)
or, E = \(\frac{400}{3}\) = 133.33N
ii. VR = No.of pulleys used = 4
iii.\(\eta \)= \(\frac{MA}{VR}\) \(\times\) 100% = \(\frac{3}{4}\) = 75%
Hence, effort applied in it is 133.33N , VR is 4 and \(\eta \)is 75%
Here,
Load (L) = 700N
Effort (E) = 500N
Length of slope (L) = 8m
Height of slope (h) = 5m
i. Output Work = L \(\times\) Ld (h) = 700 \(\times\) 5m = 3500J
ii. Input Work = E \(\times\) Ed (l) = 500 \(\times\) 8m = 4000J
iii. MA = \(\frac{L}{E}\) = \(\frac{700}{500}\) = 1.4
iv. VR = \(\frac{l}{h}\) = \(\frac{8m}{5m}\) = 1.6
v. \(\eta \) = \(\frac{MA}{VR}\)\(\times\) 100%
Here,
Radius of wheel (R) = 20 cm
Radius of axle (r) = 5 cm
Load (L) = 1000N
Effort (E) = 200N
i. Mechanical advantage(MA)= ?
ii, Velocity Ratio(VR)= ?
iii. Efficiency \(\eta \) = ?
Accrding to the formua
i. MA = \(\frac{L}{E}\) = \(\frac{1000}{200}\) = 5
ii. VR = \(\frac{R}{r}\) = \(\frac{20}{5}\) = 4
iii. \(\eta \) = \(\frac{MA}{VR}\) \(\times\) 100%
= \(\frac{5}{4}\) \(\times\) 100% = 125%
Hence, in that wheel and axle MA is 5, VR is 4 and \(\eta \) is 125%
Here,
First weight (L_{1}) = 30N
Second weight (E_{1}) = 20N
Third weight (E_{2}) = 10N
Distance between L_{1} and fulcrum (Ld_{1}) = 30cm
Distance between L_{2} and fulcrum (Ed_{1}) = 5cm
Distance between E_{1} and fulcrum (Ed_{2}) = 20cm
Now,
Anticlockwise moment = L_{1} \(\times\) Ld_{1}
= 30 \(\times\) 30 = 900N
Clockwisw moment = E_{1} \(\times\) Ed_{1} \(\times\) E_{2} \(\times\) Ed_{2}
= 20 \(\times\) 5 + 10 \(\times\) 20
= 300N
iii. The lever will not be balanced, as the clockwise moment and anticlockwise moment are not equal.
iv. To balance the lever by changing the location of 10N weight, there should be -
= E_{1} \(\times\) Ed_{1} + E_{2} \(\times\) Ed_{2} = L_{1} \(\times\) Ld_{2}
= 20 \(\times\) 5 + 10 \(\times\) Ed_{2} = 30 \(\times\) 30
= 100+10Ed_{2} = 900
= \(\frac{900-100}{10}\) = \(\frac{800}{10}\) = 80cm
Thus, the lever can be belanced by keeping the 10N weight at a distance of 80cm from the lever.
Which is not a way to reduce friction?
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Roshan
principle of simple machine
Jan 07, 2017
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Roshan
principle of simple machine
Jan 07, 2017
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