Sunday, 5 August 2018

Machines: Mechanical Advantage, Velocity Ratio and efficiency formula

Mechanical Advantage, Velocity Ratio, efficiency

Machines

A machine is a device that makes work to be done easier and faster. It uses a basic concept of applying effort to overcome load.




Some classification of Machines 

  • Lever
  • Pulley
  • Inclined plane
  • Wheel and axle
  • Gear
  • Hydraulic press
  • Screw


Mechanical Advantage 

The mechanical Advantage of a simple machine is the ratio of "load"  (which is the resistive force to be overcome) to "effort"  (which is the force applied to overcome load.

Therefore,

Mechanical Advantage

Mechanical Advantage (M.A) = L/E


Let's assume,

L = load
E = Effort
Ld = distance moved by load
Ed = distance moved by Effort
M.A = mechanical advantage
V. R = Velocity Ratio


Velocity Ratio

The velocity ratio of a simple machine is the ratio of the "distance moved by effort" to the "distance moved by load of the machine.

Therefore,

Velocity Ratio (V.R) = (Distance moved by effort)  / (Distance moved by load) 

Velocity ratio



Efficiency

This may be defined as the ratio of the useful work done by the machine (Work Output) to the total work input (I.e the total work put into the machine).

Efficiency formula



Work Output = useful work done by the machine
Work output = Load x Distance moved by load

Work Output = L x Ld

While,

Work input = total work put into the machine
Work input = Effort x Distance moved by effort

Work input = E x Ed

Efficiency formula

Efficiency formula


Why Can't the Efficiency of the machine ever be 100%?

For ideal or perfect machine, work output is equal to the work input. Ideal machines are those imaginary machines which are frictionless. In practice, the work output of a machine is always less than work input due to the effect of friction. If the frictional force in the machine increases the efficiency decreases because machines are frictionless in practice, the efficiency of a machine can never be 100%.


An Example


The Velocity Ratio of a Machine is 5 and it's efficiency is 75%. What effort would be needed to lift a load of 150N with the machine?

Solution 

Effort needed (E) = ? 

Load = 150N

V.R = 5

Recall,

V.R = Ed / Ld = 5

Efficiency = 75%

Recall,



75 = M.A ÷ 5 x 100

M.A = (75)(5)/100

M.A = 3.75

Recall,



3.75 = 150/E

E = 40N






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