Derive a relationship between mechanical advantage, velocity ratio and efficiency of a simple machine.

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Solution

Let a machine overcome a load $L$ by the application of an effort $E$ . In time $t$ , let the displacement of effort of $d_{E}$ ad the displacement of load be $d_{L}$ .
Work input $= E f f o r t \times$ displacement of effort
$= E \times d_{E}$
Work output $= L o a d \times$ displacement of load
$= L \times d_{L}$
$E f f i c i e n c y = \frac{Work output}{Work input}$
$= \frac{L \times d_{L}}{E \times d_{E}} = \frac{L}{E} \times \frac{d_{L}}{d_{E}}$
$= \frac{L}{E} \times \frac{1}{d_{E} / d_{L}}$
But $\frac{L o a d (L)}{E f f o r t (E)} = M . A .$
and $\frac{d_{E}}{d_{L}} = V . R .$
$∴ E f f i c i e n c y η = \frac{M . A .}{V . R .}$ or $M . A . = V . R . \times η$
Thus, the mechanical advantage of a machine is equal to the product of its efficiency and Velocity Ratio.

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Similar questions

(a) State the relationship between mechanical advantage, velocity ratio and efficiency.

(b) Name the term that will not change for a machine of a given design.

What is the relationship between the mechanical advantage and the velocity ratio for:

1) An ideal machine; 2) A practical machine?

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