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Question

(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.

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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 be dE and the displacement of the load be dL.

Work input = Effort × displacement of effort

= E × dE

Work output = Load × Displacement of load

= L × dL

e f f i c i e n c y equals fraction numerator w o r k space o u t p u t over denominator w o r k space i n p u t end fraction

fraction numerator L cross times d subscript L over denominator E cross times d subscript E end fraction equals L over E cross times fraction numerator 1 over denominator begin display style bevelled d subscript E over d subscript L end style end fraction

But, fraction numerator L o a d open parentheses L close parentheses over denominator E f f o r t open parentheses E close parentheses end fraction equals M. A

= d subscript E over d subscript L equals V. R


E f f i c i e n c y equals eta equals fraction numerator M. A over denominator V. R end fraction

M.A. = V.R. × eta


Thus, the mechanical advantage of a machine is equal to the product of its efficiency and velocity ratio

(b) Velocity ratio will not change for the machine of a given design.


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