Work, Energy and Power

Question

If momentum of a body is decreased by 20% without changing the mass of the body, by what percentage kinetic energy of body will change?

Solution

Let p_i be the initial momentum of body and K_i be the initial kinetic energy of the body.
If momentum is decreased by 20% then final momentum is,
$p subscript f equals end subscript p subscript i minus 0.2 p subscript i equals 0.8 p subscript i$

Since, kinetic energy is given by,
 $K equals fraction numerator p squared over denominator 2 m end fraction$
∴ Final kinetic energy is,
 $K subscript f equals fraction numerator P subscript f superscript 2 over denominator 2 m end fraction equals fraction numerator left parenthesis 0.8 p subscript i right parenthesis squared over denominator 2 m end fraction$
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Now change in Kinetic energy is,
$increment K space equals space K subscript f minus K subscript i space equals space minus 0 cross times 36 space K subscript i$
Percentage change in kinetic energy is,
$fraction numerator K subscript f minus K subscript i over denominator K subscript i end fraction 100 space equals space minus 36 %$
Negative sign shows that there is decrease of energy.

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Work, Energy And Power

If momentum of a body is decreased by 20% without changing the mass of the body, by what percentage kinetic energy of body will change?

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