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Work, Energy and Power

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Physics Part I

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Physics

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When a rubber band is strecthed by a distance x, it exerts a restoring force of magnitude F = ax +bx2, where a and b are constants. The work done in stretching are unstretched rubber-band by L is

  • aL2 +bL2

  • 1 half left parenthesis aL squared plus bL cubed right parenthesis
  • aL squared over 2 space plus bL cubed over 3
  • 1 half space open parentheses aL squared over 2 plus bL cubed over 3 close parentheses

C.

aL squared over 2 space plus bL cubed over 3
straight U subscript straight f minus straight U subscript straight i space equals space minus straight W space equals space minus space integral subscript straight i superscript straight f straight F. dr
Given, F = ax +bx2
We know that work done in stretching the rubber band by L is 
|dW|= |Fdx|
vertical line straight W vertical line space equals space integral subscript 0 superscript straight L left parenthesis ax space plus bx squared right parenthesis dx
space equals space open square brackets ax squared over 2 close square brackets subscript straight O superscript straight L space plus space open square brackets bx cubed over 3 close square brackets subscript straight O superscript straight L
equals open square brackets aL squared over 2 minus fraction numerator ax space left parenthesis 0 right parenthesis squared over denominator 2 end fraction close square brackets space plus space open square brackets fraction numerator straight b space straight x space straight L cubed over denominator 3 end fraction minus fraction numerator straight b space straight x space left parenthesis 0 right parenthesis cubed over denominator 3 end fraction close square brackets
vertical line straight W vertical line space equals space aL squared over 2 plus bL cubed over 3
straight U subscript straight f minus straight U subscript straight i space equals space minus straight W space equals space minus space integral subscript straight i superscript straight f straight F. dr
Given, F = ax +bx2
We know that work done in stretching the rubber band by L is 
|dW|= |Fdx|
vertical line straight W vertical line space equals space integral subscript 0 superscript straight L left parenthesis ax space plus bx squared right parenthesis dx
space equals space open square brackets ax squared over 2 close square brackets subscript straight O superscript straight L space plus space open square brackets bx cubed over 3 close square brackets subscript straight O superscript straight L
equals open square brackets aL squared over 2 minus fraction numerator ax space left parenthesis 0 right parenthesis squared over denominator 2 end fraction close square brackets space plus space open square brackets fraction numerator straight b space straight x space straight L cubed over denominator 3 end fraction minus fraction numerator straight b space straight x space left parenthesis 0 right parenthesis cubed over denominator 3 end fraction close square brackets
vertical line straight W vertical line space equals space aL squared over 2 plus bL cubed over 3
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What are different units of energy?

The different units of energy are :

(i) Joule            
(ii) Erg
(iii) eV            
(iv) KWh
(v) Calorie.

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What is watt?

SI unit of power is Watt. 
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Define watt.

Power is said to be one watt if one joule of work is done in one second. 
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Is work a scalar or a vector quantity?

Work is dot product of two vectors. i.e. F with rightwards arrow on top times S with rightwards arrow on top.

And dot product is a scalar quantity. Therefore, work is a scalar quantity. 
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Define the unit joule.

Work done is said to be one joule if one newton of  force displaces the body through a distance of one meter in the direction of applied  force .
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