Question

calculate the work done in starching a stel wire of length 2 m crossectional area 0.0225mm^2 when a lood of 100N is slowly apply to its strain 2*10^11N/M^2




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Answer 1

Answer:

calculate the work done in starching a stel wire of length 2 m crossectional area 0.0225mm^2 when a lood of 100N is slowly apply to its strain 2*10^11N/M^2

Answer 2

Answer:

the answer is 2.222J

Explanation:

L= 2m

$A = 0.0225 {mm}^{2} = 2.25 \times {10}^{ - 8} {m}^{2}$

since,

$1m = {10}^{ 3} mm$

F=100N

$Y = 2 \times {10}^{11} N {m}^{ - 2}$

Work done =

$\frac{1}{2} \times F \times l$

where F is the force and l is the length

Now,

$Youngs \: modulus(Y) = \frac{stress}{strain} \\ = ( \frac{F }{ A } \times \frac{ L}{l} )$

where

stress = F/A

strain= l/L

Now from the formula of Young's modulus,

$l = \frac{F \times L }{ A \times Y}$

Now

putting the values

$work \: done = \frac{1}{2} \times F \times \frac{F \times L }{ A \times Y} \\ = \frac{1}{2} \times {F }^{2} \times \frac{ L }{ A \times Y} \\ = \frac{1}{2} \times {100}^{2} \times \frac{2}{2.25 \times {10}^{ - 8} \times 2 \times {10}^{11} } \\ = 2.222joules$