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Spring P has force constant k and a little boy stretches it a distance ℓ. Spring Q has force constant 2 k and the same little boy stretches it a distance 2 ℓ. What is the ratio WQ WP of the work done by the boy?

Respuesta :

Answer:

[tex]\dfrac{W_Q}{W_P}={8}[/tex]

Explanation:

For spring P

Spring constant = k

Stretches length = l

The work done by boy

[tex]W_P=\dfrac{1}{2}kl^2[/tex]

For spring Q

Spring constant = 2k

Stretches length =2 l

The work done by boy

[tex]W_Q=\dfrac{1}{2}2k(2l)^2[/tex]

[tex]W_Q=\dfrac{1}{2}\times 8kl^2[/tex]

From above equation we can say that

[tex]\dfrac{W_P}{W_Q}=\dfrac{\dfrac{1}{2}kl^2}{\dfrac{1}{2}\times 8kl^2}[/tex]

[tex]\dfrac{W_P}{W_Q}=\dfrac{1}{8}[/tex]

[tex]\dfrac{W_Q}{W_P}={8}[/tex]

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