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A force of 14 lb is required to hold a spring stretched 4 in. beyond its natural length. How much work W is done in stretching it from its natural length to 10 in. beyond its natural length?

Respuesta :

Answer:

[tex]W = 19.8 J[/tex]

Explanation:

14 lb force is required to stretch the spring by 4 inch distance

So we have

[tex]F = 14 lbf [/tex]

[tex]F = 6.35 \times 9.8 N[/tex]

[tex]F = 62.3 N[/tex]

stretch in the spring is given as

[tex]x = 4 in = 0.1016 m[/tex]

now we will have

[tex]F = kx[/tex]

[tex]62.3 = k(0.1016)[/tex]

[tex]k = 613.125 N/m[/tex]

Now we need to find the work to stretch it by x = 10 in = 0.254 m

so we have

[tex]W = \frac{1}{2}kx^2[/tex]

[tex]W = \frac{1}{2}(613.125)(0.254)^2[/tex]

[tex]W = 19.8 J[/tex]

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