Respuesta :
Answer:
11.54 ft - lb
Explanation:
F = 18 lb, x = 8 in = 8 / 12 = 0.66 ft
F = k x
k = F / x = 18 / 0.66 = 27.27 lb/ft
y = 11 in = 11 / 12 ft = 0.92 ft
Work done = 1 /2 x k x y^2
W = 0.5 x 27.27 x 0.92 x 0.92 = 11.54 ft - lb
Work done of spring is the product of average force and the displacement.
The work required in stretching spring from its natural length to 11 in. beyond its natural length is 11.54 ft-Ib.
How to calculate the work done required stretching the spring?
Work done of spring is the product of average force and the displacement. It can be given as,
[tex]W=\dfrac{1}{2}kx^2[/tex]
Here, [tex]k[/tex] is the spring constant. The spring constant can be given as,
[tex]k=\dfrac{F}{x}[/tex]
Here, [tex]F[/tex] is the force and [tex]x[/tex] is the displacement of spring.
Given information-
The value of the force is 18 Ib.
The length of spring stretched is 8 in beyond its natural length.
Change the length in feet as,
[tex]x=\dfrac{8}{12} \\x=0.66\rm ft[/tex]
Put the value in the above formula as,
[tex]k=\dfrac{18}{0.66}\\k=27.27 \rm Ib/ft[/tex]
Work W is required in stretching it from its natural length to 11 in. beyond its natural length, Change this length in feet as,
[tex]y=\dfrac{11}{12} \\y=0.94\rm ft[/tex]
Put the values in the formula of work done as,
[tex]W=\dfrac{1}{2}\times27.27\times (0.92)^2\\W=11.54 \rm ft-Ib[/tex]
Thus the work required in stretching spring from its natural length to 11 in. beyond its natural length is 11.54 ft-Ib.
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