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Recall that the spring constant is inversely proportional to the number of coils in the spring, or that shorter springs equate to stiffer springs. An object is attached to the lower end of a 14-coil spring that is hanging from the ceiling. The spring stretches by 0.174 m. The spring is then cut into two identical springs of 7 coils each. As the drawing shows, each spring is attached between the ceiling and the object. By how much does each spring stretch?

Respuesta :

davidlcastiblanco

Answer:

[tex]x_1= 0.0425m[/tex]

Explanation:

Using the tension in the spring and the force of the tension can by describe by

T = kx

, T = mg

Therefore:

[tex]m*g = k*x[/tex]

With two springs, let, T1 be the tension in each spring,  x1 be the extension of each spring.  The spring constant of each spring is 2k so:

[tex]T_1 = 2k*x_1[/tex]

[tex]2T_1 = m*g=4k x_1[/tex]

Solve to x1

[tex]x_1=\frac{m*g}{4k}[/tex]

[tex]x_1=\frac{k*x}{4*k}[/tex]

[tex]x_1=\frac{x}{4}[/tex]

[tex]x_1 = 0.170 / 4[/tex]

[tex]x_1= 0.0425m[/tex]

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