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To practice Problem-Solving Strategy 7.2 Conservation of energy with conservative forces. A basket of negligible weight hangs from a vertical spring scale of force constant 1500 N/mN/m . If you suddenly put an adobe brick of mass 3.00 kgkg in the basket, find the maximum distance that the spring will stretch.

Respuesta :

MechEngineer

Answer:

0.03924 m

Explanation:

Let g = 9.81 m/s2. Let x be the maximum distance that the spring will stretch. And let the potential energy reference point be at the the lower end where the spring is stretched to the maximum. Using mechanical energy conservation we have the following:

- At the bottom end where the spring is stretched to maximum: potential and kinetic energy is 0. Elastic energy is [tex]kx^2/2[/tex]

- At the point where the weight is placed: potential energy is mgx, kinetic energy and elastic energy is 0 (because the spring is not stretched)

[tex]E_p = E_e[/tex]

[tex]kx^2/2 = mgx[/tex]

[tex]x = 2mg/k = 2*3*9.81/1500 = 0.03924 m[/tex]

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