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A 0.73-kg metal sphere oscillates at the end of a vertical spring. As the spring stretches from 0.12 m to 0.23 m (relative to its unstrained length), the speed of the sphere decreases from 7.2 to 4.5 m/s. What is the spring constant of the spring?

Respuesta :

MechEngineer

Answer:

599 N/m

Explanation:

Let k (N/m) be the spring constant. According to the law of energy conservation, the total mechanical energy (kinetic and elastic) any any point along the spring must be the same:

[tex]kx^2/2 + mv^2/2 = constant[/tex]

[tex]k0.12^2/2 + 0.73*7.2^2/2 = k0.23^2/2 + 0.73*4.5^2/2[/tex]

[tex]0.0144k + 37.8432 = 0.0529k + 14.7825[/tex]

[tex]0.0385k = 23.0607[/tex]

[tex]k = 599 N/m[/tex]

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