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A 50-cm-long spring is suspended from the ceiling. A 270 g mass is connected to the end and held at rest with the spring unstretched. The mass is released and falls, stretching the spring by 24 cm before coming to rest at its lowest point. It then continues to oscillate vertically. Part A What is the spring constant?

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Chenk13

Answer:

k = 22.05 N/m

Explanation:

The potential energy of the mass is converted into potential energy of the spring.

Given:

mass m = 0.27 kg

gravitational constant g = 9.8 m/s²

distance falling/ stretching of spring h = 0.24 m

[tex]U_{gravity} = U_{spring}\\ mgh = \frac{1}{2} kh^{2}[/tex]

Solving for k:

[tex]k = 2mg\frac{1}{h}[/tex]

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