Please make sure to do ALL parts, including the text. How much (in m) will a spr

Question

Please make sure to do ALL parts, including the text.

How much (in m) will a spring that has a force constant of 38.5 N/m be stretched by a 0.470 kg mass hung motionless from it? Calculate the decrease in gravitational potential energy (in J) of the 0.470 kg mass when it descends this distance. Part of this gravitational energy goes into the spring. Calculate the energy stored in the spring by this stretch, and compare it in the spring with the gravitational potential energy. (energy in spring/gravitational energy) Explain where the rest of the energy might go.

Explanation / Answer

a)

using equilibrium of force

spring force = weight hanged

kx = mg

38.5 x = (0.470) (9.8)

x = 0.12 m

b)

gravitational Potential energy lost , = - mgx = - 0.470 x 9.8 (0.12) = - 0.553 J

c)

E = energy stored in spring = (0.5) k x2 = (0.5) (38.5) (0.12)2 = 0.2772 J

E/GPE = 0.2772/0.553 = 0.5

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