Suppose you have a spring with a force constant of 37.5 N/m.
1) How much is the spring stretched, in meters, by an object with a mass of 0.445 kg that is hanging from the spring at rest? \DeltaX=
2) Calculate the change in gravitational potential energy, in joules, of the 0.445-kg object when it descends this distance. \DeltaPE=
3) Calculate the energy, in joules, stored in the spring when it is stretched this amount. PEel=
4) Apparently, not all of the gravitational potential energy went into the potential energy of the spring. What happened to the rest of the potential energy?
A. The energy went into the kinetic energy of the mass on the spring.
B. The missing energy went into heat caused by friction or work from some other external force.
C. The calculation for the gravitational potential energy was incorrect - the acceleration due to gravity was not constant during this motion.
D. Not of these options are correct.
E. The calculation for the potential energy of the spring was incorrect.

According to the Hooke's law, the force that is exerted by an object on a spring is proportional to the extension as long as the elastic limit is not exceeded.

1) We have the following from the question and these would be used to solve the question.

F = mg =

m = mass of the object

g = acceleration due to gravity

F = 0.445 kg * 9.8 m/s^2

= 4.36 N

Thus;

F = Ke

F = force applies

K = force constant

e = extension

e = F/K

e = 4.36 N/37.5 N/m

e = 0.12 m

3) The change in the potential energy is given by;

W = 1/2Ke^2

W = 1/2 * 37.5 * ( 0.12)^2

W = 0.27 J

4) The missing energy went into heat caused by friction or work from some other external force.

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