Spring Potential Energy problem: Where did I go wrong?

[jmosque]

A spring with k= 53 N/m hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line up with ruler marks?

According to the book, the final reading will be 61 cm (46cm + 15cm= 61cm).

 

[jmosque]

Follow-up question: Could someone explain to me what the difference is between the Law of Conservation of Energy and Conservation of Mechanical Energy?

 

[haruspex]

Energy is always conserved (conversion between mass and energy excepted, maybe). Mechanical energy is only one form of energy; it will be approximately conserved in interactions if there is not much conversion between mechanical energy and other forms.

 

[Dick]

Energy is always conserved (conversion between mass and energy excepted, maybe). Mechanical energy is only one form of energy; it will be approximately conserved in interactions if there is not much conversion between mechanical energy and other forms.

Good advice. Now apply that advice to your first problem. It's not a case where mechanical energy is conserved. Use that the force of the spring and the force of gravity balance at the final position of the mass.

 

[jmosque]

Energy is always conserved (conversion between mass and energy excepted, maybe). Mechanical energy is only one form of energy; it will be approximately conserved in interactions if there is not much conversion between mechanical energy and other forms.

I think I got it. Energy will generally always be conserved but never created or destroyed, with the possible exception of The Mass-Energy equivalence (E=mc^2). Then in a stricter sense, Mechanical energy is only conserved in the absence of forces which would release energy such as friction. Is this correct?

 

[jmosque]

Good advice. Now apply that advice to your first problem. It's not a case where mechanical energy is conserved. Use that the force of the spring and the force of gravity balance at the final position of the mass.

I am not sure I understand why you would balance the force of the spring and the force of gravity to find the final height of the mass.

 

[Dick]

I am not sure I understand why you would balance the force of the spring and the force of gravity to find the final height of the mass.

Because the mass will be stationary when it extends the spring. So the sum of all the forces on it must be zero. Newton's laws. This isn't really an energy problem.

 

[jmosque]

Because the mass will be stationary when it extends the spring. So the sum of all the forces on it must be zero. Newton's laws. This isn't really an energy problem.

Oh okay, I see you what you mean now. The problem can be thought of as a Force of Tension problem, where the object is connected to a string. The. Spring mirrors the usual rope, and the force of the spring is akin to the tension force. Thanks for your help!

And @haruspex, thanks for answering my other question.

 

[Dick]

Oh okay, I see you what you mean now. The problem can be thought of as a Force of Tension problem, where the object is connected to a string. The. Spring mirrors the usual rope, and the force of the spring is akin to the tension force. Thanks for your help!

And @haruspex, thanks for answering my other question.

Yes, except that the force the spring exerts depends on its length via Hooke's law. You want to figure out how much the spring has to stretch to support the weight of the mass.