1
vote
2answers
50 views

Using an electric winch to compress a spring and launch an object

I'm having trouble grokking the relationship between a winch's pull/torque and a spring's potential energy. I would like to compress a spring using an electric winch and figure out how far it will be ...
2
votes
3answers
290 views

Where does the loss in gravitational energy of the load go when a spring is pulled?

A mass spring system is in equilibrium. If I pull on the load by $x$ meters, the energy stored in the spring is (this is what is given in my book): $$E=\frac12kx^2 $$ However, doesn't the load lose ...
6
votes
2answers
160 views

What can be known about the formulas for energy only from the fact that it is conserved?

The question is to figure out how the energy can be derived knowing just one thing: There is a quantity called Energy that is conserved over time. The goal is to get an equation that somehow ...
1
vote
2answers
408 views

Energy stored in a clothespin spring (non linear spring)

I was wondering how one would go about figuring out the energy stored in a spring in a clothespin. When opened the spring is deformed, but I don't have any intuition for why it gets stronger with ...
3
votes
3answers
234 views

What is the mathematical justification for the quadratic approximation to the energy of a spring in a one-dimensional lattice?

It follows easily from this draw, the length $l$ of this spring as a function of the vertical distance $x$, as $l(x)=\sqrt{1+x^{2}}$ Now, $l$ can be expressed as a MacLaurin expansion: $$l(x) = ...
4
votes
2answers
389 views

Potential energy of a spring

I'm puzzled about the potential energy of a spring. A spring is a conservative system. So the potential energy should be defined only up to a constant -- can be defined to be 0 anywhere. However, ...
0
votes
2answers
175 views

Why is the spring constant $W_p''(0)$?

According to my physics book, the spring constant can be calculated from knowing the potential energy, with the formula $k = W_p''(0)$. I don't really understand why, and the book doesn't explain it ...
1
vote
0answers
191 views

Potential energy of a spring

I have a little problem with the potential energy of a spring... I hope you can help me! I have two coupled pendula, given by two masses $m$ fixed to two rigid bars (that haven't any mass) and with ...