Extremely Confusing Energy Question - Involves Springs

In summary, the conversation discusses a question about finding the maximum distance a spring is compressed when a 1.5kg steel mass is dropped onto it from a height of 0.37m. The solution involves using work and energy considerations, specifically the integral of force over distance and conservation of energy. Without calculus, the problem is solved by setting the gravitational potential energy equal to the elastic potential energy of the spring when compressed. This leads to a quadratic solution.
  • #1
Foon
5
0
I drew out a diagram for this question and wrote out all my givens. I looked through all the formula's I have and I just can't put the pieces of the puzzle together. If anyone can help that would be greatly appreciated.

Question:

A 1.5kg steel mass is dropped onto a vertical compression spring of force constant 2.1 x 10^2 N/m, from a height of 0.37m above the top of the spring. Find, from energy considerations, the maximum distance the spring is compressed.

Thanks!
 
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  • #2
Work is the integral of force over distance.

The spring applies a force equal to F = kx. The work done in compression is the integral of that force over distance:

W = integral (from 0 to p) (k x dx)
= 1/2 k x^2 | p
= 1/2 k p^2

where p is the maximum compression distance.

Find the gravitational potential energy released by a 1.5 kg mass moving 0.37m downwards (it's just [delta]E = m g y). Set it equal to the work done in the spring's compression, and solve for p.

- Warren
 
  • #3
I'm guessing that this is not a calculus-based class, is it?

Without calculus it's the same as Chroot said, but it looks a little different. Use conservation of energy, the gravitational potential energy at height "h" above the spring equals the total elastic potential energy of the spring when compressed a distance "x." The trick here is that the distance the mass falls is "h+x." THis is going to lead you to a quadratic solution.
mg(h+x) = 1/2 kx^2.
 

1. What is potential energy in a spring?

Potential energy in a spring is the energy that is stored when the spring is stretched or compressed. This energy is stored in the bonds between the atoms in the spring and can be released to do work when the spring is released.

2. How is the potential energy of a spring calculated?

The potential energy of a spring can be calculated using the equation U = 1/2*k*x^2, where U is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

3. What is the relationship between spring constant and potential energy?

The spring constant and potential energy have a direct relationship. This means that as the spring constant increases, the potential energy also increases. This is because a higher spring constant means that the spring is stiffer, and more energy is required to stretch or compress it.

4. Can potential energy in a spring be negative?

Yes, potential energy in a spring can be negative. This happens when the spring is compressed, and the displacement (x) in the potential energy equation is negative. It is important to keep track of the signs in the equation to ensure an accurate calculation of potential energy.

5. How is potential energy in a spring related to kinetic energy?

Potential energy in a spring is related to kinetic energy through the principle of conservation of energy. When the potential energy in a spring is released, it is converted into kinetic energy as the spring returns to its equilibrium position. This is why we often see objects bouncing back and forth when attached to a spring.

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