Is Potential Energy Equal at Maximum Height & Max Compression with Springs?

In summary, the conversation discusses the potential energy of an object launched from a spring and whether it is equal to the potential energy of the compressed spring. The equation mgh=1/2kx^2 is suggested, but it is noted that the variables need to be clarified. The conversation also mentions the possibility of making mistakes and provides a thread for further information. It is suggested that the equation mgh+mgx=1/2kx^2 is correct, but the zero-level of gravitational potential energy must be defined.
  • #1
Battle_Pope
3
0
Alright I am in a high school physics course and my teacher isn't always correct. I asked him if the potential energy for an object at its maximum height after being launched from a spring is equal to that of the potential energy when the object is compressing the spring most(right before it is released) and he said no, but I am not sure if he's right. The equation would look like this I believe mgh=1/2kx^2. Would that equation be correct?
 
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  • #2
Battle_Pope said:
Alright I am in a high school physics course and my teacher isn't always correct. I asked him if the potential energy for an object at its maximum height after being launched from a spring is equal to that of the potential energy when the object is compressing the spring most(right before it is released) and he said no, but I am not sure if he's right. The equation would look like this I believe mgh=1/2kx^2. Would that equation be correct?

If you are talking massless springs, no friction, etc... the concept of energy conservation (in that all the potential energy in the spring is converted to potential energy from the height of the object) is correct.

However, your equation might be wrong... mainly because you haven't really specified some variables. From where do you measure x? From where do you measure h? :confused:

I'm very glad you are interested in this! This problem is similar to one discussed on the forum earlier this week... someone jumping from a cliff and getting caught by a rope that had some elastic characteristics. You might try to look that one up. :biggrin:

Then -- Remember everybody makes mistakes... Being a teacher (especially a high school teacher) is HARD... I've been there. I'm sure I made mistakes ALL the time.
 
  • #3
Yes they are massless springs with no friction, and I am not sure on the specifics of how we measure x and h. Also I realize everyone makes mistakes, even teachers, I just wanted to make sure if he was right or not.
 
  • #4
You're right. Your equation is probably slightly wrong. Try to actually do the full problem, and see what the answer is (you may have the right equation, explain the variables)
 
  • #5
It not really a problem, I was wondering if that equation could be used for solving for x in the equation mgh+mgx=1/2kx^2 (vertical spring equation) i think it was, since mgh=potential energy and 1/2kx^2=potential energy when a spring is compressed shouldn't they be equal to each other?
 
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  • #7
Maybe it's useful to add that you always have to define the 'zero-level' (or whatever you call it, doesn't really matter) of gravitational potential energy. In your case, it's the point at which the spring is compressed by an amount x.
 

FAQ: Is Potential Energy Equal at Maximum Height & Max Compression with Springs?

What is potential energy with springs?

Potential energy with springs is the energy that is stored in a spring when it is stretched or compressed. This energy can be released when the spring is allowed to return to its original shape.

How is potential energy with springs calculated?

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

What factors affect the potential energy of a spring?

The potential energy of a spring is affected by its spring constant, the amount of displacement, and the mass attached to the spring. A stiffer spring with a larger displacement and a heavier mass will have a higher potential energy.

How is potential energy with springs used in real life?

Potential energy with springs is used in various everyday objects, such as toys, trampolines, and cars. It is also used in more complex systems, such as shock absorbers in cars and springs in watches.

Can potential energy with springs be converted into other forms of energy?

Yes, potential energy with springs can be converted into kinetic energy when the spring is released and the stored energy is used to move an object. It can also be converted into thermal energy due to the friction between the spring and the object it is attached to.

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