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

[Battle_Pope]

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?

 

[physics girl phd]

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?

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.

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.

 

[Battle_Pope]

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.

 

[Office_Shredder]

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)

 

[Battle_Pope]

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?

 

[physics girl phd]

Battle_Pope:
Your first equation in the above post looks good:
mgh+mgx=1/2kx^2
You may find this thread useful:
https://www.physicsforums.com/showthread.php?t=143538

 

[radou]

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.