Conservation of Energy and Springs

AI Thread Summary
The discussion revolves around a physics problem involving a mass sliding down a frictionless incline and compressing a spring. The key point is the conservation of energy, where the initial gravitational potential energy of the mass is converted into the potential energy of the spring upon maximum compression. One participant questions whether gravitational potential energy should also be considered after the mass compresses the spring, given the incline's angle. Ultimately, the correct approach simplifies the problem by equating the initial gravitational potential energy directly to the spring's potential energy, leading to the correct solution. The conversation highlights the importance of understanding energy conservation in different contexts.
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Homework Statement


A mass starts from rest and slides a distance d down a frictionless θ deg incline. While sliding, it comes into contact with an unstressed spring of negligible mass, as shown in the figure below. The mass slides an additional distance as it is brought momentarily to rest by compression of the spring . Calculate the initial separation d between the mass and the spring. (I am given mass, the angle, additional distance, and spring constant)

Homework Equations


Energy is conservative

The Attempt at a Solution


I got the answer in my textbook after two attempts
However my first attempt I've been wondering.
The final energy equation that I originally came up with did not work
But I'm thinking about it like this: if the spring is at an angle, wouldn't there also be a gravitational potential energy at the end as well? It's on a ramp, and the spring keeps it on the ramp. It doesn't ever tell us to consider that the mass actually slides onto ground level.
I had Initial Gravitational Potential Energy = Final Potential Energy Of the Spring + Final Gravitational Potential Energy (well I couldn't really solve it since I couldn't figure out how far above it was afterwards since there wasn't a distance of the whole ramp)
The method that worked was that Initial gravitational potential energy = final potential energy of the spring
I have a picture of how I visualized it, the red line just represents how high up it is from the ground.
(Left side is initial, right side is final. Just ignore the size difference)
Please note, (restating) that I did get the answer in the end. I'm just asking a question of why it isn't another solution
 

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Redfire66 said:
wouldn't there also be a gravitational potential energy? It's on a ramp, and the spring keeps it on the ramp.
Sure.
You can combine both parts to a single distance, that makes equations easier.
 
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