Conservation of Energy and Springs

In summary, the problem involves a mass sliding down a frictionless incline and coming into contact with a spring. The mass slides an additional distance due to the compression of the spring, and the goal is to calculate the initial separation between the mass and the spring. The solution involves using the conservation of energy, and while the initial equation did not work, it was eventually solved by considering the initial gravitational potential energy to be equal to the final potential energy of the spring. The spring keeps the mass on the ramp, and this can be visualized by combining the two distances into a single one.
  • #1
Redfire66
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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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  • #2
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.
 

FAQ: Conservation of Energy and Springs

What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, it can only be transferred from one form to another. This means that the total amount of energy in a closed system remains constant.

How does conservation of energy apply to springs?

Conservation of energy applies to springs because when a spring is compressed or stretched, it stores potential energy. This potential energy is then converted into kinetic energy when the spring is released, and the energy is conserved throughout the entire process.

Can energy be lost in a spring system?

No, energy cannot be lost in a spring system. As stated by the law of conservation of energy, energy can only be transferred between forms. In a spring system, potential energy may be converted into kinetic energy and vice versa, but the total amount of energy remains constant.

What factors affect the conservation of energy in a spring?

The conservation of energy in a spring is affected by factors such as the spring's stiffness, the distance it is compressed or stretched, and the mass attached to the spring. These factors determine the amount of potential energy stored in the spring and how much kinetic energy is produced when the spring is released.

How is conservation of energy important in the field of sustainability and renewable energy?

Conservation of energy is crucial in sustainability and renewable energy because it emphasizes the importance of using energy efficiently and reducing energy waste. By conserving energy, we can reduce our dependence on non-renewable energy sources and promote the use of renewable energy, which is crucial for the long-term sustainability of our planet.

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