Conservation of Energy and Springs

Click For Summary
SUMMARY

The discussion centers on the conservation of energy principles applied to a mass sliding down a frictionless incline and compressing a spring. The key conclusion is that the initial gravitational potential energy of the mass equals the final potential energy stored in the spring when the mass comes to rest. The participant initially struggled with incorporating gravitational potential energy at the end of the incline but ultimately confirmed that the correct approach is to equate the initial gravitational potential energy directly with the spring's potential energy. The mass's position relative to the ground does not affect the energy conservation calculations in this scenario.

PREREQUISITES
  • Understanding of gravitational potential energy
  • Knowledge of spring potential energy and Hooke's Law
  • Familiarity with energy conservation principles
  • Basic trigonometry for incline angles
NEXT STEPS
  • Study the principles of energy conservation in mechanical systems
  • Learn about Hooke's Law and its applications in spring mechanics
  • Explore the effects of friction on energy conservation in inclined planes
  • Investigate the relationship between gravitational potential energy and height in various contexts
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators looking for practical examples of energy principles in action.

Redfire66
Messages
36
Reaction score
0

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
 

Attachments

  • Potential Energy.png
    Potential Energy.png
    4.7 KB · Views: 597
Last edited:
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 20 ·
Replies
20
Views
4K
Replies
29
Views
3K
Replies
7
Views
1K
  • · Replies 12 ·
Replies
12
Views
3K
Replies
17
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
20
Views
3K