Calculating Energy Conservation in a Spring-Mass System

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Discussion Overview

The discussion revolves around the conservation of energy in a spring-mass system, specifically examining the energy transformations as a spring is compressed and then released. Participants explore the relationships between elastic potential energy, kinetic energy, and gravitational potential energy in this context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant proposes that the total energy in the system when the spring is compressed is the sum of the elastic potential energy (1/2 kx^2) and gravitational potential energy (mgh).
  • Another participant agrees with this assessment, stating that it represents the total mechanical energy of the system.
  • A later reply suggests that when the spring is released and the ball moves horizontally, the total energy should also account for gravitational potential energy, not just kinetic energy.
  • One participant asserts that the gravitational potential energy would cancel out in the energy equation, leading to the relationship 1/2 mv^2 = 1/2 kx^2.
  • Another participant confirms that the spring potential energy is converted into kinetic energy, noting that gravitational potential energy remains constant if the height does not change.
  • A final question is raised regarding the expression for kinetic energy in the context of projectile motion, specifically whether it is half the mass times the square of the constant horizontal velocity.

Areas of Agreement / Disagreement

Participants generally agree on the transformation of energy from potential to kinetic in the spring-mass system, but there are differing views on the role of gravitational potential energy in the equations presented.

Contextual Notes

There are assumptions regarding the constancy of height and the conditions under which energy conservation applies. The discussion does not resolve how gravitational potential energy interacts with the kinetic energy in the context of the spring's release.

Pseudo Statistic
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In the attached picture below I am compressing a spring...
In picture 2, I've compressed the spring a distance x and thus the elastic potential is 1/2 kx^2 and the total energy in the system AT THAT POINT is 1/2 kx^2 + mgh, isn't it? (m is the mass of the ball and h the height from my reference level, the floor) Or am I wrong in thinking this?
Assuming energy conservation, let's say I let go of the spring and it's at that point where it has JUST gone over the edge of the table with its constant horizontal velocity Vx; would the total energy at that point be equal to 1/2 mVx^2 (where m is the mass of the ball) or would I be wrong in assuming this?
Thanks for any help.
 

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Pseudo Statistic said:
In the attached picture below I am compressing a spring...
In picture 2, I've compressed the spring a distance x and thus the elastic potential is 1/2 kx^2 and the total energy in the system AT THAT POINT is 1/2 kx^2 + mgh, isn't it? (m is the mass of the ball and h the height from my reference level, the floor) Or am I wrong in thinking this?
Your thinking seems correct. That would be the total mechanical energy of the ball/spring/earth system.

Assuming energy conservation, let's say I let go of the spring and it's at that point where it has JUST gone over the edge of the table with its constant horizontal velocity Vx; would the total energy at that point be equal to 1/2 mVx^2 (where m is the mass of the ball) or would I be wrong in assuming this?
You forgot the gravitational PE (mgh). The total mechanical energy at that point would be its KE + mgh.
 
Alright so, the mghs in the equality would cancel out leaving us with 1/2mv^2 = 1/2 kx^2, wouldn't it?
Thanks for the reply.
 
That's right. The spring PE is transformed into KE. (Since the height never changes, the gravitational PE remains constant.)
 
Alright, thanks, but one more thing...
The kinetic energy would be equal to half of the mass times by the constant horizontal velocity the ball would experience when under projectile motion squared, correct?
 

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