Potential energy and energy conservation question

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SUMMARY

The discussion centers on the conservation of energy equation: K1 + Uel1 + Ugrav1 + Wothers = K2 + Uel2 + Ugrav2, which encompasses kinetic energy, gravitational potential energy, elastic potential energy, and work done by non-conservative forces. Participants emphasize the importance of identifying which terms can be considered zero based on the specific problem context, particularly when analyzing a scenario involving a 2kg block dropped onto a spring with a force constant of 1960 N/m. The conversation highlights the necessity of understanding energy transformations rather than merely 'cancelling' terms in the equation.

PREREQUISITES
  • Understanding of kinetic energy (K = ½MV²)
  • Knowledge of gravitational potential energy (Ugrav = mgy)
  • Familiarity with elastic potential energy (Uel = ½KX²)
  • Concept of work done by non-conservative forces (Wothers)
NEXT STEPS
  • Study the application of the conservation of energy in various physics problems.
  • Learn how to derive and manipulate the conservation of energy equation in different contexts.
  • Explore the concept of reference points in gravitational potential energy calculations.
  • Practice solving problems involving springs and energy transformations, such as maximum compression scenarios.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation principles, as well as educators seeking to clarify these concepts for their students.

Tastosis
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Homework Statement


My teacher told me that this will be the general equation that we will be using. My question is how do I know what to cancel out given a problem? I don't even know what these variables mean.

I was absent during the intro of this lesson and I need a quick answer. Thanks!


Homework Equations


K1 + Uel1 + Ugrav1 + Wothers = K2 + Uel2 + Ugrav2
½MV1^2 + ½KX^2 + mgy1 + Wothers = ½MV2^2 + ½KX2^2 + mgy2
 
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Tastosis said:
K1 + Uel1 + Ugrav1 + Wothers = K2 + Uel2 + Ugrav2
½MV1^2 + ½KX^2 + mgy1 + Wothers = ½MV2^2 + ½KX2^2 + mgy2
This is a general equation that applies when you have kinetic energy, gravitational PE, elastic PE, and external work. Depending on the particular problem, one or more terms may be zero.

If you pose a specific problem perhaps we can be more helpful.
 
This is the general conservation of total energy equation that states that the initial energy of a system plus the work done on it by forces other than gravity and springs is equal to the final energy of the system, where K is kinetic energy, Uel is elastic spring potential energy, Ugrav is gravitational potential energy, Wothers is work done by non conservative forces (forces that are not gravitataional or spring forces), M is mass, V is speed, K is the spring constant, x is the spring displacement, g is the acceleration of gravity, y is the vertical position of the gravity (weight) force with respect to a reference elevation, and the subscripts 1 and 2 refer to initial and final, respectively. It is an extremely important and useful equation, and I suspect you will learn more about each of these terms and the application of such, as your course of study unfolds. Basically it states that energy cannot be created or destroyed ...just transformed into different forms of energy.

Edit: Doc Al is quick!
 
Last edited:
nice. Thanks guys!

Here's a sample problem. A 2kg block is dropped from a height of 0.4m onto a spring whose force constant is 1960N/m. Find the maximum distance the spring will be compressed.

Based on the equation, what should and shouldn't be cancelled? And why??
 
Well, now you are getting specific, and you must show an attempt at a solution, per forum rules.
 
Tastosis said:
Based on the equation, what should and shouldn't be cancelled? And why??
Rather than think in terms of things 'cancelling', compare the initial and final positions and their associated energy terms.
 
Sorry it took me long to get back to you guys...

[PLAIN]http://img407.imageshack.us/img407/6095/73837542.jpg

Do I cancel U2g? =3
 
Last edited by a moderator:
Tastosis said:
Sorry it took me long to get back to you guys...

[PLAIN]http://img407.imageshack.us/img407/6095/73837542.jpg

Do I cancel U2g? =3
When you say 'cancel', what you mean is 'ignore because it equals zero'. (OK.) As far as U2g is concerned, whether it equals zero or not depends on where you measure it from. Hint: If you measure gravitational PE from the lowest point of the block's motion, then you can set U2g = 0. (But then what does U1g equal?)
 
Last edited by a moderator:

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