Energy and Simple Harmonic Motion of block

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Homework Help Overview

The problem involves a block hanging from a vertical spring, focusing on the elastic potential energy of the system when the mass is changed. The subject area includes concepts of energy in the context of simple harmonic motion and gravitational effects.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the implications of the system being stationary and the meaning of the extension 'x' in relation to the equilibrium position of the spring. Questions arise about the values for gravitational potential energy and spring constant.

Discussion Status

The discussion is ongoing, with participants exploring the relationship between the forces acting on the block and the implications of changing the mass. Some guidance has been provided regarding the interpretation of the stationary condition and its effect on the spring's extension.

Contextual Notes

Participants note that the spring constant 'k' and gravitational acceleration 'g' remain constant, and there is a focus on the ratios involved when changing the mass of the block.

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Homework Statement



A 3.2-kg block is hanging stationary from the end of a vertical spring that is attached to the ceiling. The elastic potential energy of this spring/mass system is 1.8J. What is the elastic potential energy of the system when the 3.2-kg block is replaced by a 5.0-kg block?

Homework Equations



Elastic potential energy=1/2kx^2
Gravitational potential energy=mgh

The Attempt at a Solution


Help me please!
 
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The problem is that you have the extension x of the spring in your formula, which you do not know. However, there is an extra clue in the word "stationary". What does that mean?
 
it is not moving, x=0?
 
What should I put in for h and k? Thank you, CompuChip!
 
Exactly, it is not moving. But that does not mean that x = 0 (then the spring would be in its equilibrium position... but it is stretched by the mass that's hanging on it)... it merely says that x is a constant. But what can you say about the net force acting on the block. Which forces are there?
 
'x' is the extension from the equilibrium point in the spring when the 3.2kg mass is changed to 5kg. Because 'g' and 'k' stay constant it is just simple ratios...
 

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