I solved this Conservation of Energy problem but I don't fully understand how

In summary, the conversation discusses the use of the kinetic and potential energy equations in solving a physics problem involving a compressed spring. The expert explains that in this problem, energy is conserved and the stored elastic potential energy of the spring is converted into kinetic and potential energy for the mass. The solution method involves setting the equations for kinetic and potential energy equal to the equation for elastic potential energy.
  • #1
coldjeanz
22
0

Homework Statement



6maut.png



Homework Equations



K.E = 1/2(m)(v final)^2
P.E = mgh
1/2k(x)^2 <--I don't understand how you would know to use this one


The Attempt at a Solution



Ok so I said that energy would be conserved so E initial would equal E final.

This is what I did to solve the problem but it was more luck than anything:

1/2k(x)^2 = 1/2(m)(v final)^2 + mgh

I solved for (v final) to get an answer of 1.9 m/s which is correct I think. But what I don't understand is why you are adding the potential and kinetic formulas together and then setting them equal to the 1/2k(x)^2 formula (what is this called, is it elastic?). What is the physics behind setting up the problem this way?

Thanks
 
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  • #2
The only way the mass can gain energy in this problem is from the stored elastic potential energy of the compressed spring.
This energy is converted into KE and PE of the mass.
Your answer is good, I got the same by your method
 
  • #3
Alright that makes sense, thanks.
 

What is Conservation of Energy?

Conservation of Energy is a fundamental law of physics that states that energy cannot be created or destroyed, only transformed from one form to another.

How do you solve a Conservation of Energy problem?

To solve a Conservation of Energy problem, you need to identify all the forms of energy involved, such as kinetic, potential, and thermal energy. Then, you can use equations and principles of Conservation of Energy to analyze the system and determine the final energy state.

Why is it important to understand Conservation of Energy?

Understanding Conservation of Energy is crucial because it allows us to predict and explain the behavior of physical systems, from simple objects to complex systems, such as the universe. It also helps us to design and optimize energy-efficient systems.

What are some common mistakes when solving Conservation of Energy problems?

Some common mistakes when solving Conservation of Energy problems include neglecting certain forms of energy, such as thermal energy, or not considering all the forces acting on the system. It is also essential to pay attention to the direction and sign of the energy changes.

How can I improve my understanding of Conservation of Energy?

To improve your understanding of Conservation of Energy, you can practice solving different types of problems, read and research about the topic, and seek help from a teacher or tutor if needed. It is also useful to connect the concept to real-life examples to better visualize and comprehend it.

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