How can the energy stored in a spring be calculated?

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SUMMARY

The energy stored in a spring can be calculated using the formula \( \frac{1}{2} k x^2 \), where \( k \) is the spring constant and \( x \) is the displacement from the equilibrium position. In the discussion, a participant successfully applied the kinetic energy formula \( \frac{1}{2} mv^2 \) to solve part (i) of their problem. However, they struggled with part (ii) until prompted to recall the specific equation for spring energy. This highlights the importance of knowing the correct formulas for different physical scenarios.

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  • Understanding of Hooke's Law and spring constants
  • Familiarity with kinetic and potential energy concepts
  • Basic knowledge of linear motion equations
  • Ability to manipulate algebraic equations
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  • Research the derivation of the spring energy formula \( \frac{1}{2} k x^2 \)
  • Learn about Hooke's Law and its applications in physics
  • Explore the relationship between kinetic and potential energy in mechanical systems
  • Practice solving problems involving energy conservation in springs
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smr101
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Hi, I've attached the question and answer below.

I've got (i) but I'm unsure how to achieve the answer for (ii).

I've tried using the linear motion equations and also a combination of the kinetic/potential energy questions but haven't had any luck as of yet...

Help is much appreciated, thanks!

uTp1B.jpg
 
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smr101 said:
Hi, I've attached the question and answer below.

I've got (i) but I'm unsure how to achieve the answer for (ii).

I've tried using the linear motion equations and also a combination of the kinetic/potential energy questions but haven't had any luck as of yet...

Help is much appreciated, thanks!

uTp1B.jpg

(In the future, please use the Homework Help Template that you are provided, and fill out each section. That makes it easier for us to help.)

What method did you use for (i)? Can you show us your calculations?

For (ii), Hint -- what is the equation for the energy stored in a spring?
 
berkeman said:
(In the future, please use the Homework Help Template that you are provided, and fill out each section. That makes it easier for us to help.)

What method did you use for (i)? Can you show us your calculations?

For (ii), Hint -- what is the equation for the energy stored in a spring?

Hi, thanks, will do.

I used the kinetic energy formula 1/2mv^2 for the first answer.

I've been able to work it out using that formula, thanks, I wasn't aware of it previously.
 

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