Two springs one trolley, find velocity

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SUMMARY

The discussion focuses on solving a physics problem involving two springs and a trolley, emphasizing the importance of energy conservation over kinematic formulas. Participants clarify that Hooke's law and the concept of elastic potential energy, specifically the equation 0.5 kx^2, are crucial for determining the system's behavior. The incorrect assumption made was applying a kinematic formula for uniformly accelerated motion, which is not suitable due to the variable acceleration based on displacement. The correct approach involves calculating the total spring potential energy at both equilibrium and when the trolley is displaced.

PREREQUISITES
  • Understanding of Hooke's Law
  • Familiarity with Newton's Second Law
  • Knowledge of elastic potential energy calculations
  • Basic principles of energy conservation in physics
NEXT STEPS
  • Study the application of Hooke's Law in dynamic systems
  • Learn about energy conservation principles in mechanical systems
  • Explore the relationship between displacement and potential energy in springs
  • Investigate kinematic equations and their limitations in variable acceleration scenarios
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Students studying physics, particularly those tackling mechanics and energy conservation, as well as educators seeking to clarify common misconceptions in spring dynamics.

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Homework Statement



Please refer to the image.

My workings= pencil
Answer= pen

Why is my working wrong? What wrong assumptions did I make?

Homework Equations



Hooke's law/Newton's second law/ Elastic potential energy =0.5 kx^2

The Attempt at a Solution


As shown in the image.
 

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You used a kinematic formula for uniformly accelerated motion. That won't apply here, since the acceleration varies with displacement.

Stick to energy conservation.

What is the total spring PE at equilibrium?

What is the total spring PE when the trolley is displaced?
 
Got it, thank you.
 

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