Acceleration When Pulled By Elastic Cord

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SUMMARY

The discussion centers on the acceleration of a cart being pulled by an elastic cord, specifically exploring the relationship between elastic potential energy and acceleration. The equation for elastic potential energy, PEelastic = 1/2 kx2, is identified as relevant, but participants express uncertainty about how to connect potential energy to acceleration. The suggestion to utilize work done and conservation of energy principles is introduced as a method to analyze the motion of the cart.

PREREQUISITES
  • Understanding of elastic potential energy and its formula PEelastic = 1/2 kx2
  • Basic principles of Newtonian mechanics, particularly acceleration
  • Familiarity with the concepts of work and energy conservation
  • Knowledge of motion equations in physics
NEXT STEPS
  • Research the application of Hooke's Law in dynamic systems
  • Study the relationship between work done by forces and kinetic energy
  • Explore the derivation of motion equations for systems involving elastic forces
  • Investigate examples of oscillatory motion and its relation to elastic potential energy
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the dynamics of systems involving elastic forces will benefit from this discussion.

mill4864
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1. How does a cart being pulled by an elastic cord effect the acceleration of that cart?



2. That's the problem. I can't find any equations that deal with motion of an object pulled by an elastic cord. I was thinking there may be something to do with elastic potential energy [tex]\mbox{PE_e_l_a_s_t_i_c}[/tex] = [tex]\frac{1}{2} kx^2[/tex] but I don't know of any equations that relate potential energy to acceleration.




3. This is more of a conceptual question, so I'm not sure how I'd write my attempt at a solution, other than saying I think there may be some relation between elastic potential energy and the motion of an object being pulled by an elastic cord.
 
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Hi mill4864! Welcome to PF! :wink:

Let the cart be at position x, and the other end of the cord be at position y …

then use work done and conservation of energy :smile:
 

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