How to Calculate the Increase in KE in a Two-Cart System with Spring Release

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SUMMARY

The discussion centers on calculating the increase in kinetic energy (KE) in a two-cart system consisting of a blue cart with a mass of 350g and a silver cart with a mass of 500g. Initially, both carts move together at a velocity of 0.20 m/s. After the spring on the silver cart is released, it moves at a final velocity of 0.40 m/s. The increase in the total kinetic energy of the system can be determined by calculating the initial and final kinetic energies and finding the difference.

PREREQUISITES
  • Understanding of kinetic energy formula: KE = 0.5 * m * v^2
  • Basic knowledge of momentum conservation principles
  • Familiarity with mass and velocity units (grams and meters per second)
  • Ability to perform algebraic calculations
NEXT STEPS
  • Calculate initial kinetic energy for both carts using KE = 0.5 * m * v^2
  • Calculate final kinetic energy for the silver cart after the spring release
  • Determine the increase in kinetic energy by subtracting initial KE from final KE
  • Explore the implications of energy conservation in spring systems
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in understanding energy transformations in dynamic systems.

misyg
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Two carts, a blue one with a mass of 350g and a silver one with a mass of 500g, move down a frictionless, level track together at .20 m/s to the right. When the two carts reach the center of the track, the spring on the silver cart is released, and the two carts move apart. The final velocity of the silver cart is .40 m/s to the right. How much does the final KE of the two cart system increase by when the spring is released?

I tried combining the masses and velocity but it just ended badly...please help.
 
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hi misyg! :wink:

show us your full calculations, and then we'll see what went wrong, and we'll know how to help! :smile:
 

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