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

AI Thread Summary
To calculate the increase in kinetic energy (KE) in the two-cart system after the spring is released, first determine the initial KE of both carts moving together at 0.20 m/s. The initial KE is calculated using the formula KE = 0.5 * m * v^2 for both carts combined. After the spring releases, the final velocity of the silver cart is 0.40 m/s, which requires recalculating the KE for both carts separately. The increase in KE is found by subtracting the initial KE from the final KE of the system. Providing full calculations will clarify the process and identify any errors made in the initial attempt.
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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