Conservation of mechanical energy (help)

AI Thread Summary
To solve the problem of a 0.50 kg object released from a compressed spring on a frictionless incline, the conservation of mechanical energy principle is applied. The potential energy stored in the spring (0.5 * k * x^2) converts into gravitational potential energy (m * g * h) as the object moves up the incline. The height (h) can be related to the distance traveled (d) up the incline using the sine of the incline angle. The correct calculation shows that the distance traveled up the incline is approximately 0.57 meters, indicating that the initial calculation of 0.43 meters was incorrect. Understanding the energy transformation is crucial for accurately solving this type of physics problem.
shorti2406
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I just can't seem to derive the correct formula for this one.

A spring with k=40.0 N/m is at the base of a frictionless 30 degree inclined plane. A 0.50 kg object is pressed against the spring, compressing in 0.3m from its equilibrium position. The object is then released. If the object is not attached to the spring, how far up the incline does it travel before coming to res and then sliding back down?
 
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I keep getting d=.43, and I am almost positive that is not correct!
 
How are you solving this problem?
 

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