How Far Does a Block Fall When Released from an Unstretched Spring?

[mathewings]

A block is susoended from the end of a spring. The spring is hanging off the ceiling. An external force holds the block so that, initially, the spring is not stretched or compressed. When the block is released, it oscillates up and down between positions A and B. If the mass of the block is 0.5kg and the spring constant is 10N/m, how far will the block fall when it is released?

I've tried equating gravitational potential and spring potential energy, but the height of the block can't be determined. I don't believe there's enough information to isolate a velocity to find kinetic energy. I'm fairly certain I'm on the right track in that I need to use conservation of energy. Any suggestions would be appreciated.

 

[OlderDan]

A block is susoended from the end of a spring. The spring is hanging off the ceiling. An external force holds the block so that, initially, the spring is not stretched or compressed. When the block is released, it oscillates up and down between positions A and B. If the mass of the block is 0.5kg and the spring constant is 10N/m, how far will the block fall when it is released?

I've tried equating gravitational potential and spring potential energy, but the height of the block can't be determined. I don't believe there's enough information to isolate a velocity to find kinetic energy. I'm fairly certain I'm on the right track in that I need to use conservation of energy. Any suggestions would be appreciated.

You are on the right track. The spring has no PE in the initial configuration. You are free to pick the zero of gravitational potential energy anywhere you like. If you say it is zero initially, then it becomes negative as the mass falls. If you prefer, you can call it zero at the bottom and use the unknown distance it falls as the initial height. Either way, the change in potential energy is proportional to the falling distance, and the falling distance is the extension of the spring.