Block and Spring Problem: Solving for Compression and Height

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To solve the problem of a 2kg block falling onto a spring, the conservation of energy principle is key. The block's gravitational potential energy converts into kinetic energy just before impact and then into elastic potential energy when compressing the spring. For the first part, calculate the compression of the spring using the formula for elastic potential energy. The second part involves determining how high the block will rise after leaving the spring, which requires calculating the energy transfer back into gravitational potential energy. Understanding these energy transformations is crucial for solving both parts of the problem effectively.
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Homework Statement


I. A 2kg block is falling at a speed of 20 m/s and is 18 meters above the spring. The spring constant is 4134 N/m, to the nearest tenth of a cm how far is the spring compressed?

II. In the previous problem to the nearest hundredth of a meter to what height will the block rise after it hits and leaves the spring?

Can I get some direction on this problem? It really stumps me. I know the first one will lead to the second answer.
 
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I have a similar problem that I am working on as well. I have a 2.0kg block dropped 48 cm onto a spring with a k(s) of 1600 J/m^2. I worked the first part of the problem to determine the potential energy(gravity) and kinetic energy before the block hit the spring. Now I am trying to work on the 2nd part to determine compression.

Does this help?
 

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