A pogo stick has a spring with a force constant of , which can be compressed . To what maximum height can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of ? Explicitly show how you follow the steps in the Problem-Solving Strategies for Energy.
The child can jump up to the maximum height of .
Spring potential energy: When a spring is stretched or compressed by the application of force, the potential energy stored in the spring is,
Here, k is the force constant of the spring and x is the compression in the spring 12.0 cm.
When a child jumps on the spring, the spring potential energy in the spring gets converted into gravitational potential energy and the child attains some height. Mathematically,
Here, m is the mass of the child , g is the acceleration due to gravity , and h is the maximum height attained by the child.
The expression for the maximum height attained by the child is,
Putting all known values,
Therefore, the child can jump up to the maximum height of .
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