What's the equation to find the maximum height after a spring decompresses?
To find the maximum height after a spring decompresses, you need to consider the principles of conservation of energy. The total mechanical energy of the system is conserved, which includes the potential energy of the spring and the kinetic energy of the object attached to the spring.
The equation to find the maximum height can be derived by equating the initial potential energy of the compressed spring to the potential energy at maximum height:
(1/2)kx² = mgh
In this equation:
- k represents the spring constant (a measure of the stiffness of the spring)
- x represents the displacement of the spring from its equilibrium position (the amount it has stretched or compressed)
- m represents the mass of the object attached to the spring
- g represents the acceleration due to gravity
- h represents the maximum height reached by the object after the spring decompresses
By rearranging the equation, we can solve for h:
h = (kx²) / (2mg)
Therefore, the equation to find the maximum height after a spring decompresses is given by h = (kx²) / (2mg).