The components that make up the initial energy of the system consisting of a metal ball placed in a device that is one meter above the floor with a spring compressed are the gravitational potential energy and spring potential energy (option C).
When the metal ball is placed in a device with a spring compressed, located at one meter above the floor, the initial energy is given by:
[tex] \Sigma E_{i} = E_{g} + E_{s} [/tex]
[tex] \Sigma E_{i} = mgh + \frac{1}{2}kx^{2} [/tex]
Where:
[tex] E_{g}[/tex]: is the gravitational potential energy
[tex] E_{s}[/tex]: is the spring potential energy
m: is the mass of the metal ball
g: is the acceleration due to gravity
h: is the height above the floor
k: is the spring constant
x: is the distance of spring compression
Initially, there is no kinetic energy because the metal ball is at rest in the spring.
When the spring is released, the ball will be propelled into the air so the energy now is:
[tex] \Sigma E_{f} = E_{g} + E_{k} [/tex]
[tex] \Sigma E_{f} = m(h + H)g + \frac{1}{2}mv^{2} [/tex]
Where:
[tex]E_{k}[/tex]: is the kinetic energy
v: is the velocity of the metal ball
H: is the maximum height reached in the air
Therefore, the components that make up the initial energy of the system are the gravitational potential energy and spring potential energy. The correct option is C.
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