To determine the correct equation that represents how the gravitational potential energy (GPE) of a system relates to its kinetic energy (KE) and total mechanical energy (ME), we need to understand the basic concepts of energy in a mechanical system.
In physics, the total mechanical energy (ME) of a system is the sum of its gravitational potential energy (GPE) and kinetic energy (KE). This can be represented by the following equation:
[tex]\[ ME = GPE + KE \][/tex]
Given this relationship, we can rearrange the equation to solve for gravitational potential energy (GPE):
[tex]\[ GPE = ME - KE \][/tex]
This rearranged equation shows that the gravitational potential energy of a system is equal to the total mechanical energy minus the kinetic energy.
Now, let's review the provided options to see which one matches our derived equation:
A. [tex]\( GPE = ME + KE \)[/tex]
B. [tex]\( GPE = KE - ME \)[/tex]
C. [tex]\( GPE = ME - KE \)[/tex]
D. [tex]\( GPE = ME \times KE \)[/tex]
Out of these options, the correct equation is:
[tex]\[ C: \; GPE = ME - KE \][/tex]
Therefore, the correct relation representing how the gravitational potential energy (GPE) of a system relates to its kinetic energy (KE) and total mechanical energy (ME) is:
[tex]\[ C: \; GPE = ME - KE \][/tex]
