In a closed system where kinetic, potential, and thermal energy are changing, the kinetic
energy decreases by 54 J, and the thermal energy increases by 13 J. What is the
change in the potential energy?
system is closed
so if
Ke = kinetic
U = potential
T = thermal
then
Ke + U + T = constant
Ke1 + U1 + T1 = Ke2 + U2 + T2
Ke2 = Ke1 - 54
T2 = T1 + 13
Ke1 + U1 + T1 = Ke1-54 + U2 + T1+13
so
41 = U2-U1
To determine the change in potential energy, we need to apply the principle of conservation of energy. In a closed system, the total energy remains constant, meaning the sum of kinetic energy, potential energy, and thermal energy stays the same.
Given that the kinetic energy decreases by 54 J and the thermal energy increases by 13 J, we can write the equation as follows:
Change in Kinetic Energy + Change in Potential Energy + Change in Thermal Energy = 0
Substituting the given values, we have:
-54 J + Change in Potential Energy + 13 J = 0
Now, isolate the change in potential energy by rearranging the equation:
Change in Potential Energy = 54 J - 13 J
Simplifying this expression, we find:
Change in Potential Energy = 41 J
Therefore, the change in potential energy is 41 J.