Question

if the kinetic and potential energy in a system are equal, then the potential energy increases. what happens as a result?
total energy increases.
stored energy decreases.
energy of motion decreases.
total energy decreases.

Explanation:

Step1: Recall the law of conservation of energy

The total mechanical energy \(E\) of a system is the sum of kinetic energy \(K\) and potential energy \(U\), i.e., \(E = K+U\). In a conservative system (assuming no non - conservative forces like friction do work), the total mechanical energy is conserved.

Step2: Analyze the change in kinetic energy when potential energy increases

Since \(E=K + U\) and \(E\) is constant (conservation of mechanical energy), if \(U\) increases (\(\Delta U>0\)), then \(K\) must change such that \(\Delta K=-\Delta U\). Kinetic energy \(K=\frac{1}{2}mv^{2}\) is the energy of motion. A decrease in \(K\) means a decrease in the energy of motion.

Stored energy is another term for potential energy. If \(U\) increases, stored energy increases. Total energy \(E\) remains constant because of the law of conservation of mechanical energy.

Answer:

Energy of motion decreases.