Question

conservation of mechanical energy quick check
a swimmer jumps from a diving board into a pool. what would a graph of the swimmers potential energy and total mechanical energy look like? (1 point)
potential energy would remain constant, while total mechanical energy would increase.
potential energy would remain constant, while total mechanical energy would decrease.
potential energy would increase, while total mechanical energy would remain constant.
potential energy would decrease, while total mechanical energy would remain constant.

Explanation:

• Potential energy: The formula for gravitational potential energy is \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, and \(h\) is height). As the swimmer jumps from the diving board into the pool, the height \(h\) decreases. Since \(m\) and \(g\) are constant (assuming no air - resistance effects on mass and \(g\approx9.8\ m/s^{2}\) near the Earth's surface), the potential energy \(U\) decreases.
• Total mechanical energy: In the absence of non - conservative forces (such as air resistance, which is often neglected in basic mechanical energy conservation problems for simplicity), the total mechanical energy \(E = K+U\) (where \(K\) is kinetic energy and \(U\) is potential energy) is conserved. As the swimmer falls, potential energy is converted into kinetic energy (\(U\) decreases and \(K=\frac{1}{2}mv^{2}\) increases), but the sum \(E = K + U\) remains constant.

Answer:

Potential energy would decrease, while total mechanical energy would remain constant.