Question

rita throws a ball straight up into the air and catches it at the same position from which she threw it. the ball has 18 j of mechanical energy when it leaves her hand. if no energy is lost due to friction, which statements about the energy of the ball are true? check all that apply. the potential energy at the top of the balls motion is 18 j. the kinetic energy is less when the ball is thrown than when it is caught. the kinetic energy increases as the potential energy decreases. the kinetic energy decreases as the potential energy increases. the total mechanical energy of the ball stays constant. the mechanical energy decreases as the ball moves up and increases as the ball comes down.

Explanation:

Step1: Understand energy conservation

In the absence of friction, mechanical - energy (sum of kinetic and potential energy) is conserved. $E = K+U$, where $E$ is mechanical energy, $K$ is kinetic energy and $U$ is potential energy.

Step2: Analyze upward motion

As the ball moves up, its height $h$ increases. Using the formula for gravitational potential energy $U = mgh$ (where $m$ is mass, $g$ is gravitational acceleration and $h$ is height), potential energy increases. Since $E$ is constant, kinetic energy $K=\frac{1}{2}mv^{2}$ (where $v$ is velocity) decreases as the ball slows down.

Step3: Analyze downward motion

As the ball comes down, its height $h$ decreases, so potential energy $U = mgh$ decreases. Kinetic energy $K=\frac{1}{2}mv^{2}$ increases as the ball speeds up. The total mechanical energy $E$ remains $18\ J$ throughout the motion as there is no energy loss due to friction. The potential energy at the top is not necessarily $18\ J$ (it depends on mass and height), and the kinetic energy when thrown and caught is the same because it returns to the same position with the same mechanical - energy and same height.

Answer:

C. The kinetic energy increases as the potential energy decreases, D. The kinetic energy decreases as the potential energy increases, E. The total mechanical energy of the ball stays constant