Question

question 4 of 20
a ball was positioned in the middle of a smooth ramp and allowed to roll downward. how does the total mechanical energy of the ball at the bottom of the ramp compare to its total mechanical energy before it is released? assume there is no friction.

Explanation:

Step1: Recall energy - conservation principle

In the absence of non - conservative forces (no friction here), mechanical energy is conserved.
Mechanical energy $E = K+U$, where $K$ is kinetic energy and $U$ is potential energy.

Step2: Analyze initial and final states

Initially, the ball has only potential energy $U_{i}$ (since it is at rest, $K_{i}=0$). At the bottom of the ramp, it has only kinetic energy $K_{f}$ (assuming the bottom as the zero - potential level, $U_{f} = 0$).
According to the law of conservation of mechanical energy $E_{i}=E_{f}$, which means $K_{i}+U_{i}=K_{f}+U_{f}$. Since $K_{i} = 0$ and $U_{f}=0$, we have $U_{i}=K_{f}$.

Answer:

The total mechanical energy of the ball at the bottom of the ramp is equal to its total mechanical energy before it is released.