Question

question 8 of 10 in a closed system that has 85 j of mechanical energy, the gravitational potential energy of a weight being lowered by a pulley decreases from 9 j. how does the systems kinetic energy change if there is no friction? a. it decreases from 76 j to 73 j. b. it decreases from 85 j to 76 j. c. it increases from 73 j to 76 j. d. it increases from 85 j to 94 j.

Explanation:

Step1: Recall energy - conservation principle

In a closed - system with no friction, the total mechanical energy $E = K+U$ is conserved, where $K$ is kinetic energy and $U$ is potential energy.

Step2: Calculate initial total mechanical energy

The initial potential energy $U_1 = 85\ J$ and initial kinetic energy $K_1=9\ J$. So the initial total mechanical energy $E_1=K_1 + U_1=9 + 85=94\ J$.

Step3: Calculate final potential energy

The final potential energy $U_2 = 73\ J$.

Step4: Calculate final kinetic energy

Since $E_1 = E_2$ (energy conservation) and $E_2=K_2 + U_2$, then $K_2=E_1 - U_2$. Substituting $E_1 = 94\ J$ and $U_2 = 73\ J$, we get $K_2=94 - 73 = 21\ J$. The initial kinetic energy $K_1 = 9\ J$ and the final kinetic energy $K_2 = 21\ J$. So the kinetic energy increases from $9\ J$ to $21\ J$. Another way to look at it in terms of the given values of potential - energy change:
The potential energy decreases from $85\ J$ to $73\ J$. The decrease in potential energy $\Delta U=85 - 73 = 12\ J$. This decrease in potential energy is converted into kinetic energy. Since the initial kinetic energy is $9\ J$, the final kinetic energy is $9+12 = 21\ J$. So the kinetic energy increases from $9\ J$ to $21\ J$.

Answer:

The kinetic energy increases from $9\ J$ to $21\ J$. But among the given options, the closest logic - based on the conservation of mechanical energy is that since the potential energy decreases from $85\ J$ to $73\ J$ (a decrease of $12\ J$), the kinetic energy must increase. The initial kinetic energy is $9\ J$. The correct option is that the kinetic energy increases. If we assume the question is asking about the general trend based on the potential - energy change and energy conservation, the answer is C. It increases from $9\ J$ to $21\ J$ (but in terms of the options provided, C. It increases from $85\ J$ to $94\ J$ is the closest in terms of the energy - conservation concept where the decrease in potential energy is converted to an increase in kinetic energy and the total mechanical energy remains the same). So the answer is C. It increases from $85\ J$ to $94\ J$.