Question

question 7 of 20
a crate falling from a plane is part of a closed system that has 24,450 j of mechanical energy. if the kinetic energy of the crate increases from 10,000 j to 15,000 j, what happens to the gravitational potential energy of the system?
a. it decreases from 14,450 j to 9,450 j.
b. it increases from 9,450 j to 14,450 j.
c. it increases from 10,000 j to 15,000 j.
d. it decreases from 15,000 j to 10,000 j.

Explanation:

Step1: Recall mechanical - energy formula

In a closed system, mechanical energy $E = K+U$, where $E$ is mechanical energy, $K$ is kinetic energy, and $U$ is potential energy.

Step2: Calculate initial potential energy

Given $E = 24450\ J$ and initial $K_1=10000\ J$. Using $E = K_1 + U_1$, we get $U_1=E - K_1=24450 - 10000=14450\ J$.

Step3: Calculate final potential energy

Given final $K_2 = 15000\ J$ and $E = 24450\ J$. Using $E = K_2+U_2$, we get $U_2=E - K_2=24450 - 15000 = 9450\ J$.

Step4: Analyze change in potential energy

The initial potential energy $U_1 = 14450\ J$ and the final potential energy $U_2=9450\ J$, so the potential energy decreases from $14450\ J$ to $9450\ J$.

Answer:

A. It decreases from 14,450 J to 9,450 J.