Question

in a closed system that has 45 j of mechanical energy, the gravitational potential energy of a ball rolling down an inclined plane decreases from 8 j to 5 j. how does the systems kinetic energy change if there is no friction??

a. it increases from 37 j to 40 j.
b. it decreases from 40 j to 37 j.
c. it decreases from 48 j to 43 j.
d. it increases from 45 j to 50 j.

Explanation:

Step1: Recall energy - conservation formula

In a closed - system with no friction, mechanical energy ($E_m$) is conserved, and $E_m=K + U$, where $K$ is kinetic energy and $U$ is potential energy.

Step2: Calculate initial kinetic energy

Given $E_m = 45\ J$ and initial $U_1=8\ J$. Using $E_m=K_1 + U_1$, we can find $K_1$ as $K_1=E_m - U_1$. So, $K_1=45 - 8=37\ J$.

Step3: Calculate final kinetic energy

Given final $U_2 = 5\ J$ and $E_m = 45\ J$. Using $E_m=K_2+U_2$, we can find $K_2$ as $K_2=E_m - U_2$. So, $K_2=45 - 5 = 40\ J$.

Step4: Determine the change in kinetic energy

The kinetic energy changes from $K_1 = 37\ J$ to $K_2 = 40\ J$, which means it increases.

Answer:

A. It increases from 37 J to 40 J.