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 42 j to 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 65 j to 94 j

Explanation:

Step1: Recall energy - conservation in a closed system

In a closed - system with no friction, the total mechanical energy ($E_{mech}$) is conserved. The total mechanical energy is the sum of kinetic energy ($K$) and gravitational potential energy ($U$), i.e., $E_{mech}=K + U$.

Step2: Calculate initial and final kinetic energies

Given that $E_{mech}=85\ J$, initially $U_1 = 12\ J$, so $K_1=E_{mech}-U_1=85 - 12=73\ J$.
Finally, $U_2 = 9\ J$, so $K_2=E_{mech}-U_2=85 - 9 = 76\ J$.

Step3: Determine the change in kinetic energy

The kinetic energy changes from $K_1 = 73\ J$ to $K_2 = 76\ J$, which means it increases from $73\ J$ to $76\ J$.

Answer:

C. It increases from 73 J to 76 J