Question

2.1.4 quiz: conservation of energy question 5 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 12 j to 9 j. how does the systems kinetic energy change if there is no friction? a. it decreases from 85 j to 76 j. b. it increases from 73 j to 76 j. c. it decreases from 76 j to 73 j. d. it increases from 85 j to 94 j.

Explanation:

Step1: Recall conservation of mechanical energy

In a closed system with no friction, mechanical energy \( E_{mech} \) is conserved, so \( E_{mech} = E_{k} + E_{p} \), where \( E_{k} \) is kinetic energy and \( E_{p} \) is potential energy.

Step2: Find initial kinetic energy

Initial mechanical energy \( E_{mech, initial} = 85 \, \text{J} \), initial potential energy \( E_{p, initial} = 12 \, \text{J} \).
Using \( E_{k, initial} = E_{mech, initial} - E_{p, initial} \), we get \( E_{k, initial} = 85 - 12 = 73 \, \text{J} \).

Step3: Find final kinetic energy

Final potential energy \( E_{p, final} = 9 \, \text{J} \), mechanical energy is still \( 85 \, \text{J} \) (conserved).
Using \( E_{k, final} = E_{mech, final} - E_{p, final} \), we get \( E_{k, final} = 85 - 9 = 76 \, \text{J} \).

Step4: Determine change in kinetic energy

Kinetic energy increases from \( 73 \, \text{J} \) to \( 76 \, \text{J} \).

Answer:

B. It increases from 73 J to 76 J.