Question

2.1.4 quiz: conservation of energy
question 2 of 10
two people playing a game of table tennis make up a closed system with 12,175 j of energy. at the beginning of the game the system has 9,875 j of me, and at the end it has 8,430 j of me. how much of the total energy was transformed into thermal energy during the game?

a. 2,300 j
b. 1,445 j
c. 3,745 j
d. 10,730 j

Explanation:

Step1: Recall conservation of energy

In a closed system, total energy is conserved. The initial total energy is the sum of initial mechanical energy (ME) and initial thermal energy. The final total energy is the sum of final ME and final thermal energy. The change in ME is transformed into thermal energy. First, find the change in ME.
Initial ME: \( 9875 \, \text{J} \), Final ME: \( 8430 \, \text{J} \)
Change in ME: \( \Delta \text{ME} = 9875 - 8430 = 1445 \, \text{J} \)

Step2: Relate to thermal energy

The total energy of the closed system is constant (\( 12175 \, \text{J} \)), but the mechanical energy decreases. The energy lost from ME is transformed into thermal energy. Wait, actually, the total energy is conserved, so the initial total energy (ME + thermal) equals final total energy (ME + thermal). So the change in thermal energy is equal to the negative change in ME (since ME decreases, thermal increases). But also, we can think that the initial ME plus initial thermal equals final ME plus final thermal. Since total energy is constant, initial total (12175) = initial ME + initial thermal, and final total (12175) = final ME + final thermal. So final thermal - initial thermal = initial ME - final ME. Which is the change in ME. Wait, maybe simpler: The energy transformed into thermal is the initial ME minus final ME? Wait no, wait the total energy is 12175 J. Wait, maybe I misread. Wait the problem says "two people playing a game of table tennis make up a closed system with 12,175 J of energy". So total energy \( E_{total} = 12175 \, \text{J} \). At beginning, ME is \( 9875 \, \text{J} \), so initial thermal energy \( E_{th, initial} = E_{total} - E_{ME, initial} = 12175 - 9875 = 2300 \, \text{J} \). At end, ME is \( 8430 \, \text{J} \), so final thermal energy \( E_{th, final} = E_{total} - E_{ME, final} = 12175 - 8430 = 3745 \, \text{J} \). Then the energy transformed into thermal is \( E_{th, final} - E_{th, initial} = 3745 - 2300 = 1445 \, \text{J} \). Wait, that's the change. Alternatively, the decrease in ME is \( 9875 - 8430 = 1445 \, \text{J} \), which is transformed into thermal energy (since total energy is conserved, so the lost ME becomes thermal). So that's 1445 J.

Answer:

B. 1,445 J