Question

remember the amount of energy going in to a system must equal the amount of energy going out. 6000 j of electrical energy in, 1000 j of sound energy out, how much thermal energy out? 3300 j of electrical energy in, 900 j of thermal energy out, how much light energy out? 800 j of sound energy out, 1200 j of thermal energy out, how much electrical energy in? 5800 j of mechanical energy out, 1000 j of sound energy out, how much thermal energy out? 934 j of chemical energy (from food) in, 451 j of sound energy out, how much mechanical energy (from dancing) out? 7200 j of sound energy out, 8600 j of mechanical energy out, how much chemical energy (from fuel) in? 800 j of electrical energy (from battery) in, 220 j of sound energy out, 350 j of light energy out, how much thermal energy out? 1200 j of sound energy out, 3300 j of mechanical energy out, how much potential energy was there at the start?

Explanation:

Step1: Recall energy - conservation principle

The total energy input to a system equals the total energy output.

Step2: Solve for microwave

Input electrical energy = 6000 J, sound energy output = 1000 J. Let thermal energy output be $x$. Then $6000=1000 + x$, so $x = 6000 - 1000=5000$ J.

Step3: Solve for lamp

Input electrical energy = 3300 J, thermal energy output = 900 J. Let light energy output be $y$. Then $3300=900 + y$, so $y = 3300 - 900 = 2400$ J.

Step4: Solve for heater

Sound energy output = 800 J, thermal energy output = 1200 J. Let electrical energy input be $z$. Then $z=800 + 1200=2000$ J.

Step5: Solve for bus

Mechanical energy output = 5800 J, sound energy output = 1000 J, chemical energy from gasoline input = 9300 J. Let thermal energy output be $w$. Then $9300=5800 + 1000+w$, so $w = 9300-(5800 + 1000)=2500$ J.

Step6: Solve for singer

Chemical energy input = 934 J, sound energy output = 451 J. Let mechanical energy output be $m$. Then $m = 934 - 451=483$ J.

Step7: Solve for rocket

Sound energy output = 7200 J, mechanical energy output = 8600 J. Let chemical energy input be $n$. Then $n=7200 + 8600 = 15800$ J.

Step8: Solve for laptop

Electrical energy input = 800 J, sound energy output = 220 J, light energy output = 350 J. Let thermal energy output be $p$. Then $p=800-(220 + 350)=230$ J.

Step9: Solve for roller - coaster

Sound energy output = 1200 J, mechanical energy output = 3300 J. Let initial potential energy be $q$. Then $q=1200 + 3300=4500$ J.

Answer:

Microwave: 5000 J thermal energy out; Lamp: 2400 J light energy out; Heater: 2000 J electrical energy in; Bus: 2500 J thermal energy out; Singer: 483 J mechanical energy out; Rocket: 15800 J chemical energy in; Laptop: 230 J thermal energy out; Roller - coaster: 4500 J initial potential energy.