HS-PS3-1: Computational Models of Energy Change in a System
In plain English: HS-PS3-1 is the NGSS high school performance expectation that asks students to create a computational model that finds the energy change of one part of a system from the energy changes of the other parts and the energy flowing in or out. The key idea is that the total change equals energy in minus energy out. It is usually taught in Physics or Physical Science.
Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.
Clarification Statement: Emphasis is on explaining the meaning of mathematical expressions used in the model.
Assessment Boundary: Assessment is limited to basic algebraic expressions or computations; to systems of two or three components; and to thermal energy, kinetic energy, and/or the energies in gravitational, magnetic, or electric fields.
Next Generation Science Standards · Disciplinary Core Idea: Energy · Official standard
Students build computational models that track energy through a system of two or three components. The core model is one line of algebra: the sum of the energy changes of the components equals the energy that flows in minus the energy that flows out. When every term but one is known, the model gives the missing one. Students write the model for a cart on a track, a kettle of water, a supercapacitor running a motor and a falling skydiver, and then turn it into a spreadsheet that runs on many trials at once.
The NGSS Clarification Statement says: "Emphasis is on explaining the meaning of mathematical expressions used in the model." The Assessment Boundary says: "Assessment is limited to basic algebraic expressions or computations; to systems of two or three components; and to thermal energy, kinetic energy, and/or the energies in gravitational, magnetic, or electric fields." So every model on this page uses only kinetic energy, thermal energy, and energy in gravitational, electric or magnetic fields, and every term is explained in words. All data sets are invented for teaching. Constants used: g = 9.8 m/s², specific heat of water 4180 J/(kg·°C), of steel 450 J/(kg·°C).
Learning Objectives
By the end of this lesson, students will be able to:
Define a system of two or three components and identify the energy that flows across its boundary
Write the model ΔE1 + ΔE2 + ΔE3 = Ein - Eout for a situation and explain what each term means physically
Use the expressions mgh, ½mv², mcΔT, ½CV² and P × t to compute the known terms, with units
Solve the model for the energy change of the one unknown component and judge whether the result is physically possible
Turn the model into a spreadsheet that computes the unknown energy change for many trials
Prior Knowledge Required
Students should already be comfortable with:
Kinetic energy depends on mass and speed MS-PS3-1
Energy is transferred when the kinetic energy of an object changes MS-PS3-5
Rearranging formulas to solve for a quantity of interest HSA.CED.A.4
Units of energy (joule) and power (watt), and converting minutes or hours to seconds
Drop a rubber ball from shoulder height and let it bounce several times without catching it.
Warm-Up Prompt
"Each bounce is lower than the one before. Draw a box around what you would call the system. Where did the missing energy go, and what would you need to measure to find out how much went there?"
Collect answers on the board. Students usually name the ball, the floor and the air, and some say the energy "disappeared". Keep the list: it becomes the component list for the first model.
Direct Instruction15-20 minutes
The model. Choose a system and list its components. Energy that crosses the boundary is a flow (electrical work in, heat to the room out). Energy is conserved, so ΔE1 + ΔE2 + ΔE3 = Ein - Eout. Each term has a meaning: a positive ΔE means that component gained energy, Ein is energy that entered from outside, and Eout is energy that left. The expressions for the terms are: gravitational field energy change mgΔh, kinetic energy change ½m(vf² - vi²), thermal energy change mcΔT, electric field energy in a capacitor ½CV², and electrical energy delivered P × t. Use Diagram 1 with the first example and Diagram 2 with the second.
Two components, no flows: cart on a track
A 2.0 kg cart is released from rest 1.5 m above the bottom of a curved track and reaches 5.0 m/s at the bottom. System: cart, track and Earth, with nothing crossing the boundary.
Result: ΔEgrav = -(2.0)(9.8)(1.5) = -29.4 J and ΔKE = ½(2.0)(5.0)² = +25.0 J. Model: ΔEthermal = 0 - (-29.4 + 25.0) = +4.4 J, the energy that warmed the wheels and track.
Energy in and out: electric kettle
A 1400 W kettle runs for 100 s. It holds 0.60 kg of water, and its 0.40 kg steel body warms from 20 °C to 70 °C with the water. About 5,600 J leaves as heat to the room.
Result: Ein = 1400 W × 100 s = 140,000 J. ΔEbody = (0.40)(450)(50) = 9,000 J. ΔEwater = 140,000 - 5,600 - 9,000 = 125,400 J, so ΔT = 125,400 ÷ (0.60 × 4180) = 50 °C: the water also ends at 70 °C.
Three components: electric field energy runs a motor
A 1.0 F supercapacitor charged to 5.0 V runs a small motor that lifts a 0.50 kg mass by 1.0 m. The capacitor ends at 3.0 V. System: capacitor, motor and wires, mass and Earth.
Result: ΔEfield = ½(1.0)(3.0)² - ½(1.0)(5.0)² = 4.5 - 12.5 = -8.0 J. ΔEgrav = (0.50)(9.8)(1.0) = +4.9 J. ΔEthermal = 0 - (-8.0 + 4.9) = +3.1 J in the motor and wires.
Constant speed: skydiver at terminal speed
A 75 kg skydiver falls at a steady 55 m/s for 10 s, so she drops 550 m. System: skydiver, Earth and the surrounding air.
Result: ΔKE = 0 because the speed does not change. ΔEgrav = -(75)(9.8)(550) = -404,250 J. Model: ΔEthermal = 0 - (-404,250 + 0) = +404,250 J, the energy that warms and stirs the air.
After each example, ask students to read one term aloud in words, for example: "-29.4 J means the gravitational field between the cart and Earth stores 29.4 J less at the bottom." Then ask the plausibility question: could the answer have come out negative? In the first example a negative thermal change would mean the cart went faster than a frictionless cart could, which is impossible.
Guided Practice15 minutes
Pairs turn the track model into a spreadsheet. The invented data below come from one 0.50 kg cart released from rest at four heights on the same ramp. Column formulas: ΔEgrav = -m × 9.8 × h, ΔKE = 0.5 × m × v², and ΔEthermal = -(ΔEgrav + ΔKE).
Guided practice data (invented): 0.50 kg cart released from rest. Students fill in the three energy columns.
Trial
Height h (m)
Speed at bottom v (m/s)
ΔE grav (J)
ΔKE (J)
ΔE thermal (J)
1
0.20
1.80
2
0.40
2.60
3
0.60
3.20
4
0.80
3.70
Fill in the first row by hand and check that the three energy changes add to zero, because no energy crosses the boundary.
Write the spreadsheet formulas and let them fill the other rows. Explain in words what the minus sign in the gravitational column means.
Check plausibility: for each trial, is the measured speed below √(2gh), the frictionless speed? What would a negative thermal value tell you about the data?
Describe the pattern in the thermal column and give a physical reason for it.
Independent Practice10-15 minutes
Each student models a paddle-wheel apparatus like the one James Joule used. A 6.0 kg mass is lowered 2.0 m at a slow, steady speed, turning a paddle that stirs 0.25 kg of water in an insulated can. The mass is wound back up and lowered 20 times. An invented measurement says 262 J escapes as heat through the can.
Students list the components (mass and Earth, water), explain why the kinetic energy term is close to zero, compute ΔEgrav = -20 × (6.0)(9.8)(2.0) = -2352 J, solve the model for the water's energy change (2352 - 262 = 2090 J) and find the temperature rise (2.0 °C). They finish with two sentences explaining what the 262 J term means and why the temperature rise is so small.
Closure5 minutes
Exit ticket: "A 0.30 kg ball is dropped from 2.0 m and hits the floor at 6.0 m/s. Write the model, name each term in words, and find the thermal energy produced by air resistance." (ΔEgrav = -5.88 J, ΔKE = +5.4 J, thermal +0.48 J.) Return to the warm-up list and ask which components the bouncing ball model would need.
Differentiation Strategies
For Struggling Students
Give an energy accounting table with one row per component and one row per flow, with the sign of each entry already marked
Start with two-component systems and no flows before adding Ein and Eout
Provide a sentence frame for each term: "ΔE of ___ is ___ J, which means ___ gained or lost energy because ___."
For Advanced Students
Ask students to redraw the boundary for the kettle so the room air is inside the system, and show that the flow term becomes a component term
Have students add an uncertainty column to the spreadsheet (height ± 0.005 m, speed ± 0.05 m/s) and decide which thermal values are distinguishable from zero
Ask students to design a spreadsheet model for a magnet pulling a steel ball, and explain which quantity they would need to measure to find the change in magnetic field energy
Assessment Guidance
What to Look For
Check that every model states the system and lists the flows before any number appears. Look for correct signs: a component that loses energy has a negative ΔE, and energy leaving the system is subtracted. Listen for students who can say what each term means in words, not only compute it, as the Clarification Statement asks. Watch for students who add a flow to the wrong side, mix km/h with m/s, or accept a negative thermal energy without questioning the data.
02
Classroom Activities
3 Activities
1
Ramp Lab: A Spreadsheet Energy Model
25 minGroups of 3-4
Groups release a cart from rest at three heights on a ramp, measure its speed at the bottom, and build a spreadsheet model that computes the thermal energy produced in each trial. The model is the same one-line equation from the lesson, applied row by row.
Procedure
Measure the cart's mass on a balance. Mark release points at vertical heights of 0.25, 0.50 and 0.75 m above the bottom of the ramp (measure vertically, not along the ramp).
Find the speed at the bottom with a photogate, or with slow-motion phone video (240 frames per second): count the frames the cart takes to cross a 0.10 m strip of tape at the bottom and divide by 240 to get the time.
Run three trials per height and average. Enter mass, height and speed in the spreadsheet, and write formulas for ΔEgrav, ΔKE and ΔEthermal.
Safety: put a stop block at the end of the ramp and keep hands clear of the moving cart.
Sample Data (invented)
Cart mass 0.60 kg. Height 0.25 m: 2.10 m/s. Height 0.50 m: 2.90 m/s. Height 0.75 m: 3.50 m/s. The model gives thermal energy of 0.147 J, 0.417 J and 0.735 J.
Discussion Questions
The fraction of the gravitational energy that became thermal is 10% for the lowest release and about 17% for the highest. Propose a reason the fraction grows with height.
What does each spreadsheet column mean physically? Which column would change if the ramp were waxed?
A group's model gives a negative thermal energy for one trial. List two measurement errors that could cause this.
Modification for Distance Learning
Students use a free ramp or skate-park energy simulation, record height and speed for three runs with friction turned on, and build the same spreadsheet from their simulation data.
2
Kettle Energy Audit
20 minGroups of 3-4
Groups measure the electrical energy that enters an electric kettle with a plug-in energy meter, measure the temperature rise of the water, and use the model to find how much energy went into the kettle body and the room. They then explain each term of the model in words.
Procedure
Measure 0.80 kg of room-temperature water on a balance and pour it into the kettle. Record the starting temperature.
Plug the kettle into the energy meter, reset it, and switch the kettle on. Switch it off when the water reaches about 60 °C, stir, and record the final temperature and the meter reading in kWh.
Convert kWh to joules (1 kWh = 3,600,000 J) and solve the model for the energy that did not go into the water.
Safety: wear goggles, keep the kettle on a stable bench away from the edge, let only the teacher pour hot water, and use heat-resistant gloves when handling the kettle. Stop well below boiling.
Sample Data (invented)
Water 0.80 kg, from 20 °C to 60 °C. Energy meter: 0.042 kWh. Students compute Ein = 151,200 J and ΔEwater = 0.80 × 4180 × 40 = 133,760 J, so 17,440 J went to the kettle body and the room.
Discussion Questions
About 88% of the electrical energy ended up in the water. What happened to the rest, and how could you measure each part separately?
If you used 0.40 kg of water and the same final temperature, would the energy lost to the room be larger or smaller? Explain using the terms of the model.
The kettle is rated at 1500 W. Use the model to estimate how long it ran, and compare with your stopwatch.
Modification for Distance Learning
Students run the audit at home with an adult present, using a kitchen scale, a cooking thermometer and the kettle's rated power with a timer instead of an energy meter, and post their model and results.
3
Model Critique Cards
20 minPairs
Pairs receive six cards. Each card describes a system and shows a student's computational model and answer. Pairs decide whether the model is correct, find the error if there is one, write a corrected model, and explain the meaning of the term that was wrong.
The Six Cards
Card A, skier: a 60 kg skier starts from rest and descends 12 m vertically, reaching 14 m/s. Student: "ΔEthermal = mgh - ½mv² = 7056 - 5880 = 1176 J."
Card B, ball thrown up: a 0.50 kg ball rises 3.0 m, air resistance negligible. Student: "ΔEgrav = +14.7 J, so ΔKE = +14.7 J because energy is conserved."
Card C, microwave: 0.30 kg of water warms by 25 °C in a microwave oven. Student: "Energy is conserved, so the water's energy does not change: ΔEwater = 0."
Card D, magnet: a 0.020 kg steel ball starts from rest on a smooth level track and is pulled to a magnet, reaching 1.5 m/s. Student: "ΔKE = +0.0225 J, so ΔEmagnetic = +0.0225 J."
Card E, camera flash: the capacitor's field energy decreases by 3.2 J and 0.3 J leaves as light. Student: "ΔEthermal = 3.2 + 0.3 = 3.5 J."
Card F, braking car: a 1000 kg car traveling at 72 km/h brakes to a stop. Student: "ΔKE = -½(1000)(72)² = -2,592,000 J."
Discussion Questions
Only Card A is correct as written. For each other card, which term is wrong: a sign, a missing flow, or a unit?
On Card C, what flow did the student leave out, and what is its size?
On Card D, what does a negative ΔEmagnetic mean about the magnet-ball system?
Challenge Variation
Pairs write a seventh card with a subtle error of their own, trade with another pair, and critique each other's card.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Energy Accounting Bar Chart for the Cart on a Track
Energy changes of the three kinds of energy in the cart, track and Earth system from the first worked example, drawn to scale. Nothing crosses the boundary, so the bars add to zero: the 29.4 J lost from the gravitational field becomes 25.0 J of kinetic energy and 4.4 J of thermal energy.
Diagram 2: System Model of an Electric Kettle
A two-component system (water and kettle body) with one flow in and one flow out, from the second worked example. The model sets the sum of the component changes equal to energy in minus energy out, so the unknown water term can be found from the other three.
04
Homework Assignment
~30 min
HS-PS3-1 Homework: Building and Using Energy Models
Directions: All data are invented for practice. Use g = 9.8 m/s², cwater = 4180 J/(kg·°C) and csteel = 450 J/(kg·°C). For every problem, name the system and its components, list any flows in or out, write the model, and explain the meaning of the term you solve for.
Part 1: Motion and Gravitational Fields (Problems 1-2)
A cyclist and bike (80 kg together) coast down a hill that drops 15 m vertically. The speed rises from 4.0 m/s to 12.0 m/s without pedaling. (a) Find ΔEgrav and ΔKE. (b) Find the thermal energy produced in the air, tires and road. (c) Is 12.0 m/s possible? Compare with the speed a frictionless bike would reach.
A 0.057 kg tennis ball is dropped from 1.80 m. Its bounce heights are 1.08 m, 0.65 m and 0.39 m. (a) Build a spreadsheet or table model that gives the thermal energy produced in each bounce. (b) Explain why the kinetic energy term does not appear when you compare the tops of two bounces. (c) The ball keeps about the same fraction of its height each bounce. Use the model to predict the fourth bounce height.
Part 2: Thermal Energy and Flows (Problems 3-4)
A microwave oven delivers 1000 W to a mug of water for 50 s. The mug holds 0.25 kg of water, and the 0.35 kg ceramic mug (c = 850 J/(kg·°C)) warms from 20 °C to 40 °C. About 2,250 J leaves the mug and water as heat to the air. (a) Find the energy delivered. (b) Find ΔE of the mug. (c) Solve the model for ΔE of the water and its temperature rise. (d) Explain what each term means.
A 1,600 kg car traveling at 25 m/s (90 km/h) brakes to a stop on a level road. During the stop, 95,000 J leaves the brakes as heat to the air. (a) Find ΔKE. (b) Find the thermal energy that stays in the brakes. (c) The steel brake discs have a total mass of 30 kg. Find their temperature rise.
Part 3: Electric and Magnetic Fields (Problems 5-6)
A 10 F supercapacitor charged to 2.7 V runs a motor that lifts a 0.40 kg load 2.5 m. The capacitor ends at 2.0 V. (a) Find the change in electric field energy of the capacitor. (b) Find ΔEgrav of the load. (c) Find the thermal energy produced in the motor and wires. (d) What fraction of the field energy went into lifting the load?
A magnet pulls a 0.050 kg steel cart from rest along a level track. The cart reaches 0.60 m/s just before it touches the magnet, and 0.004 J becomes thermal energy from friction. (a) Find ΔKE. (b) Solve the model for the change in magnetic field energy. (c) Explain what the sign of your answer means.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
System and Flows
Names the system, its components and every flow in or out
Components listed but a flow missing or misplaced
Computation
Every term computed with correct sign and units, and the model solved for the unknown
Method correct with one sign, unit or arithmetic error
Meaning of Terms
Explains in words what the solved term means physically and judges whether it is possible
Explanation given but vague, or plausibility not checked
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All data are invented. Use g = 9.8 m/s² and cwater = 4180 J/(kg·°C). Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
In the model ΔEsystem = Ein - Eout, what does a negative value of ΔEsystem mean?
Answer: C
ΔEsystem is a change, so a negative value means the system ended with less energy: Eout was larger than Ein. Choice A confuses a change with an amount; changes can be negative. Choice B contradicts conservation of energy. Choice D would make ΔEsystem zero.
Question 2 of 20 · Multiple Choice
A 1.2 kg book slides off a shelf and falls 1.5 m. Air resistance is negligible. What is its kinetic energy just before it lands?
Answer: B
The gravitational field energy decreases by mgh = 1.2 × 9.8 × 1.5 ≈ 17.6 J, and with no thermal term all of it becomes kinetic energy. Choice A halves it, confusing mgh with ½mv². Choice C leaves out g. Choice D doubles the correct value.
Question 3 of 20 · Multiple Choice
A 0.40 kg ball is thrown straight up. As it rises, its kinetic energy decreases by 12 J, and air resistance is negligible. What is the change in gravitational field energy of the ball-Earth system?
Answer: A
With no flows and no thermal term, ΔKE + ΔEgrav = 0, so ΔEgrav = -(-12 J) = +12 J. Choice B copies the sign of the kinetic term, a sign error. Choice C assumes the field stores nothing. Choice D counts the change twice.
Question 4 of 20 · Multiple Choice
2.0 kg of water in an insulated container absorbs 50,160 J from a heater, and no energy leaves. By how much does its temperature rise?
Answer: D
ΔT = ΔE ÷ (mc) = 50,160 ÷ (2.0 × 4180) = 6.0 °C. Choice A forgets to divide by the mass. Choice B divides 50,160 by 2,000 instead of by m × c. Choice C misplaces a decimal.
Question 5 of 20 · Multiple Choice
A 25 kg sled starts from rest at the top of a hill 8.0 m high and reaches 10 m/s at the bottom. How much thermal energy is produced by friction with the snow and air?
Answer: C
ΔEgrav = -(25)(9.8)(8.0) = -1960 J and ΔKE = ½(25)(10)² = +1250 J. The model gives ΔEthermal = 0 - (-1960 + 1250) = 710 J. Choice A is the kinetic energy and choice D is the gravitational change. Choice B adds the two magnitudes instead of using signs.
Question 6 of 20 · Multiple Choice
In a ramp spreadsheet model, ΔEthermal = mgh - ½mv². What does the term ½mv² stand for?
Answer: A
The cart starts from rest, so ½mv² is its kinetic energy at the bottom, all of which it gained on the way down. Choice B is the left side of the model, ΔEthermal. Choice C is what mgh stands for. Choice D is wrong because no energy crosses the boundary in this model.
Question 7 of 20 · Multiple Choice
An 800 W space heater runs for 5.0 minutes inside a closed system of the heater and the room air. How much electrical energy flows into the system?
Answer: D
Energy = power × time = 800 W × 300 s = 240,000 J. Choice A multiplies by minutes instead of seconds. Choice B divides power by time. Choice C treats the 5.0 minutes as 5.0 hours.
Question 8 of 20 · Multiple Choice
A magnet pulls a 0.030 kg steel ball from rest along a table. The ball reaches 2.0 m/s just before contact, and 0.010 J becomes thermal energy. What is the change in magnetic field energy?
Answer: B
ΔKE = ½(0.030)(2.0)² = 0.060 J. The model gives ΔEmagnetic = -(0.060 + 0.010) = -0.070 J: the field stores less energy once the ball has moved closer. Choice A leaves out the thermal term. Choice C has the wrong sign. Choice D subtracts the thermal term instead of adding it.
Question 9 of 20 · Multiple Choice
A charged capacitor's field energy decreases by 6.0 J while it lights an LED. 1.2 J leaves the system as light. By how much does the thermal energy of the LED and wires increase?
Answer: D
ΔEfield + ΔEthermal = -Eout, so -6.0 + ΔEthermal = -1.2 and ΔEthermal = 4.8 J. Choice A adds the light leaving instead of subtracting it. Choice B ignores the light. Choice C is the light, not the thermal energy.
Question 10 of 20 · Multiple Choice
A student models a ball falling through air as ½mv² = mgh + ΔEthermal. What is wrong with the model?
Answer: B
The gravitational energy released, mgh, is shared between kinetic and thermal energy: mgh = ½mv² + ΔEthermal. The student's version gives the ball more kinetic energy than mgh when air resistance acts, which is impossible. Choice A uses the thermal expression for the ball's motion. Choice D reverses the direction of energy transfer.
Question 11 of 20 · Multiple Choice
A 0.20 kg hockey puck slides across a level floor and slows from 3.0 m/s to rest. How much thermal energy is produced in the puck and floor?
Answer: B
ΔKE = 0 - ½(0.20)(3.0)² = -0.9 J, so ΔEthermal = +0.9 J. Choice C forgets the ½. Choice D multiplies mass by speed. Choice A uses the speed instead of its square.
Question 12 of 20 · Multiple Choice
In a spreadsheet, column B holds release height (m), column C holds speed at the bottom (m/s), and cell F1 holds the cart's mass (kg). Which formula in row 2 gives the thermal energy?
Answer: C
Thermal energy is the gravitational energy released minus the kinetic energy gained: m × 9.8 × h - ½mv². Choice A adds the two terms. Choice B reverses the order and gives the negative of the answer. Choice D swaps the height and speed columns.
Question 13 of 20 · Multiple Choice
90,000 J of electrical energy enters a kettle. The water gains 80,500 J and the kettle body gains 3,600 J. How much energy leaves to the room?
Answer: A
ΔEwater + ΔEbody = Ein - Eout, so 84,100 = 90,000 - Eout and Eout = 5,900 J. Choice B forgets the kettle body. Choice C is the total gained by the components. Choice D adds the body's energy to the 9,500 J difference instead of subtracting it.
Question 14 of 20 · Multiple Choice
A lab group reports that a 0.50 kg cart released from rest 0.45 m above the bottom of a ramp reached 3.5 m/s. Why should the teacher question this result?
Answer: D
The frictionless speed is √(2 × 9.8 × 0.45) ≈ 2.97 m/s. At 3.5 m/s the kinetic energy (3.06 J) exceeds the gravitational energy released (2.21 J), so the model gives a negative thermal energy, which is impossible without an energy input. Choice A ignores friction. Choices B and C state rules that do not exist.
Question 15 of 20 · Short Answer
An elevator motor does 150,000 J of work lifting a 500 kg elevator car 25 m at constant speed. Model the system (car, Earth, motor and cables) and find the thermal energy produced in the motor and cables.
Ein = 150,000 J. ΔKE = 0 (constant speed). ΔEgrav = (500)(9.8)(25) = 122,500 J. Model: 122,500 + 0 + ΔEthermal = 150,000, so ΔEthermal = 27,500 J.
Question 16 of 20 · Short Answer
A 60 W immersion heater warms 0.50 kg of water in a foam cup for 5.0 minutes, and 1,280 J escapes through the cup. Find the temperature rise of the water.
Ein = 60 W × 300 s = 18,000 J. ΔEwater = 18,000 - 1,280 = 16,720 J. ΔT = 16,720 ÷ (0.50 × 4180) = 8.0 °C.
Question 17 of 20 · Short Answer
A student writes the model ΔEwater = P × t - Eloss - mkckΔTk for a kettle. Explain in words what each of the three terms on the right means and why each has the sign it does.
P × t is the electrical energy that flows into the system, so it adds to the water's energy. Eloss is heat that leaves the system to the room, so it is subtracted. mkckΔTk is the thermal energy gained by the kettle body, a second component; energy it keeps cannot also end up in the water, so it is subtracted too.
Question 18 of 20 · Short Answer
A 1.8 kg pendulum bob is released from rest 0.35 m above its lowest point and passes the lowest point at 2.5 m/s. Find the thermal energy produced by air resistance and friction at the pivot.
ΔEgrav = -(1.8)(9.8)(0.35) ≈ -6.17 J. ΔKE = ½(1.8)(2.5)² ≈ +5.63 J. ΔEthermal = 6.174 - 5.625 ≈ 0.55 J. This is positive and small, so the data are plausible.
Question 19 of 20 · Short Answer
A 1,200 kg car coasts in neutral up a hill. Its speed drops from 20 m/s to 12 m/s while it rises 10 m. Find ΔKE, ΔEgrav and the thermal energy produced.
ΔKE = ½(1200)(12² - 20²) = -153,600 J. ΔEgrav = (1200)(9.8)(10) = +117,600 J. Model: -153,600 + 117,600 + ΔEthermal = 0, so ΔEthermal = 36,000 J from air resistance and rolling friction.
Question 20 of 20 · Short Answer
An advertisement claims that a 1500 W kettle heats 1.0 kg of water from 20 °C to 100 °C in 60 s. Use a computational model to decide whether the claim is possible.
In 60 s the kettle can deliver at most 1500 × 60 = 90,000 J. Heating the water needs 1.0 × 4180 × 80 = 334,400 J. Even with no losses, the model needs more energy in than the kettle supplies, so the claim is impossible; it would take at least about 223 s.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HS-PS3-1 mean?
HS-PS3-1 asks students to build a computational model that finds the energy change of one part of a system when the changes of the other parts and the energy flowing in and out are known. In practice, students write one conservation equation, compute the known terms, and solve for the unknown one. The code means High School, Physical Science, core idea 3 (Energy), performance expectation 1.
What is a computational model in HS-PS3-1?
It is a set of equations, or a spreadsheet built from them, that takes measured quantities and computes an energy change. The central equation is ΔE1 + ΔE2 + ΔE3 = Ein - Eout. A spreadsheet version applies that equation to many trials at once, so students can see patterns and spot data that cannot be right.
What is the assessment boundary for HS-PS3-1?
Assessment is limited to basic algebra, to systems of two or three components, and to thermal energy, kinetic energy and energy in gravitational, magnetic or electric fields. Chemical energy, nuclear energy and models that need calculus are beyond this standard. Batteries and food can appear only as a known energy flow into the system, not as a component whose stored energy students calculate.
Is HS-PS3-1 a physics or chemistry standard?
It is usually taught in Physics or Physical Science, often at the start of an energy unit. Chemistry courses meet the same conservation idea in HS-PS1-4, which is about bond energy, and in calorimetry labs, but HS-PS3-1 itself is limited to motion, thermal energy and field energy.
What does "explaining the meaning of mathematical expressions" look like?
Students say what each term stands for physically, not only its value. For example, for mcΔT a student should be able to say that it is the thermal energy a substance gains, that it is larger for more mass or a larger temperature change, and that c tells how much energy one kilogram needs per degree. Ask for the meaning of the sign too: a negative ΔE means that component lost energy.
What is the difference between a component and an energy flow?
A component is inside the system boundary and has its own energy change, such as the water in a kettle. A flow crosses the boundary, such as electrical energy entering from the outlet or heat leaving to the room. Where you draw the boundary decides which is which: if the room air is inside the system, heat to the room becomes a component change instead of a flow.
What mistakes do students make when building energy models?
Common errors are sign errors (writing a loss as a gain), adding an outflow instead of subtracting it, forgetting a component such as the container, mixing km/h with m/s or minutes with seconds, and forgetting to square the speed in ½mv². Many students also accept an answer that is physically impossible, such as a negative thermal energy from friction. A quick check against the frictionless limit catches that.
Why do the answers include a check against a frictionless or lossless limit?
A computational model is only as good as its data. Comparing a measured speed with √(2gh), or a heating time with the minimum a heater of that power needs, tells students whether their data are physically possible. This habit is part of using a model, not an extra step.
Can students do HS-PS3-1 without lab equipment?
Yes. The standard is about building and using the model, so invented data sets, energy simulations with adjustable friction, or home measurements with a kitchen scale and thermometer all work. A plug-in energy meter and a kettle make a strong low-cost lab when they are available.
What comes after HS-PS3-1?
HS-PS3-2 asks students to model macroscopic energy as motion of particles or energy stored in fields. HS-PS3-3 asks them to design a device that converts energy, and HS-PS3-4 has them investigate thermal energy transfer between two components at different temperatures. The energy accounting from this standard is the tool used in all three.
07
Related Standards
6 standards
These standards connect to HS-PS3-1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-PS3-5Prerequisite
Argue that energy is transferred to or from an object when its kinetic energy changes
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