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Model Energy
Transfer Between Objects

Learn to develop models that describe how energy flows between objects through work, heat, and radiation: using \( \Delta E = Q - W \) as the foundation.

High School Physics

What Is Energy?

Energy is the capacity to do work or cause change. It cannot be created or destroyed: only transferred between objects or transformed from one form to another. We measure energy in joules (J).

Kinetic Energy
Energy of motion: \( KE = \frac{1}{2}mv^2 \)
Potential Energy
Stored energy due to position: \( PE = mgh \)
Thermal Energy
Internal energy from particle motion: \( Q = mc\Delta T \)

Transfer vs Transformation

Energy Transfer
Energy moves between objects. A hot cup warms your hands: thermal energy flows from cup to hand.
Energy Transformation
Energy changes form within a system. A falling ball converts gravitational PE to kinetic energy.

Three Mechanisms of Transfer

Work (\( W \))
A force applied over a distance: \( W = Fd\cos\theta \). Transfers energy mechanically.
Heat (\( Q \))
Energy flows from hot to cold via conduction, convection, or radiation.
Radiation
Energy carried by electromagnetic waves: no medium needed. The Sun heats Earth this way.

The First Law of Thermodynamics

System
\( \Delta E \)
\( Q \)
 Heat in
\( W \)
 Work out
\( \Delta E = Q - W \)

Conservation of Energy

In an isolated system, total energy is constant. When energy leaves one object, it must enter another (or change form). Mathematically:

This principle is the foundation for every energy transfer model: tracking where energy goes and what form it takes.

Heat Transfer: Three Methods

Conduction Convection Radiation
Mechanism Direct contact Fluid circulation EM waves
Medium? Solid (best) Liquid or gas None needed
Example Metal spoon in soup Boiling water Sunlight warming Earth
Key Equation \( \frac{Q}{t} = kA\frac{\Delta T}{d} \) \( Q = mc\Delta T \) \( P = \sigma A T^4 \)

How to Build an Energy Model

1
Define the system. Identify which objects are "inside" and which are "surroundings."
2
Identify energy types. List all forms of energy present: kinetic, potential, thermal, etc.
3
Map the transfers. Draw arrows showing how energy moves: work, heat, or radiation between objects.
4
Apply conservation. Write \( E_{\text{in}} = E_{\text{out}} + \Delta E_{\text{stored}} \) for each object.
5
Solve and verify. Calculate unknowns and check that total energy is conserved.

Example 1: Falling Ball

Ground (\( h = 0 \))
\( h = 10 \text{ m} \)
 2 kg
\( v = 0 \)
\( PE = 196 \text{ J} \)
 Transfer 2 kg
\( KE = 196 \text{ J} \)
\( v = 14 \text{ m/s} \)

Example 2: Hot Block in Cold Water

Water: 0.5 kg at \( 20\,^{\circ}\text{C} \)
 Iron: 0.2 kg
\( 80\,^{\circ}\text{C} \)
\( Q \) flows
 hot → cold
\( Q_{\text{lost}} = Q_{\text{gained}} \)

Example 3: Inelastic Collision

BEFORE 3 kg
\( 4 \text{ m/s} \)
 1 kg
\( 0 \text{ m/s} \)
 AFTER 4 kg
\( 3 \text{ m/s} \)
\( KE_i = \frac{1}{2}(3)(4^2) = 24 \text{ J} \)
\( KE_f = \frac{1}{2}(4)(3^2) = 18 \text{ J} \)
\( \Delta E_{\text{thermal}} = 24 - 18 = 6 \text{ J} \)
 6 J transferred to thermal energy (heat, sound)

Energy Bar Charts: A Visual Model

Energy bar charts (LOL diagrams) are a powerful way to model energy transfer visually. Each bar represents a type of energy, and the total height stays constant.

Initial PE KE Final PE KE Total E

Energy Flow Diagrams

An energy flow diagram uses boxes for objects and arrows for transfers. Arrow thickness represents the amount of energy transferred.

Sun Radiation Solar Panel
\( 1000 \text{ J} \) in
\( 200 \text{ J} \) electrical
 Battery
\( 800 \text{ J} \) thermal
 Surroundings

The Work-Energy Theorem

The net work done on an object equals its change in kinetic energy. This is one of the most direct models for energy transfer via mechanical forces.

Positive Work
Force in the direction of motion: speeds up the object. Energy transfers into kinetic energy.
Negative Work
Force opposes motion: slows down the object. KE transfers out (often to thermal energy via friction).

Common Mistakes

✕ Energy "Used Up"
Energy is never destroyed. When we say energy is "lost," it has been transferred to the surroundings as thermal energy, not consumed.
✕ Confusing Heat and Temperature
Heat (\( Q \)) is energy transferred due to a temperature difference. Temperature (\( T \)) is a measure of average kinetic energy per particle.
✕ Ignoring System Boundaries
Energy is only "lost" if it leaves the system. Always define your system first: what counts as "inside" vs "surroundings" changes the model.

Summary: Energy Transfer Models

Bar Chart Flow Diagram Equation
Shows Energy amounts per type Transfer paths between objects Precise numerical relationships
Best For Before/after comparison Multi-object systems Calculating unknowns
Conservation Total bar height constant Arrows in = arrows out \( E_i = E_f \)
Limitation No transfer direction Less precise quantities No visual intuition

Question 1 of 5

A \( 5 \text{ kg} \) box is pushed across a rough floor at constant velocity by a \( 20 \text{ N} \) force over \( 3 \text{ m} \). Where does the energy transferred by the pushing force go?

Question 2 of 5

A ball is dropped from rest at height \( h \). At the halfway point (\( h/2 \)), which statement is correct?

Question 3 of 5

A hot \( 200 \text{ g} \) iron block (\( c = 450 \text{ J/(kg}\cdot\text{^\circ C)} \)) at \( 100\,^{\circ}\text{C} \) is placed in \( 500 \text{ g} \) of water (\( c = 4186 \text{ J/(kg}\cdot\text{^\circ C)} \)) at \( 20\,^{\circ}\text{C} \). Which equation correctly models the energy transfer at equilibrium?

Question 4 of 5

In the energy flow diagram of a car engine, \( 1000 \text{ J} \) of chemical energy enters. If \( 250 \text{ J} \) becomes kinetic energy and \( 50 \text{ J} \) becomes sound, how much becomes thermal energy?

Question 5 of 5

Two identical objects at different temperatures are placed in an insulated container. Which best describes the energy transfer model?