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Energy Transfer
Through Interactions

Understand how energy flows between objects via work, heat, and radiation: the mechanisms that drive every physical process in the universe.

High School Physics

What Is Energy?

Energy is the capacity to do work or cause change. It is a scalar quantity measured in joules (J). Energy cannot be created or destroyed: it can only be transferred from one object to another or transformed from one form to another.

Key Forms of Energy

Kinetic
Energy of motion: \( K = \tfrac{1}{2}mv^2 \)
Potential
Stored energy due to position or configuration
Thermal
Internal energy from molecular motion

Three Mechanisms of Transfer

Work
A force acts on an object over a displacement: \( W = F\,d\cos\theta \)
Heat
Energy flows due to a temperature difference: \( Q = mc\,\Delta T \)
Radiation
Energy carried by electromagnetic waves, no medium required

The Work-Energy Theorem

The net work done on an object equals the change in its kinetic energy. This is the fundamental link between force interactions and energy transfer.

m
F
d
m
\(v_i\)
\(v_f\)

Conservation of Energy

In an isolated system, the total energy remains constant. Energy can transfer between objects or change form, but the total is conserved.

m
Max PE
\(KE=0\)
m
Max KE
\(PE=0\)
h
\(PE \to KE\)

Transfer vs Transformation

Energy Transfer Energy Transformation
Definition Energy moves between objects Energy changes form within a system
Example Bat hits ball: KE from bat to ball Falling ball: PE converts to KE
Number of objects At least two Can occur within one
Mechanism Work, heat, or radiation Internal forces or processes

How to Analyze Energy Transfer

1
Define the system. Identify which objects are inside and outside the system boundary.
2
Identify interactions. List all forces acting between the system and its surroundings.
3
Classify each transfer. Is energy entering or leaving the system? Via work, heat, or radiation?
4
Apply conservation. Write: \( E_i + W_{\text{in}} - W_{\text{out}} = E_f \).
5
Solve. Substitute known values, solve for the unknown quantity.

Work as Energy Transfer

When a force \( F \) acts on an object over displacement \( d \) at angle \( \theta \) to the direction of motion, the work done is:

m
d
F
θ

Heat as Energy Transfer

Heat flows spontaneously from a hotter object to a cooler one until thermal equilibrium is reached. The energy transferred is:

Hot
\(T_1 = 90^\circ\text{C}\)
Cold
\(T_2 = 20^\circ\text{C}\)
Q
Energy flows from hot to cold

Example 1: Pushing a Crate

A 50 N horizontal force pushes a crate 4 m across a frictionless floor. How much energy is transferred to the crate?

1
Identify: \( F = 50\;\text{N} \), \( d = 4\;\text{m} \), \( \theta = 0° \) (force parallel to displacement).
2
Apply: \( W = Fd\cos\theta = 50 \times 4 \times \cos 0° \).
3
Solve: \( W = 200\;\text{J} \). The crate gains 200 J of kinetic energy.

Example 2: Heating Water

How much energy is needed to heat 0.5 kg of water from 20°C to 80°C? The specific heat of water is \( c = 4{,}186\;\text{J/(kg·°C)} \).

1
Identify: \( m = 0.5\;\text{kg} \), \( c = 4{,}186\;\text{J/(kg·°C)} \), \( \Delta T = 80 - 20 = 60°\text{C} \).
2
Apply: \( Q = mc\,\Delta T = 0.5 \times 4{,}186 \times 60 \).
3
Solve: \( Q = 125{,}580\;\text{J} \approx 125.6\;\text{kJ} \). That is 125.6 kJ transferred via heat.

Example 3: Roller Coaster Drop

A 600 kg roller coaster car starts from rest at a height of 30 m. Neglecting friction, find its speed at the bottom.

1
Conservation: \( mgh = \tfrac{1}{2}mv^2 \). Mass cancels: \( gh = \tfrac{1}{2}v^2 \).
2
Solve for \( v \): \( v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 30} \).
3
Result: \( v = \sqrt{588} \approx 24.2\;\text{m/s} \). All gravitational PE converted to KE.

When Friction Is Present

Non-conservative forces like friction transfer mechanical energy into thermal energy. The modified conservation equation becomes:

\(v\)
\(f_k\)
\(KE \to \text{Thermal}\)

Common Mistakes

✕ Confusing Heat and Temperature
Heat is energy transferred; temperature is a measure of average kinetic energy of molecules. They are not the same.
✕ Ignoring the Angle in Work
Work depends on \( \cos\theta \). A force perpendicular to motion does zero work, even if the force is large.
✕ Forgetting Friction Losses
In real systems, friction converts mechanical energy to thermal energy. Ignoring it leads to overestimating final speed.

Summary of Energy Transfer

Property Work Heat Radiation
Equation \( W = Fd\cos\theta \) \( Q = mc\Delta T \) Depends on temperature and surface properties
Requires contact? Yes (force on object) Yes (or through medium) No (EM waves)
Requires medium? Yes Conduction/convection: yes No
Direction Along displacement Hot to cold All directions

Question 1 of 5

A person pushes a box with a force of 80 N over a distance of 5 m along a horizontal floor. The force is applied at an angle of 60° above the horizontal. How much work does the person do on the box?

Question 2 of 5

A ball is dropped from rest at a height of 20 m. Neglecting air resistance, what is its speed just before hitting the ground? (Use \( g = 10\;\text{m/s}^2 \).)

Question 3 of 5

A force acts perpendicular to the direction of an object's motion. How much work does this force do on the object?

Question 4 of 5

When a car brakes to a stop on a road, where does the car's kinetic energy go?

Question 5 of 5

How much heat is required to raise the temperature of 2 kg of water by 25°C? (Specific heat of water: \( c = 4{,}186\;\text{J/(kg·°C)} \).)