Module 2 · Lesson

Work, Energy, and Power

Dynamics

Work, Energy, and Power

Orientation

Lesson goal: build accurate physics fluency for work, energy, and power and use that fluency to support clear HSC-style scientific writing.

This page is materialised into the MentorMind course shell from existing teaching, textbook, and eduKG material. Use it as the main lesson surface; use the tutor for targeted repair, worked examples, and concise writing feedback.

Source Lesson Material

Syllabus inquiry question

From The Feynman Lectures on Physics, Vol I, Chapter 4:

Energy accounting does not depend on the path taken. What matters is the initial and final states and the work done by non-conservative forces.

Learning Objectives

Content

Work

Work is the energy transferred by a force acting through a displacement:

$$W = Fd\cos\theta$$

where:

SI unit: Joule (J), where 1 J = 1 N·m

Kinetic Energy

Kinetic energy is the energy of motion:

$$KE = \frac{1}{2}mv^2$$

Interactive: Energy Bar Chart - Motion

Visualise kinetic energy as an object speeds up:

Gravitational Potential Energy

Gravitational potential energy (GPE) is the energy stored due to height:

$$GPE = mgh$$

where:

GPE depends on the chosen reference height. Usually, we set GPE = 0 at the lowest point in a problem.

Work-Energy Theorem

The net work done on an object equals its change in kinetic energy:

$$W_{net} = \Delta KE = KE_f - KE_i = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$

This powerful theorem connects force, displacement, and speed change.

Interactive: Energy Conservation - Falling Object

As an object falls, GPE converts to KE:

Key observation: Total mechanical energy (KE + GPE) remains constant (in the absence of friction).

Conservation of Mechanical Energy

In the absence of friction and air resistance:

$$KE_i + GPE_i = KE_f + GPE_f$$

Or equivalently: $$\frac{1}{2}mv_i^2 + mgh_i = \frac{1}{2}mv_f^2 + mgh_f$$

This is one of the most useful equations in physics!

Interactive: Pendulum Energy

A pendulum swings back and forth, continuously converting between KE and GPE:

At the highest points, all energy is GPE (momentarily stationary). At the lowest point, all energy is KE (maximum speed).

Power

Power is the rate of doing work or transferring energy:

$$P = \frac{W}{t} = \frac{E}{t}$$

For constant force and velocity: $$P = Fv$$

SI unit: Watt (W), where 1 W = 1 J/s

Efficiency

Efficiency measures how much input energy becomes useful output:

$$\eta = \frac{E_{useful}}{E_{input}} \times 100% = \frac{P_{output}}{P_{input}} \times 100%$$

No machine is 100% efficient-some energy is always lost to friction, heat, sound, etc.

Interactive: Energy with Friction

When friction is present, some mechanical energy is lost:

Friction does negative work, removing mechanical energy and converting it to thermal energy.

Worked Examples

Example 1: Work by a force

A 25 N force pulls a sled 8.0 m on level ground, parallel to motion.

Solution:

  1. Force and displacement are parallel, so $\theta = 0 degrees$

  2. Work: $W = Fd\cos\theta = 25 \times 8.0 \times \cos0 degrees = 25 \times 8.0 \times 1 = 200$ J

  3. Positive work-energy is transferred to the sled

Example 2: Speed from energy conservation

A 2.0 kg object falls 5.0 m from rest. Find its speed at the bottom (ignore air resistance).

Solution:

  1. Use energy conservation: $GPE_i = KE_f$

  2. $mgh = \frac{1}{2}mv^2$ (mass cancels!)

  3. $v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5.0} = \sqrt{98} = 9.9$ m/s

Example 3: Work-energy theorem

A 1.2 kg cart speeds up from 2.0 m/s to 6.0 m/s. Find the net work done.

Solution:

  1. Initial KE: $KE_i = \frac{1}{2} \times 1.2 \times 2.0^2 = 2.4$ J

  2. Final KE: $KE_f = \frac{1}{2} \times 1.2 \times 6.0^2 = 21.6$ J

  3. Net work: $W_{net} = KE_f - KE_i = 21.6 - 2.4 = 19.2$ J

Example 4: Power and efficiency

A motor lifts a 150 N load at 0.60 m/s using 200 W of electrical power.

Solution:

  1. Mechanical power output: $P_{out} = Fv = 150 \times 0.60 = 90$ W

  2. Efficiency: $\eta = \frac{P_{out}}{P_{in}} \times 100% = \frac{90}{200} \times 100% = 45%$

  3. The motor is 45% efficient-55% of input power is lost to friction and heat

Example 5: Roller coaster speed

A 500 kg roller coaster car starts from rest at 20 m high. Find its speed at 8 m high (ignore friction).

Solution:

  1. Energy conservation: $KE_i + GPE_i = KE_f + GPE_f$

  2. Initial: $KE_i = 0$, $GPE_i = mgh_i = 500 \times 9.8 \times 20 = 98000$ J

  3. Final: $GPE_f = mgh_f = 500 \times 9.8 \times 8 = 39200$ J

  4. $KE_f = 98000 - 39200 = 58800$ J

  5. Speed: $v = \sqrt{\frac{2 \times KE_f}{m}} = \sqrt{\frac{2 \times 58800}{500}} = \sqrt{235.2} = 15.3$ m/s

Alternatively, using height difference: $$v = \sqrt{2g\Delta h} = \sqrt{2 \times 9.8 \times 12} = 15.3 \text{ m/s}$$

Common Misconceptions

Practice Questions

Easy (2 marks)

A 10 N force moves an object 3.0 m in the direction of the force. Calculate the work done.

Answer: 30 J

Medium (4 marks)

A 1.2 kg cart speeds up from 2.0 m/s to 6.0 m/s. Find the net work done on the cart.

Answer: 19.2 J

Hard (5 marks)

A pump raises 500 kg of water by 4.0 m in 60 s. Determine the output power and efficiency if the electrical input is 600 W.

Answer: Output power = 327 W; Efficiency = 54%

Multiple Choice Questions

Test your understanding with these interactive questions:

Quick Quiz: Energy Transformations

Extended Response Practice

Summary

Self-Assessment

Check your understanding:

After studying this section, you should be able to:

Module 2 Complete

Congratulations on completing Module 2: Dynamics!

Scientific Writing And Exam Support

When answering questions from this lesson, separate:

For explanation questions, write in the pattern: claim -> physics reason -> consequence. For calculation questions, state the formula, substitute with units, calculate, then interpret the answer.

Tutor Context

Use this lesson context when the student asks about work, energy, and power, related calculations, representations, or scientific writing. Prefer a short diagnostic before re-teaching. Check whether the student is confusing closely related categories such as force, velocity, acceleration, field, energy, momentum, model evidence, or mathematical representation.

Useful tutor diagnostic:

Which quantity is changing here, what causes that change, and what unit should the final answer use?

Maintenance Loop

One-minute retrieval:

  1. State the key law, model, or relationship used in this lesson.
  2. Identify one common misconception that would lead to a wrong answer.
  3. Write one sentence that links the calculation or evidence back to the physical meaning.

Source Trace

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