FULL REVIEW
Full Review — Work and the Work–Energy Theorem — Algebra-Based
Review the essential ideas, relationships, and problem-solving tools for Work and the Work–Energy Theorem.
TIME
45–60 minutes
BEST FOR
A complete topic review
FINISH WITH
A readiness check
After this full review, you'll be able to...
recall the essential ideas, apply them to representative problems, and determine what to study next.
Choose how you want to review
Course Alignment
This Physics Sensei Topic Review is an independent learning resource. Use it to reinforce key concepts, prepare for homework, or review before a quiz or exam.
Related Unit Review: If you need to review the complete unit material, review Work, Energy, and Power here →
RESOURCE: Physics Sensei Topic Review | TOPIC ID: MEC-U06-T01 | TOPIC: Work and the Work–Energy Theorem | PARENT UNIT: MEC-U06 — Work, Energy, and Power | COURSE LEVEL: Algebra-Based
BEST USED ✓ After learning the topic ✓ Before starting homework ✓ Before a quiz or exam
Your Review Plan
Complete these six stages in order. Each stage builds on the previous one and prepares you for the final readiness check.
6 Stages • Approximately 45–60 minutes.
Warm-Up Check
Before you begin, take a moment to see what you already remember. Do not worry about getting everything right. This is only a starting point.
ACTIVITY 1
Recall Activity 1
Answer before revealing the response.
Write the work formula for a constant force at angle θ to the displacement.
Reveal Answers
W = Fd cos θ.
Why it works: The cosine factor is the dot-product geometry.
ACTIVITY 2
Recall Activity 2
Answer before revealing the response.
Explain why the normal force often does zero work on an object moving horizontally.
Reveal Answers
The normal force is perpendicular to the horizontal displacement, so its work is zero.
Why it works: Perpendicular vectors have a zero dot product.
ACTIVITY 3
Recall Activity 3
Answer before revealing the response.
A 35 N force acts over 4 m at 60°. Find the work done.
Reveal Answers
70 J because (35)(4)cos 60° = 70.
Why it works: At 60°, only half the force contributes along the displacement.
Ready to strengthen your understanding?
You've refreshed what you already know. Next, you'll reinforce the essential concepts that will help you solve problems with confidence. Need to see the learning path again?
Core Concepts
Let's rebuild the key ideas one step at a time. Focus on understanding the relationships before worrying about solving problems.
KEY CONCEPT 1
Work as a Dot Product
For a constant force, work is the dot product of force and displacement. The cosine factor automatically gives positive, zero, or negative work based on the angle between the vectors.
W = Fd cos θ
Example: A 10 N force over 5 m at 120° does -25 J of work.
Sensei note: The angle belongs between force and displacement, regardless of how the diagram is oriented.
KEY CONCEPT 2
The Work–Energy Theorem
The sum of the work done by all forces equals the change in kinetic energy. This theorem packages the combined effect of forces over a displacement into an energy equation.
Wnet = ΔK
Example: If the total work is +45 J, kinetic energy increases by 45 J.
Sensei note: Net work means the algebraic sum of the work by all forces.
KEY CONCEPT 3
Kinetic Energy Connects Work to Speed
Kinetic energy depends on mass and speed squared. Combining its expression with the work–energy theorem lets you solve for an unknown initial or final speed.
K = ½mv²
Example: For a 2.0 kg object with 36 J of kinetic energy, the speed is 6.0 m/s.
Sensei note: Keep units consistent: joules for energy, kilograms for mass, meters per second for speed.
Ready to apply these ideas?
You've reinforced the essential concepts. Now it's time to put them into practice by working through guided examples and building your problem-solving confidence. Need a quick reminder?
Guided Practice
Now it's time to apply what you've reviewed.
Work through each activity in order. The examples become gradually more challenging, and each one prepares you for the final readiness check.
PRACTICE 1
Worked Example
Compute work for an angled constant force.
A rope pulls with 80 N at 25° above horizontal while a crate moves 10 m horizontally. Find the work done by the rope.
Reveal Answers
About 725 J: (80)(10)cos 25°.
Why it works: The horizontal component of the rope force transfers energy along the motion.
PRACTICE 2
Guided Problem
Use the theorem to find final kinetic energy.
A 3.0 kg cart moving at 4.0 m/s experiences +30 J of net work. Find its final kinetic energy.
Reveal Answers
Initial kinetic energy is 24 J; final kinetic energy is 54 J.
Why it works: Net work adds directly to the initial kinetic energy.
PRACTICE 3
Independent Problem
Use kinetic energy to determine speed after a known net work.
Continue the previous problem and find the cart’s final speed.
Reveal Answers
6.0 m/s, obtained from 54 J of kinetic energy for a 3.0 kg cart.
Why it works: Solve the kinetic-energy expression for speed.
Ready to check your understanding?
You've practiced the essential skills with guidance. Now it's time to solve a few short problems on your own and confirm you're ready to move forward. Need a quick reminder?
Confidence Check
You've rebuilt the key ideas and practiced them with guidance. Now try these short questions on your own to check your understanding before moving on.
QUICK CHECK 1
Negative Work
Solve independently before checking the solution.
A 40 N force acts through 3 m at 150°. Is its work positive or negative, and what is its value?
Reveal Answers
Negative, about -104 J: (40)(3)cos 150°.
Why it works: An obtuse angle gives a negative cosine.
QUICK CHECK 2
Net-Work Update
Solve independently before checking the solution.
An object with 22 J of kinetic energy experiences -7 J of net work. What is its final kinetic energy?
Reveal Answers
15 J.
Why it works: Negative net work reduces kinetic energy.
QUICK CHECK 3
Speed from Energy
Solve independently before checking the solution.
A 2.0 kg object has 49 J of kinetic energy. What is its speed?
Reveal Answers
7.0 m/s.
Why it works: Rearranging kinetic energy gives the speed.
How did it go?
You've checked your understanding. Take one final look at the essential ideas before deciding what to do next. Need a quick reminder?
Summary
Before moving on, take one final look at the most important ideas from this review.
KEY TAKEAWAY 1
Work Is Direction-Sensitive
The dot product makes work depend on both magnitudes and the angle between force and displacement.
KEY TAKEAWAY 2
Net Work Equals the Kinetic-Energy Change
Add the work of all forces and set that total equal to the change in kinetic energy.
KEY TAKEAWAY 3
Energy Gives Speed
Use kinetic energy with the theorem to move efficiently between work and speed.
MY ONE-SENTENCE SUMMARY
In my own words, the most important idea is:
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