FOCUSED REVIEW
Focused Review: Work, Energy, and Power
Reinforce the highest-leverage ideas and representative problem-solving tools for Work, Energy, and Power.
TIME
Approximately 15 minutes
BEST FOR
Targeted reinforcement
FINISH WITH
A readiness check
After this focused review, you’ll be able to apply algebraic energy equations, calculate representative quantities, and choose efficient solution models.
Choose how you want to review
Unit Alignment
This public Unit Review is aligned to the approved Physics Sensei mechanics architecture and is independent of textbook chapter numbering.
ARCHITECTURE: Physics Sensei Independent Mechanics
UNIT: MEC-U06 — Work, Energy, and Power
RESOURCE: Unit Review
PROFILE: Algebra-Based college physics
BEST USED
✓ Before homework on work or energy
✓ Before a quiz or exam
✓ When choosing between force-based and energy-based methods
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 15 minutes.
Warm-Up Check
Before you begin, reactivate the core ideas. Attempt each item before revealing the answer.
ACTIVITY 1
Constant-Force Work
Use the force component parallel to displacement.
A 40 N force pulls a crate 5.0 m at 60° above horizontal. Find the work done by that force.
Reveal Answers
100 J.
Why it works: W = Fd cos θ = (40)(5.0)cos60° = 100 J.
ACTIVITY 2
Work-Energy Theorem
Relate net work to the change in kinetic energy.
A 2.0 kg object speeds up from 3.0 m/s to 7.0 m/s. Find the net work.
Reveal Answers
40 J.
Why it works: Wnet = ΔK = ½m(vf2 − vi2) = 40 J.
ACTIVITY 3
Power
Use energy transferred divided by elapsed time.
A motor does 2400 J of work in 6.0 s. Find its average power.
Reveal Answers
400 W.
Why it works: P = W/Δt = 2400/6.0 = 400 W.
Ready to strengthen your understanding? Now reinforce the essential concepts that control this unit.
Core Concepts
Rebuild the key energy relationships and connect each equation to its physical meaning.
KEY CONCEPT 1
Work and Kinetic Energy
For a constant force, work is the dot product of force and displacement. The sum of the work by all forces equals the change in translational kinetic energy.
W = Fd cos θ; Wnet = ΔK; K = ½mv2
Example: Net work is often the fastest route to a final speed when time is not required.
KEY CONCEPT 2
Potential Energy and Mechanical Energy
Conservative interactions can be represented with potential energy. Near Earth use gravitational potential energy; for an ideal spring use elastic potential energy.
Ug = mgy; Us = ½kx2; Emech = K + U
Example: For conservative interactions, Ki + Ui = Kf + Uf.
KEY CONCEPT 3
Nonconservative Work and Power
When external or nonconservative work changes mechanical energy, include that transfer explicitly. Power is the rate of doing work.
Wnc = ΔK + ΔU; Pavg = W/Δt; P = Fv when F ∥ v
Example: Use a consistent system boundary so every energy term has a clear physical meaning.
Ready to apply these ideas? Work through representative applications before the confidence check.
Guided Practice
Apply the energy model deliberately: define the system, identify the states, choose the equation, and check units and signs.
PRACTICE 1
Speed from Energy
Use conservation of mechanical energy.
A 2.0 kg object starts from rest and drops 5.0 m with negligible air resistance. Find its speed using g = 9.80 m/s².
Reveal Answers
9.90 m/s.
Why it works: mgh = ½mv², so v = √(2gh) = 9.90 m/s.
PRACTICE 2
Spring Compression
Convert kinetic energy into elastic potential energy.
A 1.5 kg cart moving at 4.0 m/s compresses a spring with k = 300 N/m on a frictionless track. Find maximum compression.
Reveal Answers
0.283 m.
Why it works: ½mv² = ½kx², so x = v√(m/k) = 0.283 m.
PRACTICE 3
Friction and Energy
Account for mechanical-energy reduction.
A 3.0 kg block slides 4.0 m on a level surface with kinetic friction 6.0 N. How much mechanical energy is transformed?
Reveal Answers
24 J.
Why it works: The friction work is −fd = −24 J, so 24 J of mechanical energy is transformed.
Ready to check your understanding? Solve the short checks without looking back at the concept cards.
Confidence Check
Use these questions to confirm that you can select and apply the correct energy model independently.
QUICK CHECK 1
Net Work to Speed
Use Wnet = ΔK.
A 4.0 kg cart initially at 2.0 m/s receives 32 J of net work. Find its final speed.
Reveal Answers
4.47 m/s.
Why it works: 32 = ½(4)(vf² − 2²), so vf = √20 = 4.47 m/s.
QUICK CHECK 2
Energy Conservation
Choose the correct states.
A ball is thrown upward at 14.0 m/s. Neglect air resistance. How high does it rise above release?
Reveal Answers
10.0 m.
Why it works: ½mv² = mgh, so h = v²/(2g) = 10.0 m.
QUICK CHECK 3
Force-Speed Power
Apply P = Fv.
A constant 500 N driving force acts parallel to a vehicle moving at 20 m/s. What power is delivered?
Reveal Answers
10.0 kW.
Why it works: P = Fv = 10,000 W = 10.0 kW.
How did it go? Use the revealed explanations to identify one specific relationship to revisit if needed.
Summary
Take one final look at the most important ideas from this review.
KEY TAKEAWAY 1
Net Work Changes Kinetic Energy
Use Wnet = ΔK when force work is easy to calculate.
KEY TAKEAWAY 2
Energy Methods Connect States
Relate initial and final states without solving every intermediate motion variable.
KEY TAKEAWAY 3
System Choice Controls the Accounting
Include external work, frictional transformation, and power consistently.
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