You will be able to
- Calculate the work done by a constant or variable force using the dot product and integration along a path.
- Apply the work-energy theorem to relate changes in kinetic energy to net work on a particle.
- Identify conservative forces and write the corresponding potential energy functions, such as gravitational and spring potentials.
- Use conservation of mechanical energy to solve motion problems involving springs, gravity, and inclined paths.
- Distinguish conservative from non-conservative forces and account for energy losses such as friction.
Good to know first
- Newton's laws of motion and free-body diagrams
- Basic vector algebra, including dot products
- Single-variable calculus, including integration
- Familiarity with velocity and acceleration for constant-acceleration motion
Syllabus
6 lessons
- 1
Motivation and recap of kinetic energy Free
This lesson recaps why energy is a powerful idea in physics, using a problem set on a ball moving in a circle to show that Newton's force equations can get messy. It sets up the work-energy ideas that the rest of the chapter develops.
- 2
Work Done by a Constant Force Beyond Pass
This lesson shows how work is defined as force times displacement along the force, and how it links to the change in kinetic energy. It also introduces power as work per second and the units used for them.
4 formulas3 exercises3 questions - 3
Deriving the Work-Energy Theorem Beyond Pass
This lesson shows how the work done by a varying force, added up in tiny steps, equals the change in kinetic energy. You will see why the work is the area under a force-versus-position graph and how that area becomes a difference of one function evaluated at two points.
4 formulas1 exercise3 questions - 4
Work by variable forces and integration along a path Beyond Pass
When a force changes along the path, the work it does is found by adding up tiny pieces of work, which is exactly what an integral does. This lesson shows how the work-energy theorem turns that integral into kinetic energy and potential energy terms, and how a spring and gravity fit this pattern.
4 formulas2 exercises3 questions - 5
Conservative forces and potential energy Beyond Pass
A conservative force lets us store work as potential energy U, so that the total energy K + U stays constant. We see how U follows from the force for gravity and for a spring, and how friction breaks this rule.
4 formulas3 exercises4 questions - 6
Conservation of Mechanical Energy and Taylor Expansions in Worked Examples Beyond Pass
This lesson shows how the work-energy theorem turns into a conserved quantity, the total mechanical energy E = K + U, when only conservative forces do work. It also reviews the Taylor expansion idea used to approximate small changes, such as ΔF ≈ (dF/dx)Δx, which the lecturer uses to justify the work and energy bookkeeping.
1 code4 formulas3 build steps3 exercises3 questions
Free preview · Lesson 1 in full
Motivation and recap of kinetic energy
This lesson recaps why energy is a powerful idea in physics, using a problem set on a ball moving in a circle to show that Newton's force equations can get messy. It sets up the work-energy ideas that the rest of the chapter develops.
Lessons 2–6
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Made by Beyond from the video “5. Work-Energy Theorem and Law of Conservation of Energy” by YaleCourses. The video plays in YouTube's own player. Watch it on YouTube · All lessons