Nonconservative Work and Energy Loss
For a chosen system, the change in K+U equals work by external nonconservative forces; a stated energy loss must remain distinct from momentum changes during an impact.
Why this shows up in the exam
Rough tracks and inclines · Penetration and stopping · Repeated bounces or resisting media
Learn the idea
Friction and resistance change mechanical energy into other forms. Mechanical energy can decrease while total energy is conserved because friction, drag, or deformation transfers energy into thermal or internal modes.
🧠 Memory hook: Mechanical energy lost is energy transferred, not destroyed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- W_nc = Delta(K+U) — nonconservative energy balance
- W_f = -integral f_k ds — kinetic-friction work
- E_diss = E_i-E_f — positive dissipated energy
How to approach it
- 1Choose the system and states
- 2Calculate conservative energy changes
- 3Add signed nonconservative work and retain losses
Common slip-ups that cost marks
- •Conserving K+U despite friction
- •Using displacement instead of traveled distance for friction
- •Assigning dissipation a positive work sign
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg body speeds up from 3 m/s to 7 m/s. What net work is done on it?
More from Work, Energy and Power
Work and its calculation
Work is the energy transferred by a force acting over a distance, and can be calculated using the dot product, area under a force-displacement graph, or for variable and constant forces.
Conservation of energy
The law of conservation of energy states that energy cannot be created or destroyed, only transformed, including cases with energy loss and efficiency considerations.
Work-energy theorem
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, and applies to both constant and variable forces.
Conservative and non-conservative forces
Conservative forces, like gravity and spring force, conserve mechanical energy, while non-conservative forces, like friction, dissipate energy as heat.
Elastic potential energy
Elastic potential energy is the energy stored in a stretched or compressed spring, proportional to the square of its displacement.
Power
Power is the rate at which work is done or energy is transferred, and can be calculated as the product of force and velocity at any instant.