Where mechanical energy goes with friction
You will be able to: Include dissipated energy in a complete energy account and find stopping distance.
When a sliding block stops, has its energy disappeared?
A sliding book slows on a table. Its kinetic energy decreases, while the book and table become imperceptibly warmer. Total energy is conserved even though the mechanical-energy total decreases.
A useful starting point: Static and kinetic friction →
Words and symbols before equations
- Dissipation
- Conversion of organized mechanical energy into forms such as thermal energy or sound.
- Thermal-energy increase ΔE_th
- Internal energy gained by the contacting materials, in J.
- Sliding distance d
- Length of the relative sliding path, in m.
What this picture assumes
2 kg block starts at 4 m/s on a fixed horizontal surface; constant kinetic friction 4 N. No other work. Thermal energy is assigned to the combined block–surface system. The motion stops at 4 m.
Connect the picture to the physics
For a block sliding on a fixed level surface with constant kinetic friction f_k, friction’s work on the block is −f_kd. The lost kinetic energy is positive f_kd. This sign difference matters.
Include block and surface in a larger isolated system: K_i=K_f+ΔE_th, assuming thermal energy is the only other change. If the surface is left outside, describe the effect through external friction work on the block instead. Do not include both accounts for the same transfer.
For constant friction and no other working forces, stopping occurs when f_kd_stop=½mv_i². Doubling the starting speed quadruples the stopping distance if friction stays constant. Beyond the stopping point, the original sliding model no longer applies.
A worked example, step by step
A 2 kg block slides at 4 m/s on a fixed level surface with 4 N kinetic friction. Find its kinetic energy after 2 m and the full stopping distance.
- Initial K=½(2)(4²)=16 J.
- After 2 m, friction has done −8 J, so K=8 J and the book–surface system has gained 8 J of thermal energy.
- At stopping, all 16 J have been converted: d_stop=16/4=4 m.
- Do not extend the expression to negative K for distances beyond 4 m. The block has already stopped.
Mechanical energy can decrease without violating total-energy conservation.
If the thermal-energy increase is 6 J, what is the friction work on the block in this fixed-surface model?
Compare with an explanation
−6 J, provided friction is the only source of that thermal increase and the stated assumptions hold.
Predict. Change one thing. Explain.
The 2 kg block begins with 16 J and friction is 4 N. Change the proposed sliding distance. Track kinetic and thermal energy up to the stopping point, then inspect why longer distances are flagged.
Actual reached distance 2 m; K=8 J; thermal gain=8 J; speed=2.83 m/s. Still sliding.
2 kg block starts at 4 m/s on a fixed horizontal surface; constant kinetic friction 4 N. No other work. Thermal energy is assigned to the combined block–surface system. The motion stops at 4 m.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use a work, energy or power relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA 1 kg block slides at 6 m/s with constant friction 3 N. (a) Find K_i. (b) Find stopping distance. (c) Find ΔE_th when stopped. (d) Explain why the isolated block+surface system can conserve total energy but not mechanical energy.
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Compare with the answer and four-point rubric
- 1 point: 18 J.
- 1 point: 6 m.
- 1 point: 18 J.
- 1 point: Kinetic energy converts to internal thermal energy; the total remains constant while K+U decreases.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Is thermal-energy gain negative?
No; the modeled increase is positive f_kd.
RECALL 2Why is friction work negative here?
Its force opposes the block’s sliding displacement.
RECALL 3When must the sliding calculation stop?
When available kinetic energy reaches zero.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Where mechanical energy goes with friction
- Fixed surface, constant sliding friction: ΔE_th=f_kd and W_f=−f_kd.
- K_i=K_f+ΔE_th in the isolated block+surface model.
- d_stop=mv_i²/(2f_k), when friction alone removes kinetic energy.
Remember: Mechanical energy can decrease without violating total-energy conservation.
Conditions: 2 kg block starts at 4 m/s on a fixed horizontal surface; constant kinetic friction 4 N. No other work. Thermal energy is assigned to the combined block–surface system. The motion stops at 4 m.
Refresh Kid · Unit 3 · Objectives 3.4.B, 3.4.C · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 3.4, objectives 3.4.B, 3.4.C. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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