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Work Done by Sliding Friction

T0 review · 1 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Sliding friction converts translational kinetic energy into internal energy because the point where friction acts shifts relative to the center of mass of the deformable body, making the real work exceed the pseudowork by exactly the…

desk verdict A clean educational model of work vs pseudowork in sliding friction, with an abstract that oversells the role of non-rigidity until the discussion section supplies the necessary caveat. read the letter →

arxiv 2608.11157 v1 pith:VK7E532C submitted 2026-08-11 physics.ed-ph physics.class-phphysics.comp-ph

J. David Brown This is my paper · ORCID
classification physics.ed-phphysics.class-phphysics.comp-ph
keywords slidingfrictionpseudoworkwork-energyprincipleinternalenergythermalasperitymodelconservativeforcesnumericalsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Sliding friction turns motion into heat, and this paper proposes a mechanism for how that can happen even though the underlying forces are conservative. The answer is that real contacting surfaces are flexible: the point where friction acts can move a different distance than the body's center of mass, and the two distances are what distinguish real work from pseudowork. Using a numerical model of two flexible asperites interacting through an electric force, the paper shows that for both forced and free sliding, and for both repulsive and attractive interactions, the real work done by friction is greater than the pseudowork. By the invariant first law of thermodynamics, the difference is exactly the increase in internal energy, which in a real material would appear as heat. The same decomposition explains why a freely sliding block slows down on a stationary table but speeds up when viewed from its own rest frame, and why the direction of energy flow is ultimately a statistical question about initial conditions.

What carries the argument

The central object is the flexible asperite: a uniform bar plus a pendulum bob connected by a torsion spring, with the upper asperite's bob and lower asperite's bob interacting through a conservative electric potential that can be repulsive or attractive. The torsion spring is the mechanism that decouples the displacement of the point of application of the friction force from the displacement of the center of mass. The paper's key identity is the invariant first law of thermodynamics, $w - w_{\rm ps} = \Delta e_{\rm int}$: the difference between the true accumulated work $w$ (computed from forces at the moving contact point) and the pseudowork $w_{\rm ps}$ (computed as if all forces acted at the center of mass) equals the change in internal energy of the body. All four simulation scenarios are analyzed by splitting the interaction into approach and recede phases and comparing contact-point and center-of-mass displacements in each phase.

What would settle it

Increase the torsion-spring constants to very large values in the same numerical model: if internal energy still increases, or if the difference between real work and pseudowork stops matching the internal-energy change, the mechanism is falsified. Experimentally, one could track the actual contact point and compare the work computed there with the center-of-mass pseudowork and the measured temperature rise.

Watch

Extended reading notes

Core claim

The paper's central claim is that the work done by friction on a flexible body is not the same as the pseudowork computed at the body's center of mass; the excess of real work over pseudowork is precisely the change in internal energy. The model realizes this with two interacting flexible asperites whose interaction is a conservative electric force. Across forced and free sliding, with both repulsive and attractive interactions, the simulations show the same pattern: the contact point is shifted forward when the force aids the motion and lags behind when it opposes the motion, so real work is always greater than pseudowork, and the difference appears as internal energy. In forced sliding the total pseudowork vanishes, so the positive real work is entirely internal heating; in free sliding on a stationary surface the pseudowork is negative, so kinetic energy is lost while internal energy rises, and in the block's rest frame the sign of the pseudowork reverses and the block speeds up.

Load-bearing premise

The model's mechanism depends on the torsion springs having finite stiffness, so that the pendulum bob's displacement can differ from the center-of-mass displacement; if the springs were infinitely stiff, the contact point would move with the center of mass and the internal-energy increase would disappear.

Editorial extensions

If this is right

  • Forced sliding: even with zero net force and constant center-of-mass velocity, the total work is positive because the applied force and friction act through different distances; this positive work is the source of the internal energy that would appear as heat.
  • Free sliding on a stationary surface: friction's pseudowork is negative and large in magnitude during the approach phase and positive and small in the recede phase, so the body slows down while its internal energy increases.
  • Reference-frame dependence: in the frame where the block is initially at rest and the table moves, the same interaction gives positive pseudowork and the block speeds up; work and pseudowork change with frame, but their difference, the internal-energy change, does not.
  • The dynamics are time-reversible, so energy can in principle flow out of internal energy; the model therefore points to a statistical account, based on initial conditions, for why heating is the typical direction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the mechanism is geometric, the same work-minus-pseudowork decomposition should apply to other contact forces, such as rolling resistance or normal forces during bouncing, not only to sliding friction.
  • Continuously tuning the torsion-spring stiffness from very soft to infinitely stiff should interpolate between maximal heating and zero heating, giving a clean numerical test of whether compliance is necessary for the effect.
  • The frame dependence of pseudowork suggests textbook statements like 'friction always does negative work' are incomplete; the frame-independent quantity is the difference between real work and pseudowork, not the sign of the pseudowork.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 5 minor

Summary. The paper presents a two-asperite mechanical model of sliding friction. Each asperite consists of a bar and a torsion-spring-coupled pendulum; the pendulum bobs interact through a conservative electric force. The equations of motion are derived from Newton-Euler mechanics, and the work-energy and pseudowork-energy principles are used to define the change in internal energy as the difference between total work and total pseudowork. Numerical simulations for forced and free sliding, with repulsive and attractive interactions, show that internal energy increases and that the pseudowork equals the change in translational kinetic energy. A change of reference frame for free sliding is also analyzed. The paper concludes that flexibility is essential for understanding energy transfer in friction, with an explicit caveat about time reversibility and initial conditions.

Significance. If the results stand, the paper provides a simple, freely available computational model that illustrates a subtle topic in physics education: why a fundamentally conservative interaction can appear dissipative in sliding friction and why work and pseudowork differ. Strengths include the first-principles derivation of Eq. (7), the exact energy identities (11)-(15), numerical consistency of W = ΔK + ΔE_int, and the explicit discussion in Sec. XII of time reversibility and the role of initial conditions. The paper is well suited to a physics education journal. The main caveat is that the abstract's causal statement about non-rigidity should be qualified to reflect the Sec. XII premise of zero initial internal energy; the paper itself contains the necessary qualification, but the abstract and Sec. IX overstate it.

major comments (1)
  1. [Abstract and Sec. XII (with Eqs. (10) and (15))] The statement that 'because the asperites are not rigid, the work done in a typical interaction is greater than the pseudowork' is not a dynamical consequence of non-rigidity. Since e_int in Eq. (10) is positive semidefinite and all simulations set e_int(0) = 0 (Secs. VII-X), Eq. (15) gives w - w_ps = e_int(t) >= 0 identically at every instant. The nontrivial content is that e_int(t) does not return to zero after the encounter, and the time-reversed processes discussed in Sec. XII would give w - w_ps < 0 with the same flexible asperites. Please revise the abstract and the 'must be negative' statement in Sec. IX to state explicitly that the sign of w - w_ps is fixed by the zero-initial-internal-energy assumption, not by flexibility alone.
minor comments (5)
  1. [Sec. VIII] The text refers to 'Figure 6 shows the asperites at times t = 15.0, 19.3 and 26.0'; the correct reference is Figure 9.
  2. [Sec. XI] The text says 'the recede phase of Fig. IX'; this should be Fig. 11.
  3. [Abstract and throughout] There are numerous typographical errors, including 'psuedowork' and 'catergories' in the abstract, 'seprate' and 'fundmentally' in Sec. I, 'transfered' in Sec. I, 'minumum' in Sec. VIII, 'quanities' in Sec. XI, 'magnitiude' in Sec. IX, 'Therefpre.' in Sec. XII, and 'loose' for 'lose' in Sec. XII.
  4. [Sec. VII] The sentence 'Figure 5 shows shows that the total work decreases during brief periods' contains a duplicated word and should be corrected.
  5. [Sec. V] For clarity, it would help to state explicitly that the applied forces f_L and f_R in Eq. (16) do zero net work on the bar when the bar translates without rotating, which is the situation enforced by the choice of parameters and initial conditions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (15) is a derived identity, the model involves no fitted parameters, and the initial-condition dependence of the sign of W−Wps is explicitly acknowledged in Sec. XII.

full rationale

The paper's derivation chain is self-contained: the equations of motion (7) define a mechanical model; the work-energy principle (12) and pseudowork-energy principle (13) are derived from those equations; and Eq. (15), W−Wps = Δeint, is an algebraic consequence of those two principles. No experimental data are fitted, and no parameter is tuned to force the reported inequality W > Wps. The inequality in the simulations does follow partly from construction—since eint in Eq. (10) is positive semidefinite and all runs start with zero internal energy, Eq. (15) gives W−Wps = eint(t) ≥ 0—but the paper does not hide this. Sec. XII explicitly states that the processes are time-reversible, that 'the direction of energy transfer depends on initial conditions,' and that the conclusion of increasing internal energy relies on the assumption that a typical encounter begins with 'little or no internal energy.' The phase-by-phase displacement arguments in Secs. VII–X add mechanistic content beyond the identity and are checked against the computed work curves. The only self-reference is the author's numerical code (ref. [20]), which is externally runnable and is not used to justify an otherwise unsupported claim. The abstract's phrasing 'because the asperites are not rigid' is a compressed statement of a conditional result, but the paper itself supplies the needed condition. Therefore no circular step meets the quoted-evidence standard.

Assumptions & free parameters 4 free parameters · 4 assumptions · 2 invented entities

The model rests on standard mechanics plus several deliberately artificial modeling choices. The free parameters are all set by hand for convenience. The key ad hoc assumption is the torsion-spring compliance that generates the work-pseudowork difference, and the initial condition of zero internal energy that fixes the direction of energy flow.

free parameters (4)
  • Torsion spring constants κ, K and masses m1, m2, M1, M2 = varied per section (m1=1, m2=2, κ=2 in Sec. VII; m1=5, m2=3, κ=1 in Sec. VIII; m1=4, m2=8, κ=2 in Sec. IX)
    Chosen 'somewhat arbitrarily' (Sec. VII) to keep dynamics simple; no data are fitted.
  • Electric interaction strength qQ/(4πε0) = ±1/5
    Set to 1/5 (repulsive, Sec. VII) or -1/5 (attractive, Sec. VIII); no physical calibration; sign controls force direction.
  • Sliding speed vi = 1/2
    Initial x-velocity of upper asperite; arbitrary value defining the stationary-table frame.
  • Contact offset s = 0.3
    Small separation in y added for attractive interaction to avoid the R=0 singularity (Sec. VIII).
assumptions (4)
  • standard math Newton's laws, torque-angular momentum, and conservation of energy hold for the modeled asperites.
    Used to derive equations of motion (7) and energy balances (11)-(13).
  • domain assumption The force between asperites is electrostatic, V = qQ/(4πε0R), treated as conservative.
    Sec. V, Eq. (17). This is a stand-in for intermolecular forces; the paper notes it can be replaced by Morse or Lennard-Jones potentials.
  • ad hoc to paper Each asperite's compliance is modeled by a torsion spring with linear restoring torque -κ(θ-φ); the bar orientation is held fixed by applied forces f_L, f_R (Eq. 16).
    Secs. II and V. Deliberately artificial mechanical design that produces the work/pseudowork difference; not derived from physical contact mechanics.
  • ad hoc to paper Initial internal energy of the asperites is taken to be zero (pendulum at equilibrium, zero angular velocity).
    Secs. VII-X. This initial-condition choice, combined with time reversibility, guarantees that internal energy can only increase; the paper acknowledges this in Sec. XII.
invented entities (2)
  • Flexible asperite (bar + pendulum with torsion spring)
    purpose: Models one high point of each contact surface; its finite compliance makes the friction contact displacement differ from center-of-mass displacement.
    Pure pedagogical construct; the paper explicitly calls it a 'simple numerical model' and does not claim real surfaces have this exact structure.
  • Electric interaction between pendulum bobs
    purpose: Represents conservative intermolecular forces, allowing study of how friction-like energy transfer emerges from conservative forces.
    Coulomb form is a placeholder; the paper mentions Morse and Lennard-Jones potentials as alternatives, so it is not a claim about real charge distributions in sliding contact.

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Cite this review

Pith. "Pith review of Work Done by Sliding Friction." pith.science (2026). https://pith.science/paper/VK7E532C

@misc{pith2026260811157,
  author       = {Pith},
  title        = {Pith review of: Work Done by Sliding Friction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VK7E532C}},
  note         = {Machine review of arXiv:2608.11157}
}
read the original abstract

Friction does work when two objects in contact slide past one another. This process is studied using a simple numerical model consisting of two flexible asperites, one for each object. The force of friction is modeled as a conservative electric force that can be either attractive or repulsive. The concept of pseudowork plays an important role throughout the analysis. The difference between work and pseudowork is equal to the change in internal energy. Because the asperites are not rigid, the work done in a typical interaction is greater than the psuedowork, leading to an increase in internal energy. For a real physical system, this is the source of thermal energy. The processes discussed here fall into two categories: forced sliding and free sliding. With forced sliding, applied forces keep the objects moving with constant velocities. With free sliding, the only force on one of the objects (in the direction of motion) is friction. For free sliding, friction not only increases the internal energy but also decreases or increases the object's translational kinetic energy. The change in translational kinetic energy is determined by the pseudowork done by friction.

Figures

Figures reproduced from arXiv: 2608.11157 by the authors.

Figure 1
Figure 1. FIG. 1: Each asperite consists of a bar and a pendulum, connected with a torsion spring. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Position vectors and forces for the upper asperite. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Pendulum angle [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The model asperites at times [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The work done on the upper asperite for forced sliding with repulsive electric [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Forced sliding with repulsive electric interaction. The sequence shows the asperites [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Pendulum angle [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: The work done on the upper asperite for forced sliding with attractive electric [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Forced sliding with attractive electric interaction. The asperites are shown at [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Work done on the upper asperite for free sliding with repulsive interaction. [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: Free sliding with repulsive interaction. Asperites are shown at times [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Work done on the upper asperite for free sliding with attractive interaction. [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: Free sliding with repulsive interaction, viewed from the inertial frame in which [PITH_FULL_IMAGE:figures/full_fig_p023_13.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Reviewed August 12, 2026 · model on record in the stance chip above.