SCIENCE · INVESTIGATE AND EXPLAIN

Close a thermal ledger at the actual stopping point

A 2 kg point begins at 4 m/s on a level surface, so its kinetic energy is 16 J. A constant kinetic friction magnitude f opposes motion. For the point alone, friction work over actual forward distance d is−fd, giving K=16−fd. This equation is valid only while that forward sliding branch exists.

Learning outcome: Compare requested distances1,2,4 m at friction 6 N, then double or halve friction where controls permit. Record requested versus actual distance and show both the point-only and object-plus-surface accounts without double-counting.

Starting recap

Choose the system, interval and reference frame before using a conservation statement. Keep vector momentum, scalar energy and transferred power distinct.

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Try

For f=8 N and requested distance 2 m, the endpoint is exactly the stop, with zero kinetic energy and 16 J thermal gain. Equality is reached; it is not an extra post-stop interval.

Open the experiment

Predict

After the unforced point stops on the level surface, this model predicts:

Your prediction and reason

Experiment

Compare requested distances1,2,4 m at friction 6 N, then double or halve friction where controls permit. Record requested versus actual distance and show both the point-only and object-plus-surface accounts without double-counting.

End the sliding energy ledger at the first stop

Worked teaching model · synthetic values · A 2 kg point starts rightward at 4 m/s on a level surface. Constant kinetic friction is the only horizontal force until it stops; afterward there is no drive and it remains at rest. Thermal gain belongs to the selected object-plus-surface system.

Constant resisting friction: 6 N Requested path length: 4 m

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Sliding energy before the first stop

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: accessible sliding energy (solid). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Sliding energy before the first stop

accessible sliding energy

traveled distance (m)	kinetic energy (J)
0	16
0.0666667	15.6
0.133333	15.2
0.2	14.8
0.266667	14.4
0.333333	14
0.4	13.6
0.466667	13.2
0.533333	12.8
0.6	12.4
0.666667	12
0.733333	11.6
0.8	11.2
0.866667	10.8
0.933333	10.4
1	10
1.06667	9.6
1.13333	9.2
1.2	8.8
1.26667	8.4
1.33333	8
1.4	7.6
1.46667	7.2
1.53333	6.8
1.6	6.4
1.66667	6
1.73333	5.6
1.8	5.2
1.86667	4.8
1.93333	4.4
2	4
2.06667	3.6
2.13333	3.2
2.2	2.8
2.26667	2.4
2.33333	2
2.4	1.6
2.46667	1.2
2.53333	0.8
2.6	0.4
2.66667	0

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

Calculated quantities under the declared measurement model
Quantity	Value	Unit
Initial kinetic energy	16	J
Stop distance	2.66667	m
Actual traveled distance	2.66667	m
Requested endpoint reached	0	flag
Friction work on point	-16	J
Object-plus-surface thermal gain	16	J
Remaining kinetic energy	0	J
Endpoint speed	0	m/s

Mechanical energy decreases while the larger object-plus-surface energy account remains closed.

Kinitial=16 J and friction removes f d until dstop=16/f. Beyond that event the point stays still without a drive, so there is no extra sliding or additional friction heating. Do not subtract friction work and add the same thermal gain as two separate losses in the same system account; they describe the transfer using different boundaries.

Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.

Mechanical energy decreases while the larger object-plus-surface energy account remains closed.

Observation to attach to a capture

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Understand

Define the energy or momentum system

Build the algebraic account

The first stop occurs at dstop=16/f. With no drive afterward, the point remains at rest. If the requested path length exceeds dstop, the actual endpoint is the stop, not the requested location. Continuing to subtract fd beyond the stop would invent negative kinetic energy and additional friction heating without motion.

Check an original packet

For a larger system containing the object and the surface, the same interaction converts16−K joules into thermal energy under the stipulated closed model. Do not subtract friction work as an external loss and then count the same thermal conversion as a second loss within that same boundary. State whether the surface belongs to the system before writing an energy equation.

Test the domain and evidence

At f=6 N, stopping distance is 8/3≈2.66667 m. A requested4 m endpoint is not reached; all16 J of initial kinetic energy have become thermal energy by the stop. A requested2 m endpoint is reached with K=4 J and speed 2 m/s. Real friction can vary, generate deformation and exchange heat with surroundings; none is measured by this virtual constant-force packet.

Worked original packet

For f=8 N and requested distance 2 m, the endpoint is exactly the stop, with zero kinetic energy and 16 J thermal gain. Equality is reached; it is not an extra post-stop interval.

Bounded investigation

Changed-case numerical practice

Try the changed case before feedback

A point has initial kinetic energy 15 J and faces constant resisting friction 3 N on a level surface, with no later drive. What is its stopping distance in metres?

Numerical result in the requested units

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and limits

Original content checked 30 October 2026 against OpenStax College Physics 2e. All packets and diagrams are synthetic teaching evidence. No physical launches, collisions, spring releases, explosive processes or equipment-safety judgments are requested. Retained self-reports and public numerical feedback do not certify supervised laboratory practice or independent mastery.

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Public practice checks a specific claim. It does not establish independent mastery.

Which system boundary makes thermal gain an internal energy change rather than an omitted transfer?

Your explanation and limitations

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