Transform relative walking into two ground displacements
An internal displacement is not necessarily a ground displacement. Model a point person of mass m on a translating 80 kg base, with no external horizontal force and initially stationary whole-system center. The model specifies only a relative displacement ℓ; it supplies no forces, walking time or energy conversion.
Learning outcome: Solve the weighted center constraint and independently verify the relative-displacement relation. Vary mass at fixed relative displacement.
Starting recap
Integrate signed force and normalized mass moments. Specify the system before conserving momentum, and independently test energy and observation constraints.
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At m = 20 kg and ℓ = 2 m, the base moves −0.4 m and the point +1.6 m. The relative difference remains exactly 2 m.
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For m = 40 kg and relative displacement 3 m, the point ground displacement is:
Experiment
Solve the weighted center constraint and independently verify the relative-displacement relation. Vary mass at fixed relative displacement.
Use the closed-system center for a moving internal load
Worked teaching model · synthetic values · Ideal horizontal base mass80 kg and point person-model initially at rest, no net external horizontal force, translation only. Relative displacement is prescribed; no water drag, rotation, balance or physical activity instructions. Initial chosen coordinates coincide at0; only changes are compared.
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Ground displacements consistent with a fixed system center
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: base (solid).2: person-model (dashed). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Ground displacements consistent with a fixed system center
base
| relative displacement (m) | ground displacement (m) |
|---|---|
| 0 | 0 |
| 3 | -1 |
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.
person-model
| relative displacement (m) | ground displacement (m) |
|---|---|
| 0 | 0 |
| 3 | 2 |
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.
| Quantity | Value | Unit |
|---|---|---|
| Base ground displacement | -1 | m |
| Person-model ground displacement | 2 | m |
| Prescribed relative displacement | 3 | m |
| Whole-system center displacement | 0 | m |
| Combined unchanged mass | 120 | kg |
Internal motion changes component positions while the force-free whole-system center remains fixed.
Let base shift d and relative motion ell. The person ground shift is d+ell, so Mbase d+mperson(d+ell)=0. Hence d=−m ell/(Mbase+m). Neither component is stationary in the ground frame simply because the total center is. The model gives endpoint displacement, not a unique time history or separate energy budget.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
Internal motion changes component positions while the force-free whole-system center remains fixed.
Let base shift d and relative motion ell. The person ground shift is d+ell, so Mbase d+mperson(d+ell)=0. Hence d=−m ell/(Mbase+m). Neither component is stationary in the ground frame simply because the total center is. The model gives endpoint displacement, not a unique time history or separate energy budget.
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Why cannot endpoint displacement data determine kinetic energy?
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