SCIENCE · INVESTIGATE AND EXPLAIN

Infer a load location while testing the support model

A uniform4 m beam has weight 12 N at its center x=2 m. A separate24 N point load is at x. Upward-only supports are at 1 and 3 m. The load and both support forces belong on the beam’s recipient diagram. Equal-and-opposite forces exerted by the beam on its supports act on different recipients and do not cancel the support forces here.

Learning outcome: Compare a centered load, both zero-reaction boundaries and an outside state. At one feasible state vary the sensor offset and retain inferred position plus force residual. Propose an independent geometry or weight check rather than treating a fitted coordinate as a measurement of truth.

Starting recap

Declare the axis, angular units, recipient and valid contact or material branch. Distinguish supplied shape factors from independently measured inertia.

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Try

At x=0.5 m, R=0,L=36 N is a marginal feasible two-support state. At x=0, R=−6 N is impossible for an upward-only support. Clipping it to zero without re-solving would break the balance equations.

Open the experiment

Predict

An inferred negative upward-only support reaction means:

Your prediction and reason

Experiment

Compare a centered load, both zero-reaction boundaries and an outside state. At one feasible state vary the sensor offset and retain inferred position plus force residual. Propose an independent geometry or weight check rather than treating a fitted coordinate as a measurement of truth.

Infer a load position only after validating support contact

Worked teaching model · synthetic values · Uniform 4 m beam weight 12 N acts at x=2; extra 24 N point load at selected x. Upward-only supports at x=1 and 3. Synthetic right-sensor offset is applied only to feasible static states. Negative required reaction invalidates assumed two-contact equilibrium; no actual load rating.

Point-load coordinate: 2 m Right reaction readout offset: 1 N

Reset keeps your prediction, captures and practice history.

Conditional right reaction versus point-load coordinate

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

Equivalent numerical coordinates for Conditional right reaction versus point-load coordinate

conditional static balance

point-load coordinate (m)	required right reaction (N)
0	-6
0.1	-4.8
0.2	-3.6
0.3	-2.4
0.4	-1.2
0.5	0
0.6	1.2
0.7	2.4
0.8	3.6
0.9	4.8
1	6
1.1	7.2
1.2	8.4
1.3	9.6
1.4	10.8
1.5	12
1.6	13.2
1.7	14.4
1.8	15.6
1.9	16.8
2	18
2.1	19.2
2.2	20.4
2.3	21.6
2.4	22.8
2.5	24
2.6	25.2
2.7	26.4
2.8	27.6
2.9	28.8
3	30
3.1	31.2
3.2	32.4
3.3	33.6
3.4	34.8
3.5	36
3.6	37.2
3.7	38.4
3.8	39.6
3.9	40.8
4	42

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
Required left upward reaction	18	N
Required right upward reaction	18	N
Two-contact equilibrium feasible	1	flag
Total downward load	36	N
Indicated right support force	19	N
Inferred point-load coordinate	2.08333	m
Coordinate inference bias	0.0833333	m
Force closure residual with unbiased left sensor	1	N

A reaction reading locates a load only under the assumed equilibrium, weight and calibration premises.

About the left support at x=1, 2R=12(2−1)+24(x−1), hence R=12x−6 and L=36−R. An additive right-force offset b produces coordinate error b/12 m. An independent left reading exposes force-closure residual b, but a consistent pair still needs other premise checks. Beyond the admissible contact interval, lift-off or another constraint must be analyzed rather than clipping the reactions.

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

A reaction reading locates a load only under the assumed equilibrium, weight and calibration premises.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Choose the axis, reference or material model

Build the algebraic relationship

Force balance gives L+R=36 N. Taking moments about the left support gives 2R=12(2−1)+24(x−1), so R=12x−6 and L=42−12x. Both must be nonnegative for the assumed two-contact state. The feasible load-coordinate interval is 0.5≤x≤3.5 m, with one reaction zero at each endpoint.

Check the original numerical packet

The original sensor packet adds offset b only to the right reaction readout when the static branch is feasible. Inverting that reading gives x_inferred=(R_read+6)/12, so coordinate bias is b/12 m. At true x=2,b=1 N, required reactions are18 N each but the right instrument reads19 N; inferred x is 25/12≈2.08333 m. An unbiased left reading gives a force-closure residual1 N.

Test the boundary and independent evidence

At x=0 or 4 the equations require one support to pull downward. That rejects the assumed static contact configuration; the workbench does not issue a fictitious static sensor reading for it. Lift-off or a different support must be modeled. A reading consistent with both balances still does not prove every calibration, load weight or geometry premise. This is not a structural load or stability certification.

Worked original case

At x=0.5 m, R=0,L=36 N is a marginal feasible two-support state. At x=0, R=−6 N is impossible for an upward-only support. Clipping it to zero without re-solving would break the balance equations.

Bounded investigation

Changed-case numerical practice

Try the changed case before feedback

For this beam, an unbiased right reaction is 24 N. Find the point-load coordinate x 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 records are supplied or generated teaching evidence. No rotating equipment, applied loads, material tests or physical assembly is requested. An admissible virtual model state does not certify real equipment safety, supervised practical skill or independent mastery.

Apply

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

Why are equilibrium equations necessary but not sufficient when contacts are unilateral?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

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