SCIENCE · INVESTIGATE AND EXPLAIN

Reject an impossible cord force before reading apparent weight

Fluid pressure increases with depth, so the resultant pressure force on a submerged body is upward. Archimedes’ principle gives its magnitude as the weight of the displaced fluid. For a completely submerged rigid object that displacement is the whole object volume; for a floating object only the immersed portion displaces liquid.

Learning outcome: Compare one cord-feasible, one floating-feasible and one neutral case. Save weight, full-submersion buoyancy, required signed tension and branch flags. Never interpret a rejected conditional force as an actual instrument value.

Starting recap

Declare density, pressure reference, flow regime and admissible force constraints. Convert area and volume units before balancing forces, mass or energy.

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Try

For 200 g in liquid density 800 kg/m³, weight is 2 N and buoyancy 1.6 N. A fully submerged overhead cord can support it with 0.4 N tension; free floating is not possible in this packet.

Open the experiment

Predict

A required upward cord tension of −0.5 N means:

Your prediction and reason

Experiment

Compare one cord-feasible, one floating-feasible and one neutral case. Save weight, full-submersion buoyancy, required signed tension and branch flags. Never interpret a rejected conditional force as an actual instrument value.

Test a cord constraint before interpreting apparent weight

Worked teaching model · synthetic values · Rigid object volume 200 cm³, g=10 m/s². Fully submerged object is attached only to an overhead cord, which can pull upward but cannot push downward. Compare freely floating equilibrium separately. No actual immersion or load test.

Object mass: 150 g Liquid density: 1000 kg/m³

Reset keeps your prediction, captures and practice history.

Required tension across liquid densities

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

Equivalent numerical coordinates for Required tension across liquid densities

conditional full-submersion balance

liquid density (kg/m³)	required upward tension (N)
600	0.3
615	0.27
630	0.24
645	0.21
660	0.18
675	0.15
690	0.12
705	0.09
720	0.06
735	0.03
750	0
765	-0.03
780	-0.06
795	-0.09
810	-0.12
825	-0.15
840	-0.18
855	-0.21
870	-0.24
885	-0.27
900	-0.3
915	-0.33
930	-0.36
945	-0.39
960	-0.42
975	-0.45
990	-0.48
1005	-0.51
1020	-0.54
1035	-0.57
1050	-0.6
1065	-0.63
1080	-0.66
1095	-0.69
1110	-0.72
1125	-0.75
1140	-0.78
1155	-0.81
1170	-0.84
1185	-0.87
1200	-0.9

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
Object weight	1.5	N
Full-submersion buoyancy	2	N
Required upward cord tension	-0.5	N
Overhead-cord equilibrium feasible	0	flag
Floating equilibrium feasible	1	flag
Floating displaced volume	0.00015	m³
Floating submerged fraction	0.75	ratio

Negative required cord tension rejects the overhead-cord constraint; it is not a negative scale reading.

Buoyancy equals displaced-fluid weight, not object weight in every state. For floating equilibrium, displaced volume is m/rho and must not exceed the object volume. At exact density matching, full submersion with zero cord tension is neutrally buoyant in this ideal model; uniqueness of vertical position is not implied.

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

Negative required cord tension rejects the overhead-cord constraint; it is not a negative scale reading.

Observation to attach to a capture

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

Understand

Declare the fluid, reference and evidence

Build the algebraic model

The packet uses a 200 cm³ object and an overhead cord. With upward positive, static force balance is T+B−mg=0, so the required cord tension is mg−ρVg. An ordinary cord can pull upward in this arrangement but cannot push down. A negative required value rejects the assumed fully submerged cord-supported equilibrium; it must not be displayed as a feasible negative scale reading.

Check the original numerical packet

At mass 150 g in liquid density 1000 kg/m³ with g=10, weight is 1.5 N and full-submersion buoyancy is 2 N. Required upward tension would be −0.5 N, so that constraint fails. If instead released to float without a cord, displaced volume is m/ρ=150 cm³, or 75% of its volume. These are two different physical configurations, not simultaneous conclusions about one supported state.

Challenge the assumptions and transfer

At mass 250 g in the same liquid, required submerged tension is +0.5 N, but free floating would require 250 cm³ displacement, more than the object has. At exact equal object and liquid densities, complete submersion gives zero cord tension and neutral buoyancy in this ideal model. It does not select a unique depth. Surface tension, trapped bubbles, compression and contact forces are excluded; no real immersion or lifting activity is requested.

Worked original case

For 200 g in liquid density 800 kg/m³, weight is 2 N and buoyancy 1.6 N. A fully submerged overhead cord can support it with 0.4 N tension; free floating is not possible in this packet.

Bounded investigation

Changed-case numerical practice

Try the changed case before feedback

A 120 g object floats in a liquid of density 800 kg/m³. Find displaced volume in cm³.

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 educational evidence. No pressure rigs, liquid handling, bodily measurements or physical exposure protocols are requested. Virtual admissibility does not certify real equipment safety, practical skill or independent mastery.

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

Why is buoyancy not always equal to the object’s weight?

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