Investigate the translational and rotational equilibrium conditions for non-concurrent parallel coplanar forces acting on a rigid beam supported at two points, verify that the sum of support reactions equals the total downward load (Σ F_y = 0) and the algebraic sum of moments vanishes about any axis (Σ τ = 0), and determine the unknown concentrated load weight and beam mass using ordinary least-squares regression. Explore a virtual apparatus, collect readings and analyse a graph.
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Readings are generated by an ideal model. The diagram is schematic and is not to scale.
The simulation assumes an idealized perfectly rigid beam without elastic bending deflection, frictionless knife-edge stirrups, and linear Hookean dynamometer springs. Simulated readings reflect a seasoned hardwood beam (tare weight W_bar = 2.000 N) carrying a reference concentrated load W_load = 5.000 N with dynamometer resolution of 0.01 N.
A seasoned 1.000 m hardwood beam of rectangular cross-section, engraved with millimeter scale graduations along its spine, exhibiting a verified center of gravity at x_cg = 0.500 m and a uniform self-weight W_bar = 2.000 N.
Two precision tubular spring dynamometers (0 to 10 N range, 0.01 N resolution) clamped to sturdy overhead retort stands, supporting the beam horizontally via knife-edge stirrups at fixed positions x_A = 0.100 m and x_B = 0.900 m.
A calibrated 5.000 N slotted brass mass secured onto a lightweight sliding collar with an index pointer that positions the concentrated load precisely along the beam span.
A miniature tubular spirit level placed centrally along the upper beam surface to ensure strict horizontal alignment, confirming that the dynamometer suspension cords remain strictly vertical.
Investigate the translational and rotational equilibrium conditions for non-concurrent parallel coplanar forces acting on a rigid beam supported at two points, verify that the sum of support reactions equals the total downward load (Σ F_y = 0) and the algebraic sum of moments vanishes about any axis (Σ τ = 0), and determine the unknown concentrated load weight and beam mass using ordinary least-squares regression. Suggested independent settings: 0.22, 0.34, 0.5, 0.66, 0.78 m.
Mount the unweighted hardwood beam between the two suspension dynamometers at support coordinates x_A = 0.100 m and x_B = 0.900 m. Adjust the vertical clamp heights on the retort stands until the central spirit level indicates perfect horizontal balance. Record tare readings R_A0 and R_B0 (each nominally 1.00 N).
Establishing a horizontal datum ensures that the suspension cords hang strictly vertical, guaranteeing that dynamometers measure pure normal reaction forces without trigonometric angular errors.
Sum the two unloaded dynamometer readings and confirm that R_A0 + R_B0 = W_bar = 2.00 N. Verify that taking moments about support A yields R_B0 · d_AB = W_bar · (x_cg - x_A), proving that the unweighted beam satisfies both equilibrium criteria.
Testing the baseline tare state verifies the absence of binding friction in the stirrups and confirms the nominal mass and center of gravity of the beam.
Attach the sliding rider with load W_load = 5.000 N at initial coordinate x = 0.22 m. Allow all motion to damp out completely, confirm the spirit level remains centered, and record the right dynamometer reaction reading R_B to the nearest 0.01 N.
Placing the load close to support A directs the majority of the concentrated weight to the left support, establishing the minimum reaction benchmark for R_B.
Simultaneously read left dynamometer reaction R_A. Verify that the sum of the reactions R_A + R_B equals the total system weight W_total = W_bar + W_load = 2.00 N + 5.00 N = 7.00 N within 0.02 N experimental tolerance.
Checking the force sum at every position confirms that vertical translational equilibrium (Σ F_y = 0) is maintained continuously without unmodeled vertical forces.
Systematically slide the load rider to positions x = 0.34 m, 0.50 m, 0.66 m, and 0.78 m. At each station, check beam horizontality, let transient oscillations settle, and record the corresponding right reaction force R_B.
Traversing the span shifts the load linearly toward support B, generating five widely spaced data points across a broad dynamic range (from 1.75 N to 5.25 N).
Plot right reaction R_B against load position x. Fit an ordinary least-squares regression line to compute slope S and intercept b. Multiply slope S by span d_AB = 0.800 m to determine W_load, and compute beam weight W_bar from intercept b.
Least-squares regression separates random reading noise from the true physical slope, yielding the load weight with quantifiable standard errors.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Load position x (m) | Support reaction R_B (N) | Load position x (m) | Support reaction R_B (N) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.