= Two-cart force-probe test of Newton's third law
Oberlin College's documented demonstration uses a track, two collision carts, two <force probes> set to the $50\,\mathrm N$ range, added $500\,\mathrm g$ bars, and a laptop with a Vernier interface. Preparation consists of entering the <measurement calibration>, securing the <force probes> to the carts, and zeroing them. Rubber stoppers serve for <elastic collisions>, clay for <inelastic collisions>, and hooks with string for pulling. Comparing the two <force> records tests the mutual interaction; adding <mass> to one cart tests whether unequal <masses> change the equality. <Collision Carts and Force Sensors>[Oberlin College, Collision Carts and Force Sensors, Apparatus, Description, and Notes: ranges, mounting, zeroing, attachments, and unequal-mass control]{ref}
Vernier's <force probe> uses a bending beam with <strain gauges>; changing <electrical resistance> produces a <voltage> readout calibrated as <force>. Its manual recommends zeroing in the working orientation. If recalibration is needed, use an unloaded reading and a known suspended <gravitational weight>; for the $50\,\mathrm N$ range its example is $1\,\mathrm{kg}$ giving $9.8\,\mathrm N$. Re-zero after changing orientation. The manual quotes calibrated accuracy $\pm0.2\,\mathrm N$, distinct from the $0.05\,\mathrm N$ resolution of that range, and warns that the interface's data-collection rate can limit collision measurements. <Dual-Range Force Sensor User Manual>[Vernier, Dual-Range Force Sensor User Manual, Using the Product; Calibration; Specifications; How the Sensor Works; Compatibility Notes, note 1]{ref}
The following sampling and control choices are proposed additions to that documented experiment. Level the track and check unloaded motion in both directions for slope and <friction>. Use a soft bumper and one interface for simultaneous records; start before contact and stop after separation. A trial <sampling rate> of $1000\,\mathrm{s^{-1}}$, if supported, would put about 100 samples across a $0.10\,\mathrm s$ interaction. Increase the <sampling rate> and repeat until the peak and integrated <impulse> comparison are stable; a large sample count alone does not establish adequate response. Measure each total moving <mass>, including the <force probe> and added bars.
Convert both channels to the same right-positive <force> convention. Oppositely facing <force probes> can have matching raw signs because their local positive directions differ; check each sign by a gentle push of known direction before the run. Overlay $F_{B\mathrm{\ on\ }A}(t)$ and $-F_{A\mathrm{\ on\ }B}(t)$, and also examine their signed sum. Integrate both over the same contact interval to compare <impulses>. Repeat with added <mass> on one cart, exchange the probes between carts, and check unloaded zeros before and after. These controls help distinguish a physical <mass> change from a channel offset or gain error.
Agreement within <measurement error> supports the pair-interaction model over the resolved interval; it does not establish exact equality at arbitrarily short <time> scales. Misalignment, a loose mounting, sensor-beam dynamics, saturation, unequal timing, and zero drift can spoil the comparison. Track <friction> and cable pulls are additional <external forces>; a probe measuring bumper contact need not measure the entire net <force> on its cart. If a massive connector carries appreciable changing <momentum>, compare the full cart–connector collection rather than assuming its endpoint <forces> are an instantaneous cart-to-cart pair. The constructed pulse diagram above illustrates what to compare, and supplies no measurements from this apparatus.
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