Precision Linear Dynamic Track and End Pulley
A rigid 2.0 m extruded aluminum guide track equipped with micro-adjusting leveling thumbscrews, metric scale, and an ultra-low-friction ball-bearing end pulley.
Physics / Newton’s second law of motion
FREE TO EXPLOREEXPERIMENT 20 · PHYSICS LABORATORY
Verification of Newton’s second law of motion: Force, mass, and acceleration on a linear track
Investigate the fundamental dynamic relation between applied net force F, system inertial mass M, and linear acceleration a on a precision air track or low-friction dynamic cart system, verifying Newton’s second law a = F / M at constant total mass M = 1.200 kg and extracting system mass from the inverse slope of the acceleration versus force graph. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
ACCELERATION A—
MEASUREMENT STATUS
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.
Simulation assumptions and limits
This virtual experiment assumes a massless, frictionless pulley, a perfectly inextensible cord of negligible mass, and exact friction compensation along the linear guide track. It neglects air resistance, cord elasticity, pulley bearing drag, and rotational inertia of the wheels and pulley. Generated readings reflect ideal Newtonian dynamics; physical experiments will exhibit small random timing scatter from photogate clock jitter. Theoretical acceleration: a = F / M_total. Linearized relation: a = (1 / M_total) · F. The ordinary least-squares regression extracts the slope S = 1 / M_total, from which total system mass is recovered as M_total = 1 / S. Reference total system mass M_total = 1.200 kg.
Know your apparatus.
Low-Friction Dynamic Cart with Mass Storage Posts
Precision wheeled cart (mass 800.0 g) with low-friction sapphire/ball-bearing axles, interrupter flag for optical gating, and brass mass mounting posts.
Dual-Beam Infrared Photogate Timing Chronometer
Two optical photogates spaced at a fixed distance D = 0.500 m along the track, connected to a digital microsecond counter that computes instantaneous velocities and uniform acceleration.
Precision Slotted Brass Weight Set and Tow Cord
Calibrated slotted masses (total 400.0 g) transferred between cart and lightweight mass hanger via an inextensible monofilament tow cord.
FOLLOW THE METHOD
A reason behind every step.
Investigate the fundamental dynamic relation between applied net force F, system inertial mass M, and linear acceleration a on a precision air track or low-friction dynamic cart system, verifying Newton’s second law a = F / M at constant total mass M = 1.200 kg and extracting system mass from the inverse slope of the acceleration versus force graph. Suggested independent settings: 0.3, 0.6, 0.9, 1.2, 1.5 N.
Track Leveling and Friction Compensation Alignment
Inspect the aluminum track with a precision spirit level. Place the unweighted cart on the track and give it a gentle nudge. Adjust the leveling screw at the non-pulley end until the cart coasts smoothly along the entire track at constant velocity without speeding up or slowing down. This small angle of inclination exactly balances mechanical rolling friction.
Why this step matters
Compensating for residual rolling friction ensures that the net accelerating force acting on the system is purely the gravitational tension supplied by the hanging mass.
Total System Mass Verification and Assembly
Determine the tare mass of the dynamic cart (800.0 g) and the empty weight hanger (50.0 g) on a digital laboratory balance. Add slotted brass weights totaling 350.0 g to the cart's storage posts, bringing the combined system mass to exactly M_total = 800.0 + 50.0 + 350.0 = 1200.0 g (1.200 kg). Record this invariant reference mass.
Why this step matters
Maintaining an exact known system mass is mandatory to isolate the direct proportionality between applied force and acceleration.
Photogate Positioning and Electronic Timer Configuration
Mount the first photogate at the 0.500 m mark and the second photogate at the 1.000 m mark, setting the inter-gate separation distance to D = 0.500 m. Measure the width w of the cart's interrupter flag using Vernier calipers (e.g., w = 0.0200 m). Set the digital timer to dual-gate acceleration mode.
Why this step matters
Accurate gate separation and flag width are required to compute initial and final velocities v₁ = w/Δt₁ and v₂ = w/Δt₂, from which a = (v₂² - v₁²) / (2D).
Setting the Initial Accelerating Force via Mass Transfer
Transfer slotted weights from the cart to the hanging hanger to achieve the first accelerating force F = 0.30 N (hanging mass m_h ≈ 30.6 g). Pass the monofilament cord over the low-friction end pulley, ensuring the cord runs parallel to the track surface.
Why this step matters
Transferring weights from the cart preserves the total mass M_total, whereas adding weights from the bench would alter the system inertia.
Cart Release and Acceleration Measurement
Pull the cart back to the starting release latch (at least 0.20 m before the first photogate to allow smooth acceleration). Release the cart from rest without imparting any initial impulse. Catch the cart gently after it clears the second photogate before it strikes the end bumper. Record the acceleration a displayed on the digital timer.
Why this step matters
Releasing smoothly from a fixed position ensures steady uniform acceleration through both photogates without mechanical disturbance.
Systematic Force Sweep and Linear Regression Analysis
Repeat the release sequence for applied forces of 0.60 N, 0.90 N, 1.20 N, and 1.50 N by transferring additional slotted masses from the cart to the hanger. Construct a graph of acceleration a versus applied force F. Perform an ordinary least-squares linear fit to evaluate the slope S, and compute the experimental system mass as M = 1 / S.
Why this step matters
A five-point systematic sweep over a five-fold force range demonstrates linearity, tests the validity of a = F/M, and extracts an unbiased estimate of total system mass.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
a = (1 / M_total) · F ⇔ M_total = 1 / S
| # | Accelerating force F (N) | Acceleration a (m s⁻²) | Applied force F (N) | Acceleration a (m s⁻²) | Remove |
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No readings yet. Take a virtual measurement and record it.
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