Precision Vertical Drop Column and Millimeter Scale
Provides a rigid, vibration-isolated vertical structural guide 1.5 m in height, equipped with a graduated millimeter rule and dual-axis leveling tripod to maintain exact plumb alignment.
Physics / Acceleration due to gravity by free fall
FREE TO EXPLOREEXPERIMENT 19 · PHYSICS LABORATORY
Uniformly accelerated motion and determination of acceleration due to gravity by free fall timing
Determine the acceleration due to terrestrial gravity g by measuring transit elapsed times of a dense metallic plummet released from rest across varying vertical drop heights h using precision spark chronometry, and verify the classical quadratic kinematic relation h = 1/2 g t² through ordinary least-squares linear regression. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
TIME OF FALL T—
MEASUREMENT STATUS
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Timing is generated from the model; a short on-screen trial represents a longer physical interval. Animation is illustrative.
Simulation assumptions and limits
This virtual experiment assumes uniform one-dimensional gravitational acceleration g = 9.80665 m s⁻² without aerodynamic drag, air buoyancy, or mechanical friction. It neglects electromagnetic release hysteresis delay, photogate optical beam transit latency, and finite bob radius offsets. The generated fall times represent an idealized vacuum trajectory; virtual data cannot reproduce physical air turbulence or building floor vibrations. Theoretical fall time: t = sqrt(2h / g). Linearized relation: h = (1/2 g) · t². The ordinary least-squares fit extracts the slope S = 1/2 g, from which g = 2 · S. Reference standard gravity g = 9.80665 m s⁻².
Know your apparatus.
Electromagnetic Plummet Release Solenoid
Suspends the ferromagnetic plummet prior to release and rapidly demagnetizes via an inductive quench diode upon circuit interruption to ensure zero initial velocity without mechanical disturbance.
Precision Digital Microsecond Chronometer
Measures the transit time interval from the instant of electrical circuit interruption to mechanical strike-plate contact with a timebase resolution of 0.1 ms (0.0001 s).
Aerodynamic Cylindrical Steel Plummet and Cushion Trap
A dense, precision-machined steel cylinder with a conical nose designed to minimize air drag and provide a repeatable electrical/mechanical impact surface, landing in an energy-absorbing foam pad.
FOLLOW THE METHOD
A reason behind every step.
Determine the acceleration due to terrestrial gravity g by measuring transit elapsed times of a dense metallic plummet released from rest across varying vertical drop heights h using precision spark chronometry, and verify the classical quadratic kinematic relation h = 1/2 g t² through ordinary least-squares linear regression. Suggested independent settings: 0.2, 0.4, 0.6, 0.8, 1.0 m.
Column Plumb Alignment and Leveling
Inspect the vertical column using a dual-axis spirit level positioned against the guide rail. Adjust the leveling foot screws at the tripod base until the spirit level bubbles are perfectly centered along two orthogonal axes. Ensure the column is clamped securely to prevent wobble during plummet impact.
Why this step matters
Any tilt in the column causes the falling plummet to drift laterally or scrape against guide brackets, introducing friction and deviating from purely one-dimensional vertical free fall.
Electromagnetic Suspension and Demagnetization Verification
Energize the release solenoid with the designated DC holding current. Place the ferromagnetic apex of the steel plummet against the pole piece. Verify that the plummet hangs freely and centralizes precisely over the impact strike pad. Test the quick-release switch to confirm that residual core magnetization does not cause mechanical sticking upon opening.
Why this step matters
Residual magnetic remanence in the core creates an unrecorded mechanical release delay of several milliseconds, systematically shortening the perceived fall distance or distorting the timebase.
Baseline Height Scale Zero-Reference Metrology
Lower the plummet manually until its bottom edge touches the top surface of the mechanical strike pad. Check the height reading on the millimeter vernier carriage. Record any index zero-offset correction so that all subsequent height settings reflect the true transit distance from the bottom of the bob to the strike plate.
Why this step matters
An uncorrected zero offset shifts all height measurements by a constant error, producing a false non-zero intercept on the h versus t² graph.
Setting Drop Height and Arming the Electronic Chronometer
Position the release carriage at the initial test height of 0.20 m (200 mm) using the vernier index mark. Lock the clamping screw firmly. Reset the digital microsecond chronometer display to 0.0000 s. Suspend the steel plummet from the electromagnet and confirm the readiness status indicator.
Why this step matters
Careful locking prevents carriage slippage during the release transient, ensuring the geometric fall distance matches the recorded scale value.
Plummet Release and Fall Transit Timing
Depress the electronic release trigger to de-energize the electromagnet simultaneously with the starting of the digital timer. The plummet falls freely under gravity until its base strikes the landing pad, instantly opening the timer gate circuit. Record the elapsed fall time t from the digital counter to 0.0001 s. Repeat for three successive trials to confirm repeatability.
Why this step matters
Averaging three trials at each height mitigates minor timing jitter caused by electrical contact micro-bouncing or minute air eddies.
Multi-Station Systematic Mapping and Regression
Repeat the release and timing sequence at heights of 0.40 m, 0.60 m, 0.80 m, and 1.00 m. Calculate the square of the mean fall time t² for each height station. Construct a graph of h versus t², evaluate the slope S via ordinary least squares, and compute the experimental acceleration due to gravity as g = 2 · S.
Why this step matters
Testing across a wide range of heights verifies that the acceleration remains constant throughout the trajectory and permits statistical evaluation of experimental uncertainty.
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
h = (1/2 g) · t² ⇔ g = 2 · S
| # | Drop height h (m) | Time of fall t (s) | Time squared t² (s²) | Drop height h (m) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING