Investigating Motion

What is actually being measured — almost every motion experiment reduces to measuring a distance and a time accurately enough that their ratio means something. The difficulty is nearly always the time.

Light gates — a beam is broken by an interrupt card on a trolley, and timing is electronic. The card's length divided by the time the beam is blocked gives the velocity at that point. Two gates a known distance apart give two velocities and hence an acceleration.

Why light gates beat a stopwatch — a hand-held stopwatch carries a reaction-time uncertainty of perhaps 0.2 s at both start and stop. Over an interval of a few tenths of a second that is a huge percentage uncertainty, and no number of repeats will remove the part of it that is systematic. Light gates remove the human from the measurement.

Example: a trolley crossing 20 cm in 0.40 s timed by hand might carry ±0.2 s, about 50%. The same measurement by light gate might carry ±0.001 s, about 0.25%. That is the difference between a meaningless result and a good one.

Interrupt card length — the card must be short enough that the trolley's velocity does not change much while the beam is blocked, since the method assumes a single velocity during that interval. A long card on an accelerating trolley measures an average over a range of speeds.

Video analysis — filming the motion and stepping through frames gives position against time directly. The frame rate sets the time resolution, and a metre rule in shot provides the distance scale.

Measuring acceleration down a ramp — release a trolley from rest and measure its velocity at two points a known distance apart, then use v² = u² + 2as. Repeat for several distances and plot v² against s: the gradient is 2a, and using a gradient is better than a single calculation because it averages random error and reveals systematic problems as a non-zero intercept.

Friction and the ramp — friction reduces the measured acceleration below g sinθ. Some experiments compensate by tilting the ramp until the trolley moves at constant velocity when given a push, so that friction is exactly balanced before the real measurements begin.