Measurement of air resistance on an air track

Abstract

An extension of a standard air track experiment is described in which the effects of air resistance can be studied. A circular disk is placed on one end of an air track cart to provide air drag. The data analysis consists of subtracting the ''ideal'' velocity for a frictionless situation from the measured velocity and plotting the difference as a function of the ideal velocity. The resulting curve is fitted with a modified power-law and the coefficient of the cubic term is studied as a function of the area of the disk, a behavior that can be predicted theoretically. Frictional effects in addition to the air drag on the disk were found to be significant and were accounted for.

Magnetic Low-Friction Track

“…These devices are in widespread use by students to study inclined planes, conservation of momentum, and Newton's second law, etc., but have also been used to study other effects such as magnetic braking 5 and air resistance. 2 The lowfriction carts and track were from Vernier (VDS), the air-track cart is from PASCO (655-007), and the 2-m air track was pressurized with a PASCO air supply (SF-9216). The mass of the air-track cart was 285 g and the mass of the low-friction cart 515 g.…”

Turning a Common Lab Exercise into a Challenging Lab Experiment: Revisiting the Cart on an Inclined Track

“…Solving Eq. (2) for the intercepts (a  = 0), we obtain m + -m -= 2| F f | /g (3) or F f = 0.032 N. Similarly,…”

“…See also Ref. 3. Figure 2 illustrates data taken using PaSco's classic Dynamics System (cart plus track) equipped with a photogate/ pulley and DataStudio software to measure v(t).…”

Conceptual and laboratory exercise to apply Newton’s second law to a system of many forces

“…The cross section of a cart with its attached force sensor is roughly square with an area of approximately A ≈ 50 cm 2 . Consequently the Reynolds number is large enough that the air resistance is quadratic (rather than linear) in the speed, F D ≈ 1 2 Aρv 2 , where ρ = 1.2 kg m −3 is the density of air [17]. We can compare this value to the coefficient of friction measured in figure 4 by dividing by the weight of the cart to get F D /mg = 6 × 10 −5 .…”

“…But for an undamped oscillator, the phase-space trajectories are ellipses [11]. Consequently, each half-cycle of the graph in figure 9 is half of an ellipse, (x/A n ) 2 + (v x /A n ω) 2 = 1 from equations (16) and (17). At the nth turning point, the semimajor and semi-minor axis lengths of a given ellipse suddenly decrease by a factor of A/A n according to equations (16) and 17, but the centre of the ellipse also shifts horizontally so that there is no discontinuity in the orbit.…”