A Fan-Cart Experiment With a Weakening Battery and a Drifting Start
An eighth-grade group investigates how cart mass affects acceleration when the same fan pushes the cart. They use a fan cart, three masses (0.5 kg, 1.0 kg, 1.5 kg), and a motion sensor. They run one trial per mass. For each trial they start the cart at the same mark and turn the fan to high. Between trials they do not recharge the fan battery. Their data: 0.5 kg -> 1.8 m/s²; 1.0 kg -> 0.95 m/s²; 1.5 kg -> 0.55 m/s². They conclude that 'heavier carts accelerate less, so mass is the only factor.' A classmate notices that the third trial's fan sounded slower and that the cart drifted left before the fan started. The teacher asks them to decide whether their conclusion is trustworthy and to revise the investigation.
1. Identify two specific flaws in the investigation and explain how each could affect the pattern in the data.
Read the worked answer
First flaw: the fan battery was not recharged between trials. If the battery weakened, the pushing force decreased across trials, so the lower accelerations at 1.0 kg and 1.5 kg are confounded with a weaker fan. The pattern could exaggerate the effect of mass because the heavier carts received both more mass and less force. Second flaw: the cart drifted left before the fan started in the third trial. That suggests an unbalanced sideways force or a misaligned track, so the fan's force was not the only horizontal force and the motion sensor may have measured a curved path. A third issue is one trial per mass, which gives no estimate of variability; a single odd run can drive the conclusion. These flaws do not mean mass has no effect; they mean the data do not isolate mass as the only factor. The conclusion 'mass is the only factor' is unsupported even if the general trend is plausible.
2. Write a revised procedure that would let the class fairly test the effect of mass on acceleration. Include at least two controls and one change that addresses the flaws.
Read the worked answer
Use the same cart, fan setting, track, and starting mark for every trial. Fully charge the fan battery before the investigation and check it with a multimeter or use a fresh battery for each block; better, use a fan powered by a constant power supply. Level and align the track, and release the cart from rest without touching it sideways. Randomize the order of masses so a weakening battery cannot systematically affect the heaviest mass last. Run at least three trials at each mass and compute a mean acceleration; use the same total cart mass by adding identical non-moving masses. Measure acceleration from the same portion of the motion-sensor graph (after the fan starts and before the cart hits the end). Controls: same fan force, same track, same starting position, same time interval. Change addressing flaw: constant power or battery check, plus repeated trials. If the class cannot control the battery, measure the fan's force directly with a force sensor and include it as a covariate.
3. A classmate says, 'Even with the flaws, the data still show that heavier carts accelerate less, so the conclusion is basically fine.' Write a response that distinguishes what the data can and cannot support.
Read the worked answer
The data are consistent with the general idea that, for a given fan setting, a more massive cart has a smaller acceleration. That is expected from a = F_net/m if force is held constant. But the investigation did not hold force constant, because the battery may have weakened and the third run drifted. So the data cannot support the stronger claim that mass is the only factor, nor can they give a trustworthy estimate of how much acceleration changes per kilogram. A fair statement is: 'In this flawed run, acceleration decreased as mass increased, but the decrease may be partly due to a weaker fan and misalignment; the result is suggestive, not conclusive.' The revision should test the same pattern with controlled force and repeated trials before the class treats the trend as established.