A pound of lead or a pound of feathers?
Stories from Physics for 11-14 14-16
The old riddle that asks whether a pound of feathers is heavier than a pound of lead is not as simple as it seems. Some approaches to weight measurement will measure forces in addition to the gravitational force on an object, complicating the riddle. In the case of the feathers, their relatively large volume means that they displace more air than the lead, so for the same mass, the feathers will experience a greater buoyancy force. Therefore, if not weighed in a vacuum, the feathers will experience a lower net downward force. A different approach to mass measurement to avoid this problem might be to measure inertial mass. For example, tethered, horizontal springs might be attached to either side of the objects to be weighed. By displacing the samples, the time periods of the system could be used to determine their mass. However, in this method, the moving bodies will ‘entrain’ (ie force to move with it) a non-negligible mass of air. In a simulation of the experiment, researchers calculated that a 5 cm by 10 cm bronze sheet (standing in for lead) would entrain 0.01 g of air, while a block of polystyrene (representing the feathers) of the same mass would entrain 0.5 g of air, giving different results for the mass of the objects. Psychologists report that blindfolded volunteers given boxes of equal size containing secured equal masses of lead and feathers, felt the box containing the lead was heavier on 74% of trials. The researchers argued that perception of heaviness is related to an object’s dynamical symmetry: objects with symmetric mass distributions feel lighter than ones with asymmetric distributions.