Q4. In a trial the distances are d1 = 10.0 cm and d2 = 8.0 cm, each uncertain by ±0.2 cm, with a known mass of 50 g taken as exact. Find the mass and its percentage uncertainty. Why is this trial worse than one with distances of about 30 cm?
m = 50 × 8.0/10.0 = 40.0 g. The first-order worst-case fractional uncertainty estimate is 0.2/10.0 + 0.2/8.0 = 0.020 + 0.025 = 0.045, that is 4.5%, or about ±1.8 g. With distances three times larger the same ±0.2 cm gives a third of the fractional error, so masses should hang far from the knife-edge.
Q5. Why does this method give the mass of the object rather than its weight? Would it work on the Moon?
Both sides of the balance equation contain g, which cancels: m = Md2/d1. The method compares the unknown mass with a known mass, so it gives mass, and it gives the same answer wherever g is the same for both masses, on the Moon too.
Q6. A non-uniform scale balances on its own at the 48.5 cm mark. With the knife-edge kept there, an object at the 18.5 cm mark balances a 20 g mass at the 78.5 cm mark. Find the object’s mass.
Measured from the knife-edge, d1 = 48.5 − 18.5 = 30.0 cm and d2 = 78.5 − 48.5 = 30.0 cm, so m = 20.0 g. Taking 50.0 cm as the fulcrum instead would give wrong distances: always measure from where the scale actually balances.