Final answer:
The maximum vertical straw length through which young children can drink milk (with a density of 1030 kg/m3) is determined by atmospheric pressure and the density of the liquid. By equating the atmospheric pressure to the pressure exerted by the milk column, the maximum height of the straw is calculated to be approximately 10 meters.
Step-by-step explanation:
The question pertains to the physical principles behind drinking liquids through a straw, focusing on the maximum length of a vertical straw that young children can use to drink milk. The question considers the density of milk (1030 kg/m3) and involves the concept of atmospheric pressure as a limiting factor for the straw's length. To determine the maximum length, one must consider the atmospheric pressure, which is typically 101325 Pascals (Pa) at sea level. The pressure exerted by the column of milk must be less than atmospheric pressure for the liquid to be drawn up the straw.
To calculate the maximum height (h) of the milk column, we use the pressure difference between the atmospheric pressure (Patm) and the pressure at the top of the milk column (which would be a vacuum if the straw is at maximum height, so it is 0 Pa). Thus, Patm = ρgh, where ρ is the density of milk and g is the acceleration due to gravity (9.81 m/s2). Solving for h gives us h = Patm / (ρg).
Substituting the known values, we find: h = 101325 Pa / (1030 kg/m3 × 9.81 m/s2)
Calculating this, we get h ≈ 10 meters. Therefore, the maximum vertical straw length a child could realistically use to drink milk on Earth, without considering additional factors like the strength of their suction or minor capillary effects, is approximately 10 meters.