The highest George can suck water up a very long straw is 2.0m
What is the lowest pressure he can maintain in his mouth?
Express to two sig figs
To determine the lowest pressure George can maintain in his mouth while sucking water up a very long straw, we can use the principles of hydrostatics. The pressure at a certain point in a fluid is given by the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height or depth of the fluid.
In this case, the height or depth of the fluid is the vertical distance George can suck the water up the straw, which is 2.0 m. We want to find the lowest pressure, so we need to consider the maximum possible density and acceleration due to gravity.
For water at its highest density, which occurs at 4°C, the density ρ is approximately 1000 kg/m³. Acceleration due to gravity, g, is approximately 9.81 m/s².
Using these values, we can calculate the lowest pressure George can maintain in his mouth:
P = ρgh
P = (1000 kg/m³)(9.81 m/s²)(2.0 m)
P ≈ 19,620 Pa
To express the answer to two significant figures, we can round the result to 20,000 Pa.
Therefore, the lowest pressure George can maintain in his mouth while sucking water up a very long straw is approximately 20,000 Pa.