The longer a straw, the harder it is to drink from. If the air pressure is 93300 Pa, and if you could create a perfect vacuum in your mouth, what is the maximum length of a straw that you could still drink from? Density of water: 1000kg/m3. Ignore capillary effects.
100m
To determine the maximum length of a straw that you could still drink from given the air pressure and the density of water, we need to consider the balance between the forces at play.
When we drink from a straw, the pressure inside the straw decreases as we create a vacuum in our mouth. However, the atmospheric pressure outside the straw pushes the liquid up to create a pressure difference that allows it to be drawn into our mouth.
Let's examine the forces involved:
1. Atmospheric Pressure: The air pressure outside the straw is given as 93,300 Pa. This is the force pushing the liquid up into the straw.
2. Pressure Difference: By creating a perfect vacuum in your mouth, you essentially reduce the pressure inside your mouth to zero. This creates a pressure difference that allows the liquid to rise into the straw.
Now, let's calculate the maximum length of the straw by considering the pressure difference:
Step 1: Calculate the pressure difference.
Since the pressure inside your mouth is essentially zero (vacuum), the pressure difference is equal to the atmospheric pressure, which is 93,300 Pa.
Step 2: Convert the pressure difference into a height difference.
To convert the pressure difference into a height difference that the liquid can rise against, we can use the hydrostatic pressure formula: pressure = density × acceleration due to gravity × height.
Rearranging the formula, we have: height = pressure difference / (density × acceleration due to gravity).
Given:
Pressure difference = 93,300 Pa
Density of water = 1000 kg/m^3
Acceleration due to gravity = 9.8 m/s^2
height = 93,300 / (1000 × 9.8)
height ≈ 9.5 meters
Therefore, the maximum length of a straw that you could still drink from, assuming a perfect vacuum in your mouth and ignoring capillary effects, is approximately 9.5 meters.