Final answer:
To drink a soda through a straw, the pressure at the top of the straw needs to be lowered. The pressure can be calculated using the formula P = Patm + ρgh, where P is the pressure at the top of the straw, Patm is the atmospheric pressure, ρ is the density of the soda, g is the acceleration due to gravity, and h is the height difference between the surface of the soda and your lips. Plugging in the given values, the pressure at the top of the straw needs to be approximately 101,472 Pa.
Step-by-step explanation:
When you drink a soda through a straw, you need to lower the pressure at the top of the straw in order for the soda to reach your lips. To calculate the pressure needed, we can use the concept of atmospheric pressure and the height difference between the surface of the soda and your lips.
The pressure at the top of the straw can be calculated using the formula P = Patm + ρgh, where P is the pressure at the top of the straw, Patm is the atmospheric pressure, ρ is the density of the soda (assumed to be the same as water), g is the acceleration due to gravity, and h is the height difference between the surface of the soda and your lips.
In this case, the height difference is 15.0 cm, which is equivalent to 0.15 m. The atmospheric pressure at sea level is approximately 101,325 Pa (N/m²). The density of water is approximately 1000 kg/m³. The acceleration due to gravity is approximately 9.8 m/s².
Plugging in the values into the formula, we get:
P = 101,325 Pa + (1000 kg/m³ * 9.8 m/s² * 0.15 m)
Simplifying the equation, we find:
P = 101,325 Pa + 147.0 Pa
P = 101,472 Pa
Therefore, the pressure at the top of the straw needs to be approximately 101,472 Pa for the soda to reach your lips.