Final answer:
To create a gauge pressure of 4.00 cm water with an effective squeezing area of 50.0 cm², a force of approximately 1961.33 N is required.
Step-by-step explanation:
The student's question is related to applying a force to a balloon in order to create a gauge pressure to assist an unconscious person's breathing. To calculate the force necessary to create a gauge pressure of 4.00 cm water on a balloon with an effective squeezing area of 50.0 cm², we need to use the pressure formula:
P = F/A,
where P is the pressure, F is the force, and A is the area.
First, convert 4.00 cm water into pascals (Pa). The conversion factor is:
1 cm water = 98.0665 Pa,
therefore:
4.00 cm water × 98.0665 Pa/cm water = 392.266 Pa.
Now, solve for F using the rearranged pressure formula:
F = P × A,
Plugging in the pressure and area:
F = 392.266 Pa × 50.0 cm² = 392.266 Pa × (50.0 × 10^-4 m²) = 1961.33 N.
The force required is therefore approximately 1961.33 N (Newton).