Final answer:
To create the required gauge pressure of 4.00 cm water in the balloon, one must exert a force of 1.9613 Newtons on an effective area of 50.0 cm².
Step-by-step explanation:
When attempting to resuscitate an unconscious, not breathing athlete, rescuers might need to create a gauge pressure to inflate the subject's lungs. In the scenario provided, the rescuer is required to force air into the person's lungs by exerting pressure on a balloon. To calculate the necessary force to create a gauge pressure of 4.00 cm water (which is the pressure needed to inflate the lungs), we would use the formula for pressure: P = F/A, where P is pressure, F is the force applied, and A is the area over which the force is applied.
To find the force, we rearrange the formula to F = P x A. Given that 1 cm water equals 98.0665 pascals, we first convert the pressure to pascals (Pa):
4.00 cm water x 98.0665 Pa/cm water = 392.26 Pa.
Now we can find the force using the converted pressure and the given area of 50.0 cm² (note that 1 cm² equals 0.0001 m²):
F = 392.26 Pa x (50.0 cm² x 0.0001 m²/cm²) = 392.26 Pa x 0.005 m² = 1.9613 N.
Therefore, you would need to exert a force of 1.9613 Newtons to create a gauge pressure of 4.00 cm water on the balloon's effective area.