What pressure, in atmospheres, is exerted on the body of a diver if they are 15 ft below the surface of the water when the atmospheric pressure is 750 torr? Assume that the density of the water is 1.00 g/cm3=1.00×103 kg/m3. The gravitational constant is 9.81 m/s2, and 1 Pa=1 kg/m-s2.

Video transcript

Hi everyone here we have a question telling us that a scuba diver is 15 m deep underwater. Given that the atmospheric pressure is 1000 kill a pascal's. And assuming that the density of water is 1.0 times 10 to the third kilograms per meters cubed, calculate the pressure in atmospheres exerted on the body of the diver. Some useful information grants equals 9.81 m per second square and one pascal equals one kg per meter square. So we're going to start off with the formula pressure equals force over area and force equals mass times acceleration, Mass equals our volume times density. So therefore volume equals area times height. And our pressure is going to equal area times height, times density, times acceleration divided by r area. So our areas here are going to cancel out. And that's going to give us pressure equals density, times height times acceleration. So we have pressure equals one Times 10 to the 3rd kilograms. Her meters cube times m Times 9.81 meters per second square. And that equals 147, 150 kilograms. Her meters times seconds squared. And that equals 147, 150 past scales. So our total pressure is going to equal our pressure plus our atmospheric pressure. So that's going to equal 147,000 Pascal's plus 100,000 pascal's And that equals 247, 150 Pascal's and one atmosphere equals 101,000 Pascal's. So we have our 247, pascal's and we're going to multiply that by one atmosphere over 101,000, 325 pascal's and our pascal's are going to cancel out here, And that's going to equal 2. atmospheres. And that is our final answer. Thank you for watching. Bye.