What were the conceptual/mathematical contributions of: Archimedes: Pascal: Bern

Question

What were the conceptual/mathematical contributions of: Archimedes: Pascal: Bernoulli: A person with a mass of 100kg stands on one ice skate with an area of 0 1 cm2 , What is the total pressure on the ice below? What would be the pressure if the person laid down flat on the and spread their body as wide as possible (estimate for a 6 ft. (2m) tall person). A circular window with a 0.2m radius on a submarine can withstand a maximum pressure of 1802894N/m2. How deep can the sub safely dive? (saltwater density = 1025kg/m3). In a hydraulic car lift, the small piston has a radius of 0.8cm. When a 300N force is applied to the piston, a 5600N force occurs on the large piston. What is the radius of the large piston? An object has a volume of 3m3. How much of a buoyant force will it experience when it is completely submerged in fresh water (density 1000kg/m3)? If it weighs 50,000 N in air, how much would it weigh in water? A rod 14cm long with a 3cm diameter will just barely float in water. What is its mass? An object weighs 8.3 N in air and 4.2N in water. What is its density? How much absolute pressure must a scuba diver withstand at a depth of 80 meters? (density of 1025kg/m3, standard air pressure = 1 times 103 N/M2) What is the pressure in the hydraulic fluid of a tractor if a 5cm diameter piston is able to push up 32000N? The density of gold is 19.3g/cm3. What buoyant force does a 3.2kg gold crown experience when it is sunk in water? Describe how you could experimentally determine the flow rate (m3/s) of a river. A river constricts into a narrow and fast canyon. If the water flowing at 3.2 m/s through the slow section with a cross-sectional area of 24m2, and flows 10.8m/s through the canyon, what is the cross sectional area of the narrower canyon? How much pressure must a pump provide to push drinking water to a fountain on the 80th floor of a skyscraper (1 floor = 3 meters)? How deep would a 100kg person sink a rectangular 2 times 3 meter raft?

Explanation / Answer

I think you need help only with question 14 and not all

14) let the depth be = H m

then at equilibrium

weight of man = buoyancy force

m.g = density of water x volume of water displaced

100 x 9.81 = 1000 x 2 x 3x H

H =0.1635 m

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