Calculate how much pressure (due to the liquid) would be on a 83 kg person if they were 53 m deep in...
a.)...freshwater. The density of freshwater is 1000 kg/m3. Express your answer in both pascals and atmospheres. 1 atm = 1.013×105 Pa.
Pa
atm
b.)...saltwater. The density of saltwater is 1030 kg/m3. Express your answer in both pascals and atmospheres. 1 atm = 1.013×105 Pa.
Pa
atm
NOTHING TO DO WITH THE mass of the person. What are you thinking???
rho g h = density in kg.m^3 * 9.81 m/s^2 * depth in meters
= Pressure in Pasals (on earth)
To calculate the pressure exerted by the liquid on the person, we can use the concept of hydrostatic pressure, which states that pressure in a fluid increases with depth.
The formula to calculate pressure at a certain depth in a fluid is:
P = ρgh
Where:
P is the pressure in pascals (Pa)
ρ is the density of the fluid in kilograms per cubic meter (kg/m³)
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the depth in meters
a) Freshwater:
Given:
Density of freshwater (ρ) = 1000 kg/m³
Depth (h) = 53 m
Using the formula, we can substitute the given values:
P(freshwater) = 1000 kg/m³ * 9.8 m/s² * 53 m
P(freshwater) = 513,400 Pa
To convert the pressure to atmospheres, we'll use the conversion factor:
1 atm = 1.013×10^5 Pa
P(freshwater, atm) = P(freshwater) / (1.013×10^5 Pa)
P(freshwater, atm) = 513,400 Pa / (1.013×10^5 Pa)
P(freshwater, atm) = 5.07 atm (rounded to two decimal places)
b) Saltwater:
Given:
Density of saltwater (ρ) = 1030 kg/m³
Depth (h) = 53 m
Using the formula, we can substitute the given values:
P(saltwater) = 1030 kg/m³ * 9.8 m/s² * 53 m
P(saltwater) = 536,740 Pa
To convert the pressure to atmospheres, we'll use the conversion factor:
1 atm = 1.013×10^5 Pa
P(saltwater, atm) = P(saltwater) / (1.013×10^5 Pa)
P(saltwater, atm) = 536,740 Pa / (1.013×10^5 Pa)
P(saltwater, atm) = 5.3 atm (rounded to two decimal places)
So, the pressure on the person at a depth of 53 meters would be:
a) In freshwater: 513,400 Pa or 5.07 atm
b) In saltwater: 536,740 Pa or 5.3 atm