What is the pressure on the feet of a person with a mass of 90 kg and a total surface area on the feet of 0.062 \(m^2\) (that’s 96.1 \(in^2\))?
After solving on your own, check the
In the example problem earlier, we saw a shipping box exerts a pressure of 6,629 Pa. What is this pressure in psi? What is this pressure in mb?
After solving on your own, check the
Atmospheric pressure is 101,325 Pa. The Earth has a surface area of 196.9 million \(mi^2\) (\(1~mi^2 = 2,590,000~m^2\)). What is the weight of the atmosphere?
After solving on your own, check the
## Question 1.6.1
1. What is the pressure on the feet of a person with a mass of 90 *kg* and a total surface area on the feet of 0.062 $$m^2$$?
$$Weight = m\cdot 9.8 = 90~kg\cdot 9.8 = 882~N$$
$$Pressure = \frac{Weight}{Area} = \frac{882~N}{0.062~m^2} = 14,226~Pa$$
## Question 1.6.2
2. In the example problem earlier, we saw a shipping box exerts a pressure of 6,629 *Pa*. What is this pressure in *psi*? What is this pressure in *mb*?
To convert units:
1. Find an equality between current and desired units
2. Multiply current number by the part of equality with desired unit, divide by other part with current unit
$$6,629~Pa\cdot\frac{14.7~psi}{101,325~Pa} = 6,629\frac{14.7~psi}{101,325} = 0.962~psi$$
So that is a weight of 0.962 pounds (lbs) by every square inch of the shipping box.
$$6,629~Pa\cdot\frac{1013.25~mb}{101,325~Pa} = 66.29~mb$$
## Question 1.6.3
3. Atmospheric pressure is 101,325 *Pa*. The Earth has a surface area of 196.9 million $$mi^2$$ ($$1~mi^2 = 2,590,000~m^2$$). What is the weight of the atmosphere?
$$Area = 196,900,000~mi^2\cdot\frac{2,590,000~m^2}{1~mi^2} = 510,000,000,000,000~m^2$$
$$Pressure = \frac{Weight}{Area} \qquad\to\qquad Weight = Pressure\cdot Area$$
$$Pressure = 101,325~Pa \cdot 510,000,000,000,000~m^2 = 51,700,000,000,000,000,000~N$$
(Your calculator likely says 5.17E19. That is 5.17 * 10,000,000,000,000,000,000 (that's 19 0's).)
That is 51.7 quintillion Newtons, or 11.24 quintillion pounds, or 5.62 quadrillion tons! Our atmosphere is really heavy!