Question

Suppose that the hatch on the side of a Mars lander is built and tested on Earth so that the internal pressure just balances the external pressure. The hatch is a disk 50.0 cm in diameter. When the lander goes to Mars, where the external pressure is 650 N/m^2, what will be the net force (in newtowns and pounds) on the hatch, assuming that the internal pressure is the same in both cases? Will it be an inward or outward force? Answer= 19.8 kN, 4440 lb. Outward force. Please explain how to get these answers. Equation in textbook : Fnet=(P2-P1)A

Answer 1

Answer:

$F=19.8kN=4442lb$

Explanation:

On Earth the atmospheric presure is $P_E=101325 N/m^2$. This will be the pressure inside the lander. Outside, the pressure on Mars will be $P_M=650 N/m^2$. This means that the net force will be outward (since inside the pressure is higher) and, since the area of the hatch is $A=\pi r^2$, of value:

$F=(P_E-P_M)\pi r^2=(101325N/m^2-650N/m^2)\pi (\frac{0.5m}{2})^2=19768N=19.8kN$

Since 1lb in weight  is equal to 4.45N, we can write:

$F=19768N=19768N\frac{1lb}{4.45N}=4442lb$