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/m2, what will be the net force (in newtons 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 1

The value is
`F_(net) = 4444 lb`

The force will be outward

Step-by-step explanation:

From the question we are told that

The diameter of the disk is
`d = 50.0 \ cm = (50)/(100) = 0.5 \ m`

The external pressure on Mars is
`P = 650 \ N/m^2`

From the question we are told that

Internal pressure = External pressure

Generally the external Force on earth is

`F_E = P_(atm) * A`

Here
`P_(atm)` is the atmospheric pressure with value
`P_(atm) = 1.013*10^(5)\ Pa`

So

`F_E = 1.013 *10^(5) * \pi * (d^2)/(4)`

=>
`F_E = 1.013 *10^(5) *3.142 * (0.50 ^2)/(4)`

=>
`F_E = 19893 \ N`

Generally the external Force on Mars is

`F= P * A`

`F = 650 * \pi * (d^2)/(4)`

=>
`F = 650 *3.142 * (0.5^2)/(4)`

=>
`F = 127.6 \ N`

Net force is mathematically represented as

`F_(net) = F_E -F`

=>
`F_(net) = 19893 -127.6`

=>
`F_(net) = 19765.6 \ N`converting to pounds

`F_(net) = (19765.6)/(4.448)`

=>
`F_(net) = 4444 lb`

Given that that the value is positive then the force will be outward