Question

(from Ohanian): A spaceship of frontal area 15 m2 moves through a large dust cloud with a speed of 2 x 106 m/s. The mass density of the dust is 7 x 10-18 kg/m3. If all the particles of dust that impact the spaceship stick to it, find the average decelerating force that the impacting particles exert on the ship. (You may assume that the mass of dust which sticks to the spacecraft is negligible compared to the mass of the spacecraft.)

Answer 1

Answer:

$F= 4.2x10^{-4}N$

Explanation:

Recognizing the data we have to,

$A= 15m^2$

$v= 2*10^6 m/s$

$\rho = 7*10^{-18}kg/m^3$

So in this way we proceed first to decompose the variables,

The density is given by the formula

$\rho = \frac{m}{v}$

$m= \rho v$

We also know that the Volume is given by

$V=A\upsilon t$

Where

$A= Area$

$\upsilon = Velocity$

$t= time$

Through this we relate volume to density

$m=\rho (A\upsilon t)$

The momentum would be given as follows

$p =mv$

$p=(\rho A \upsilon t )\upsilon$

$p= \rho A \upsilon^2 t$

$F= \frac{dp}{dt} = \frac{d}{dt}(\rho A \upsilon^2 t)$

$F= \rho A \upsilon^2$

$F= (7*10^{-18}kg/m^3)*(15m^2)(2*10^6 m/s)^2$

$F= 4.2x10^{-4}N$