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flamespirit919
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Homework Statement
A spaceship of frontal area 25 m2 passes through a cloud of interstellar dust at a speed of 1.0x106 m/s. The density of dust is 2.0x10-18 kg/m3. If all the particles of dust that impact on the spaceship stick to it, find the average decelerating force that the impact of the dust exerts on the spaceship.
Homework Equations
##p = mv##
##\frac{\text{d}p}{\text{d}t}=F##
The Attempt at a Solution
I tried using the formula for conservation of momentum $$m_1v_1+m_2v_2=m_1v^{'}_1+m_2v^{'}_2$$ and got to $$m_1v_1=\left(m_1+m_2\right)v_2$$ But I got stuck here and realized I couldn't solve for the final velocity without knowing the mass of the spaceship.
So I tried using the rate of change of momentum by using $$m_1a_1+m_2a_2=0$$I assumed the initial acceleration of both masses was 0 and it made sense that the final acceleration of the spaceship and the dust would cancel out. Again, I couldn't figure out how to solve anything without knowing the mass of the spaceship. For each of these I was taking the mass of the dust to be ##25\cdot2.0\times10^{-18}~kg##
I know the answer is supposed to be ##5\times10^{-11}~kg/s## or ##5\times10^{-5}~N##
Some guidance in the right direction would be much appreciated. Thanks!
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