A spacecraft encounters a stationary dust cloud of density rho.

In summary, the conversation is about preparing for a prelim and checking the correctness of a solution to a problem. The problem involves a spacecraft encountering a dust cloud and finding its subsequent motion. There is an update mentioning an error and a suggestion to use the conservation of momentum to find the acceleration. The conversation ends with a thank you.
  • #1
AbigailM
46
0
I'm currently preparing for a prelim and just wondering if my solution to this problem is correct. I did a plot of v(t) and it looked reasonable. You can find the question and solution both at http://oi50.tinypic.com/2e3v4e8.jpg.

The Problem states:

A spacecraft of mass m_0 and cross-sectional area A is coasting with a velocity v_o when it encounters a stationary dust cloud of density rho. Assuming that all the dust sticks to the spacecraft and that A remains unchanged, find the subsequent motion, i.e. v(t) of the spacecraft .

Update: I seem to have made an error by pulling v outside of the integral.

Thank you all for the help.
 
Last edited:
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  • #2
Welcome to PF!

You may find it easier to establish the acceleration of the rocket with its accumulating mass directly from the differential of the conservation of momentum, i.e. from [itex]\dot{m}v+m\dot{v} = 0[/itex].
 
  • #3
Thanks for the help Filip.
 

What is a spacecraft?

A spacecraft is a vehicle or device designed to travel through space. It is typically used for exploration, communication, or observation purposes.

What does it mean for a dust cloud to be stationary?

A stationary dust cloud is one that is not in motion relative to the spacecraft. It is not moving or changing position in relation to the spacecraft's trajectory.

What is density (rho) in relation to a dust cloud?

Density (rho) is a measure of the amount of mass per unit volume of a substance. In this context, it refers to the concentration of dust particles within the cloud.

Why is encountering a dust cloud of high density potentially dangerous for a spacecraft?

A high density dust cloud can pose a threat to a spacecraft because the particles within the cloud can collide with and potentially damage the spacecraft's exterior or sensitive equipment.

How does a spacecraft protect itself from a dust cloud encounter?

Some spacecraft are equipped with shielding to protect against dust cloud encounters. They may also have sensors or detectors to help detect and avoid potential encounters in space.

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