A satellite in force free space sweeps stationary...

A satellite in force free space sweeps stationary interplanetary dust at a rate $d M / d t=\alpha w$, where $M$ is the mass, $v$ is the velocity of the satellite and $\alpha$ is a constant. What is the deacceleration of the satellite? (a) $-2 \mathrm{~cm}^{2} / \mathrm{M}$ (b) $-\alpha v^{2} / M$ $(\mathbf{c})+\alpha_{\underline{ }^{2}} / M$ (d) $-\alpha v^{2}$

A satellite in force free space sweeps stationary interplanetary dust at a rate $d M / d t=\alpha w$, where $M$ is the mass, $v$ is the velocity of the satellite and $\alpha$ is a constant. What is the deacceleration of the satellite?
(a) $-2 \mathrm{~cm}^{2} / \mathrm{M}$
(b) $-\alpha v^{2} / M$
$(\mathbf{c})+\alpha_{\underline{ }^{2}} / M$
(d) $-\alpha v^{2}$

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Key Concepts

Momentum Transfer through Mass Accretion

When a moving object accretes (gathers) stationary mass, the additional mass initially has no momentum. To conserve momentum, the moving object must reduce its velocity, resulting in deceleration. This deceleration can be quantified by relating the rate of mass increase to the square of the velocity of the object, illustrating how accretion acts as an effective drag force.

Variable Mass Systems

Variable mass systems involve objects like satellites or rockets that change their mass over time by losing or accumulating material. The analysis of these systems requires a careful application of momentum conservation, accounting for the fact that the changing mass alters the dynamics of the system, which can lead to deceleration or acceleration depending on the nature of the mass change.

Conservation of Momentum

In the context of variable mass systems, the total momentum of an isolated system must remain constant if no external forces act on it. This principle is used to analyze how the addition of mass to a moving object affects its velocity, specifically by ensuring that the product of mass and velocity remains conserved, even as the mass increases.

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