Question
The magnetometer boom for a spacecraft consists of a large number of triangular-shaped units which spring into their deployed configuration upon release from the canister in which they were folded and packed prior to release. Write an expression for the force $F$ which the base of the canister must exert on the boom during its deployment in terms of the increasing length $x$ and its time derivatives. The mass of the boom per unit of deployed length is $\rho .$ Treat the supporting base on the spacecraft as a fixed platform and assume that the deployment takes place outside of any gravitational field. Neglect the dimension $b$ compared with $x$.
Step 1
The force equation for a system with variable mass is given by $\Sigma F = m \ddot{x} + \dot{m} v$, where $m$ is the mass of the system, $\ddot{x}$ is the acceleration, $\dot{m}$ is the rate of change of mass and $v$ is the velocity. Show more…
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The deployment mechanism for the spacecraft magnetometer boom of Prob. $5 / 88$ is shown again here. The driving link $O B$ has a constant clockwise angular velocity $\omega_{O B}$ of $0.5 \mathrm{rad} / \mathrm{sec}$ as it crosses the vertical position. Determine the angular acceleration $\alpha_{C A}$ of the boom for the position shown where $\tan \theta=4 / 3$
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