Meriam, Kraige & Bolton — Kinetics of Systems of Particles: Problem 4_62

4/62 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 \( x \).