Explanation Given information: The mass ( m B ) of sub satellite B is 2 kg . The mass ( m A ) of base satellite A is 20 kg . The initial velocity ( v B ) of sub satellite is 3 m / s j Calculation: Sketch the impulse momentum diagram as shown in Figure 1. The cord is inextensible, after it becomes taut, the component of v B along AB must be equal to v A . Express the velocity base satellite in vector form: v A = ( v A cos θ +v B / A sin θ ) i Express the velocity v B / A in vector form: v B / A = ( v A sin θ − v B / A cos θ ) j Express the linear momentum x component is conserved. 0 = m A v A cos θ + m B v A cos θ + m B v B / A sin θ 0 = 13.2 v A + 1.6 v B / A (1) Express the linear momentum y component is conserved. 2 kg ( 3 m / s ) = m A v A sin θ + m B v A sin θ − m B v B / A cos θ 6 = 17.6 v A − 1.2 v B / A (2) Find the velocity of base satellite using the Equation as follows: Solving the Equation (1) and (2) to get values, v A = 0.2182 m / s v B / A = − 1.8 m / s Thus, the velocity of base satellite A is 0

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 14.2, Problem 14.45P

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Find the velocity of base satellite and sub satellite.

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Chapter 14.2, Problem 14.44P

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Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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Find the velocity of base satellite and sub satellite.

Solution Summary: The author calculates the velocity of base satellite and sub satellite. The cord is inextensible after it becomes taut, and the linear momentum x component is conserved.

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