
DYNAMICS  CASE STUDY



Introduction

Problem Diagram


On July 15, 1975, NASA and the Soviet space program set a new precedent at the height of the Cold War. NASA's Apollo CSM attempts to dock with the Soviet's Soyuz Space Station.
What is known:
 The mass of the Apollo is m_{A} = 18.0 Mg.
 The mass of the Soyuz is m_{B} = 6.6 Mg.
 The Soyuz is stationary relative to the reference frame shown.
 The Apollo approaches relative to Soyus with the velocity
v_{A} = 0.20i + 0.03j + 0.02k m/s
 The force exerted by the docking collars is perpendicular to the longitudinal axis. In other words, the line of impact between the two space craft will be along the xaxis.






Questions



If the docking is successful, what is the velocity of the combined center of mass of the vehicles?
If the docking is unsuccessful, and the coefficient of restitution is e = 0.95, what is the velocity of each spacecraft after the impact.




Approach


 If the docking is successful, the conservation of linear momentum is sufficient to determine the velocity of the combined mass after the impact.
 If the docking is unsuccessful, the conservation of linear momentum, together with an equation involving the coefficient of restitution, can be used to determine the velocities of each ship after the impact




