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Chapter 9: Problem 13

Two identical satellites are going in opposite directions in the same circular orbit when they collide head-on. Describe their subsequent motion if the collision is (a) elastic or (b) totally inelastic.

Short Answer

Expert verified
In both elastic and totally inelastic collisions, the satellites will come to a rest due to the conservation of momentum.

Step by step solution

01

Understanding Elastic Collision

In an elastic collision, both momentum and kinetic energy are conserved. The two identical satellites are in the same orbit but moving in opposite directions indicates that they have equal but opposite momentums. Hence, the total momentum before the collision is 0. Therefore, after an elastic collision, the total momentum will still be zero. It means the satellites will come to rest.
02

Understanding Totally Inelastic Collision

In a totally inelastic collision, the objects stick together and move as one after the collision. Since the total momentum is conserved, and the momentum before collision is zero (as they have equal speeds in opposite directions), the two satellites will again come to a stop after the collision as their combined momentum should be zero
03

Conclusion

For both types of collisions, the final state of the satellites is that they will come to rest.

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