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Chapter 9: Problem 11

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) inelastic.

Short Answer

Expert verified
In an elastic collision, the satellites will continue their orbits but in reverse direction. For an inelastic collision, the satellites will cease all motion, either by stopping at their position in case they slide off, or stick together and stop moving in orbit.

Step by step solution

01

Understanding Elastic Collision

In an elastic collision, both momentum and kinetic energy of the system are conserved. Since the satellites are of identical mass and moving in opposite directions with the same speed, their total momentum before collision is 0. Also, their total kinetic energy is \(2 \times 0.5 \times m \times v^2\), where m is their mass and v is their velocity. One can then deduce that following an elastic collision, the total momentum of the system should still be zero and the total kinetic energy should remain the same. Hence, they will simply bounce back in opposite directions without any change in speed. Therefore, their motion will be as before, but their direction of motion will be opposite to what it was earlier.
02

Understanding Inelastic Collision

In an inelastic collision, momentum is conserved, but kinetic energy is not. Again, since the satellites are of identical mass and moving with the same speed in opposite directions, their total momentum before collision is 0. Hence, to conserve momentum, after colliding, they must either stick together and stop (which is what happens in a completely inelastic collision) or just stop at their position if they slip off (as in a partially inelastic collision). In other words, any subsequent motion is ceased as a result of the inelastic collision.

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Most popular questions from this chapter

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