Chapter 14, Problem 30A

In an accidental explosion, a satellite breaks in half while in circular orbit about Earth. One half is brought momentarily to rest. What is the fate of the half brought to rest? What is the speed of the other half? (Hint: Think momentum conservation.)

To determine

Speed of the half part of satellite and fate of the other half part which is brought to rest.

Answer to Problem 30A

First part will drop vertically to Earth and other part speed will be doubled.

Explanation of Solution

Given:

A satellite is revolving in circular orbit around the Earth.

Formula used:

Conservation of momentum:When a collision happens, the momentum before collision is equal to momentum after collision.

Calculation:

As the explosion happens, the half part of satellite which was on rest will be dropped to Earth vertically due its gravitational force.

According to conservation of momentum,

$MV=\frac{1}{2}M{V}_1+\frac{1}{2}M{V}_2$

As one part is at rest so V₁ =0

$\begin{array}{l}MV=\frac{1}{2}M{V}_2\\ V=\frac{1}{2}{V}_2\\ V_2=2V\end{array}$

So other part will double its speed.

Conclusion:

Therefore, first part will drop vertically to Earth and other part speed will be doubled.