A satellite explodes in outer space, far from any other body, sending thousands of pieces in all directions. How does the linear momentum of the satellite before the explosion compare with the total linear momentum of all the pieces after the explosion?
The momentum before and after the explosion is the same. Since there are no external forces acting on the satellite, the law of conservation of momentum states that momentum will not change. Basically the total momentum of the satellite before the explosion is equal to the momentum of all the tiny pieces added together. Keep in mind this really only works in space because on earth there are always external forces acting on something which would affect the momentum.
It is the same. Remember Linear momenum is a vector.
According to the law of conservation of linear momentum, the total linear momentum of a system remains constant if no external forces are acting on it. Therefore, the linear momentum of the satellite before the explosion will be equal to the total linear momentum of all the pieces after the explosion.
Before the explosion, the linear momentum of the satellite is the product of its mass and velocity. After the explosion, the total linear momentum of all the pieces can be calculated by adding up the individual momenta of each piece.
So, the linear momentum of the satellite before the explosion is equal to the total linear momentum of all the pieces after the explosion.
To determine how the linear momentum of the satellite before the explosion compares with the total linear momentum of all the pieces after the explosion, we need to consider the principle of conservation of linear momentum.
The principle of conservation of linear momentum states that the total linear momentum of an isolated system remains constant if no external forces act on it. In this case, since the satellite is far from any other body, we can assume there are no external forces acting on it, and therefore, the total linear momentum of the system will be conserved.
Before the explosion, the satellite has a certain linear momentum, which can be calculated by multiplying its mass by its velocity. Let's represent the linear momentum of the satellite as P_satellite.
After the explosion, the satellite breaks into thousands of pieces, each having its own mass and velocity. To determine the total linear momentum of all the pieces, we need to sum up the linear momentum of each individual piece. Let's represent the total linear momentum of all the pieces as P_pieces.
Since the system is isolated, the principle of conservation of momentum tells us that P_satellite (linear momentum before the explosion) should be equal to P_pieces (total linear momentum of all the pieces after the explosion).
Therefore, the linear momentum of the satellite before the explosion is equal to the total linear momentum of all the pieces after the explosion.