Question

Asteroid Collision. Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow. Asteroid A, which was initially traveling at 40.0 m/s, is deflected 30.0

∘
from its original direction, while asteroid B, which was initially at rest, travels at 45.0
∘
to the original direction of A (Fig. E8.30). (a) Find the speed of each asteroid after the collision. (b) What fraction of the original kinetic energy of asteroid A dissipates during this collision?

Answer 1

To solve the asteroid collision question, we use the conservation of linear momentum to find the final velocities of the asteroids after collision and to establish the energy dissipation, we compare the initial and final kinetic energies.

The question addresses a classic two-dimensional collision scenario in physics, involving momentum conservation and energy conservation principles. When two bodies collide, the momentum before and after the collision remains constant if no external forces are acting on them. In the case where asteroids A and B have equal masses and asteroid A deflects by 30 degrees while B travels 45 degrees relative to A's original direction, we can set up a system of equations based on the conservation of momentum in two dimensions (x and y components). Using the given angles, we solve for the final velocities of each asteroid. Meanwhile, kinetic energy is typically not conserved in inelastic collisions, which is suggested by the question about the fraction of the original kinetic energy dissipating, requiring a separate calculation.

The collision's aftermath can be determined by applying the laws of conservation to find the final velocities and the change in kinetic energy. This kind of problem enhances understanding of dynamics and energy concepts in physics, and also gives insight into real-world phenomena like asteroid movements and collisions in space.