Question

4. Consider two asteroids with masses mi and m2 located in outer space far away from any external forces. m2 is initially stationary but mi travels horizontally to the right towards m2 with an initial speed vo. Let's assume that after the collision the asteroids only move horizontally (in other words we'll assume this problem is purely 1-dimensional) a) Suppose the asteroids stick together after colliding. Find an expression for the final velocity of the asteroids and show that the collision must be inelastic by deriving an expression for the ratio of the final kinetic energy over the initial kinetic energy b) Now let's assume the collision is elastic. Find an expression for the final velocity of mi and the final velocity of m2 What determines whether mi continues moving to the right, stops, or changes direction? c) Did the impulse on mi have a larger magnitude for the scenario in part a) or part b)? Or are you unable to tell without being given more information? d) We are always free to work in any reference frame or inertial frame. Lct's pick an inertial frame in which the total momentum of the system is zero. How are the initial velocitics of mi and m2 rclated in this reference frame? Now let's again consider the case that the asteroids stick together and the case that the collision is elastic. Find an expression for the final velocity of mi and the final velocity of m2 for each case in this new inertial frame. Then take the velocities you found and transform back to the reference frame used in parts a) and b) (in which m2 is initially at rest) in order to show that the answers are indeed consistent. You should find that in the zero momentum frame some of the algebra is simpler Also note that the total kinetic energy of a system can have a different value in different inertial frames. This is fine; it has nothing to do with conservation of energy. In general the total energy of a system can have different values in different inertial frames and different coordinate systems

Answer 1

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