A 3200 kg police car traveling North at 40 m/s collides with another car also traveling North. The second car has a mass of 2000 kg and its velocity is 30 m/s North just before the collision. If the cars stick together on contact what will be their common velocity just after collision? Neglect the effect of friction from the road.

Two identical stars with mass m orbit around their center of mass. each orbit is circular and has radius r, so that the two stars are always on opposite sides of the circle. (a) find the gravitational force of one star on the other. (b) find the orbital speed of each star and the period of the orbit. (c) how much energy would be required to separate the two stars to infinity?