1. When s = 0, the spring on the firing mechanism is unstretched. If the arm is pulled back such that s = 100 mm and released, determine the speed of the 0.3-kg ball and the normal reaction of the circular track on the ball when u = 60°. Assume all surfaces of contact to be smooth. Neglect the mass of the spring and the size of the ball.
2. If the mass of the earth is Me, show that the gravitational potential energy of a body of mass m located a distance r from the center of the earth is Vg = - GMem >r. Recall that the gravitational force acting between the earth and the body is F = G(Mem>r2), Eq. 13-1. For the calculation, locate the datum at r S oo . Also, prove that F is a conservative force.
3. A rocket of mass m is fired vertically from the surface of the earth, i.e., at r = r1. Assuming that no mass is lost as it travels upward, determine the work it must do against gravity to reach a distance r2. The force of gravity is F = GMem >r2 (Eq. 13-1), where Me is the mass of the earth and r the distance between the rocket and the center of the earth.