A cart of mass m1 = 10 kg slides down a frictionless ramp and is made to collide with a second cart (initially at rest) of mass m2 = 20 kg, which then heads into a vertical loop of radius 0.25 m as shown in Figure P7.66. Derive the expression of height h, in terms of radius r, from which cart 1 would need to start to make sure that cart 2 completes the loop without leaving the track and, hence, determine the value of h. Assume an elastic collision.

The magnitude of the amount of energy released by burning a fuel source, measured in energy per unit mass, is called its fuel value. note that the fuel value is the negative of the isobaric specific heat of combustion for the fuel. if all the energy obtained from burning 1.23 pounds of butane with a fuel value of 10.85 kcal/g is used to heat 128.0 kg of water at an initial temperature of 18.3 °c, what is the final temperature? note that 1 lb = 453.6 g.