A roller coaster has a small vertical loop with the lowest point 5 meters above the ground. The initial elevation from which the cart was released is 62.5 m. What should be radius of that loop to make sure the vertical acceleration at the bottom point does not exceed 2g?

Alarge cruise ship of mass 7.00 ✕ 107 kg has a speed of 11.6 m/s at some instant. (a) what is the ship's kinetic energy at this time? (b) how much work is required to stop it? (give the work done on the ship. include the sign of the value in your answer.) (c) what is the magnitude of the constant force required to stop it as it undergoes a displacement of 3.00 km?