Question

A boxcar of length 9.9 m and height 2.4 m is at rest on frictionless rails. Inside the boxcar (whose mass when empty is 3600 kg) a tank containing 1800 kg of water is located at the left end. The tank is 1.1 m long and 2.4 m tall. At some point the walls of the tank start to leak, and the water fills the floor of the boxcar uniformly. Assume that all the water stays in the boxcar. After all the water has leaked out what will be the final velocity of the boxcar? (Take movement to the right as positive. Assume that the mass of the boxcar is evenly distributed.) What is the displacement of the boxcar 8 S after the water has settled in the bottom. (Take positive displacement as being to the right.)

Answer 1

Suppose b is the width of the car and the tank. Then the area of the car is A-9.9(b) The volume of the water tank is V (1.1m) (2.4m)(b) 2.64b Height of the water in the car is, V 2.64b A 9.9b 0.26m Thus, the center of mass of water is located at 0.13 m. Change in potential energy of the water must be equal to kinetic energy of the system is, 2.4m (1800kg) (9.8m/s (1.07m) (180 0 kg +3600 kg)v v 2.64 m/s Therefore the distance moved is d -vt (2.64m/s) (8s)21m