A railroad hopper car is filled with sand and rolling with an initial speed of Vi on straight, horizontal tracks. You can ignore frictional forces on the railroad car. The total mass of the car plus sand is Mtotal. The hopper door is not fully closed, so that sand leaks out of the bottom. After some time t, mass M = 1 /4Mtotal has leaked out. What is the speed of the railroad car at time t?

Athin electrical heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm. the rod (a) has a thermal conductivity of ka = 0.15 w/(m*k), while the tube (b) has a thermal conductivity of kb = 0.8 w/(m*k) and its outer surface is subjected to convection with a fluid of temperature t= -15°c and heat transfer coefficient 60 w/(m2 *k). the thermal contact resistance between the cylinder surfaces and the heater is negligible. (a) determine the electrical power per unit length of the cylinders (w/m) that is required to maintain the outer surface of cylinder b at 15°c. (b) what is the temperature at the center of cylinder a?