3. A 500 g block of wood is at the top of a ramp. It slides down the ramp and collides with a 750 g cart that is at rest at the bottom of the ramp. After the collision, the cart is traveling at 2.55 m/s and the block is at rest. How tall is the ramp?

Niobium forms a substitutional solid solution with vanadium. compute the number of niobium atoms per cubic centimeter for a niobium-vanadium alloy that contains 24 wt% nb and 76 wt% v. the densities of pure niobium and vanadium are 8.57 and 6.10 g/cm3, respectively

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

An open cart is moving along a straight frictionless horizontal track. when rain starts falling vertically into the cart, what happens to the speed of the cart?