In rural areas, water is often extracted from underground by pumps. consider an underground water source whose free surface is 60 m below ground level. the water is to be raised 5 m above the ground by a pump. the diameter of the pipe is 10 cm at the inlet and 15 cm at the exit. neglecting any heat interaction with the surroundings and frictional heating effects, determine the power input to the pump required for a steady flow of water at a rate of 15 l/s (=0.015 m3/s)

What is the length x of the side of the triangle below? (hint: use the cosine function)

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

(a) calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 10.0 g. silver has 47 electrons per atom, and its molar mass is 107.87 g/mol. (b) imagine adding electrons to the pin until the negative charge has the very large value 1.00 mc. how many electrons are added for every 109 electrons already present