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Q. Legend has it that, many centuries ago, Archimedes jumped out of his bathtub and ran across town naked screaming "Eureka!" after he solved an especially difficult problem. Though you may not have thought of things this way before, when you drink a glass of water, the water that you are drinking contains some water molecules that were in Archimedes' bathwater that day, because water doesn't get created or destroyed on a large scale. It follows the water cycle, which includes rain, evaporation, flowing of rivers into the ocean, and so on. In the more than two thousand years since his discovery, the water molecules from Archimedes' bathwater have been through this cycle enough times that they are probably about evenly distributed throughout all the water on the earth. When you buy a can of soda, about how many molecules from that famous bathtub of Archimedes are there in that can?
An object at rest explodes into three pieces of equal masses. One moves east at 23 m/s, while the second piece moves northwest at 14 meter per second. Find the velocity of the third piece?
Two cars are traveling along a straight road. Car A maintains a constant velocity of 110 km/h and car B maintains a constant speed of 110 km/h. At t= 0, car B is 45 km behind car A. How far would car A travel from t = 0, before it is overtaken by c..
Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 24.0 in a direction 60.0 west of north. Jane walks 12.0 in a direction 20.0 south of west. They then ..
Consider two dimensional simple triangular lattice for free electron metal with two electrons per atom. Assume the lattice constant is a, find the areas electron and hole pockets that are formed in the second and first Brillouin zones respectively. F..
Calculate the period T and the tension in the string F as a function of the angle. Compute the moment of inertia of this system for an axis that passes through the combined center of mass and is perpendicular to the plane of the rings.
A 65kg trampoline artist jumps vertically upward from the top of a platform that is 2 m above the trampoline with a speed of 4.80m/s.
A slab of marble is resting on the ground. It weighs 600 N and has the dimensions 0.1m x 0.2m x 1.0m. What is the greatest pressure that the slab can exert on ground.
A U-shaped tube is open to the air at both ends and is partially filled with Mercury (density = 13,600 kg/m3). Water (density = 1000 kg/m3) is poured into the left arm until the water is 10 cm deep. How long upward from its initial position does t..
A rabbit runs in the straight line with a velocity of +1.6 m/s for a period of time, rests for 12 s, and then runs again along the equivalent line at +0.52 m/s for an unidentified amount of time. The rabbit travels the total distance of 1224 m, and i..
A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end. Determine the force that the table exert on the box if the weight hanging on the other side of the pulley ..
Two freight cars, each with a mass of 2.9 x 10^5 kg, collide and stick together. One was initially moving at 2.80 m/s and the other was at rest. What is the final speed.
A loudspeaker of mass 20.00 {rm kg} is suspended the distance of h = 2.40 {rm m} below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 3.50 {rm m}.
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