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- A rod extending between x = 0 and x = 14.0 cm has uniform cross-sectional area A = 9.00 cm2. Its density increases steadily between its ends from 2.70 g/cm3 to 19.3 g/cm3. (a) Identify the constants B and C required in the expression = B + Cx to describe the variable density. (b) The mass of the rod is given by m=allmaterialdV=allxAdx=014.0cm(B+Cx)(9.00cm2)dx Carry out the integration to find the mass of the rod.A straightforward method of finding the density of an object is to measure its mass and then measure its volume by submerging it in a graduated cylinder. What is the density of a 240-g rock 89.0 cm3 of water? (Note that the accuracy and practical applications of this technique are more limited than a variety of others that are based on Archimedes' principle.)A certain hydraulic system is designed to exert a force 100 times as large as the put into it. (a) What must be the ratio of the area of the cylinder that is being controlled to area of the master cylinder? (b) What must be the ratio of their diameters? (c) By what factor is the distance through which the output force moves reduced relative to the distance through which input force moves? Assume no losses due to friction.
- What is the mass density δ(x, y, z) of a solid of volume 5 m^3 with uniform mass density and total mass 25 kg?The linear density of a rod of length 4 m is given by p(x) = 8 + 2Vx measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the ra kgThe atmospheric pressure (P), in pounds per square inch, at x miles above sea level is given approximately by P = 17.2e -0.21x 0. At what height will the atmospheric pressure be half If sea level pressure is the pressure at x = the sea level pressure?
- Let ρAl represent the density of aluminum and ρFe that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius rFe on an equal-arm balance.Approximate the change in the atmospheric pressure when the altitude increases from z=6 km to z= 6.05 km using the formula P(z) = 1000 e From z = 6 km to z=6.05 km, the change in atmospheric pressure is approximately (Type an exact answer.) etThe atmospheric pressure P(x) (measured in inches of mercury) at height x miles above sea level satisfies the differential equation P (x) = -.2P(x). Find the formula for P(x) if the atmospheric pressure at sea level is 29.92.
- by I m. They found the girths to be 6.3 m (at eround level), 5.4 m, 4.6 m, 4.4 m, 4.8 m and 3.9 m, and then the stone tapered to a point at a beight of 6 m. Assuming that the stone is made of basalt of density 2s00 kg/mand is nearly square in crosssection, find an approximation for the mass of the stone. Hint: Mass of an object m is given by the formula m = pV, where p is density and V is volume of the object.Iron has a density of 7.87 g/cm3, and the mass of an iron atom is 9.27 * 10-26 kg. If the atoms are spherical and tightly packed, (a) what is the volume of an iron atom and (b) what is the distance between the centers of adjacent atoms?A block of wood is kept on table top. The mass of wooden block is 5kg and its dimensions are 40cmx20cmx10cm. Compute the force on top and bottom surface of the wooden block.
