The density of air in the Earth’s atmosphere decreases according to the function
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Physics for Scientists and Engineers: Foundations and Connections
- How many cubic meters of helium are required to lift a light balloon with a 400-kg payload to a height of 8 000 m? Take Hc = 0.179 kg/m3. Assume the balloon maintains a constant volume and the density of air decreases with the altitude z according to the expression pair = 0e-z/8 000, where z is in meters and 0 = 1.20 kg/m3 is the density of air at sea level.arrow_forwardIn 2011, artist Hans-Peter Feldmann covered the walls of a gallery at the New York Guggenheim Museum with 100,000 one-dollar bills (Fig. P1.48). Approximately how much would it cost you to wallpaper your room in one-dollar bills, assuming the bills do not overlap? Consider the cost of the bills alone, not other supplies or labor costs. FIGURE P1.48arrow_forwardA 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.arrow_forward
- The erythrocyte sedimentation rate (heaviness) test is often used for a blood sample as a diagnosis of the body's immune disorders and some other diseases. Assuming that the red blood cells are about a sphere of diameter ( 5 um ) and density ( g / ml 1.125 ) and the density and viscosity of the plasma in which the red blood cells are settled (Pa.s), (1025 kg / m3 10-3 x 1.5) respectively The acceleration m / s 9.81 Calculate the rate of sedimentation (settling speed) of red blood cells.arrow_forwardA tank is filled with oil whose density is p-850 kg/m3. If the volume of the tank is V= 3m³, determine the amount of mass m in the tank.arrow_forwardIf you tried to smuggle gold bricks by filling your backpack, whose dimensions are 60cm×32cm×20cm60cm×32cm×20cm, what would its mass be? The density of gold is 19.3 ×× 1033 kg/m3kg/m3.arrow_forward
- A tank is filled with oil whose density is r 5 850 kg/m3. If the volume of the tank is V 5 2 m3, determine the amount of mass m in the tank.arrow_forwardThe 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.arrow_forwardBalloons are usually filled with helium gas because the density of helium gas under the same conditions is one-seventh the density of air. The buoyant force given by the relation "Fb = ρ(air).g.V(balloon)" pushes the balloon upwards. People with a mass of 70 kg get on a spherical balloon with a diameter of 10 m. The number of people getting into the cabin of the balloon is 3. In this case, calculate the acceleration of the balloon during its take-off. Take the density of the air 1.16 kg / m3 and neglect the weight of the balloon and the cabin.arrow_forward
- blood flows through the aorta at an average speed of v=18 cm/s. The aorta is roughly cylindrical with a radius r=18.0 mm. The volume rate of blood flow through the aorta is 3.14r^2v. Calculate the volume rate of blood flow through the aorta in L.min.arrow_forwardAn airplane passenger has a volume V1 of air in his stomach just before the plane takes off from a sea-level airport. What volume will this quantity of air have at cruising altitude at the same temprerature ( body temp. ), in terms of V1, the pressure on the ground P1, and the cabin pressure at cruising altitude P2? What is this volume, in cubic centimeters, if the initial volume is 110 cm^3 and the cabin pressure drops to 7.5x10^4 Pa when the plane is at cruising altitude?arrow_forwardVariation of Pressure in the atmosphere. The pressure of the atmosphere decreases as we move higher in the atmosphere. The decrease in pressure is proportional to the decrease in density of air. р = 2|2° P P Where P = pressure at any point in the atmosphere, and p = density of air at any point in the atmosphere Po pressure at sea level = 1.013 x 105 Pa, and Po air density at sea level = 1.3 kg/m³. a) What is the density p in terms of po, P, and Po? b) Start from the formula dP = - p g dy to determine the pressure at any height y. Note: P is variable c) What is the pressure if the height is 5.0 km above sea level? d) At what height above sea level is the pressure equal to ½ Po ?arrow_forward
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