Problem 9 (Buoyancy). High-altitude balloons are often filled with helium gas be

Question

Problem 9 (Buoyancy). High-altitude balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force, which can be expressed as Fbuoy Pairgallon will push the balloon upward. If we approximate the shape of the balloon as a sphere with a radius of 6 m anod a total payload of 150 kg (including the ropes, cage, and the balloon itself), determine the acceleration of the balloon when it is first released. Assume the density of air is Pair = 1.16 kg/m3 and take tenth-place. (a) 16.5 m/s2 (c 13.7 m/s (e) None of these Pne-ir. Take g = 9.8 m/s. Round to the nearest (b) 24.5 m/s (d) acceleration is negative, can't lift off Problem 10. A vertical, frictionless piston-cylinder device contains a gas that is in equilibrium with the weight of the piston balanced by the internal pressure for the gas Suppose the mass of the piston is m-10kg, the area of the piston is A = (1/10) m2, the atmospheric pressure outside the cylinder is Ptm 100 kPa, and taking g 10 m /s2 determine the pressure of the gas gas contained in the piston-cylinder device (a) 100 kPa (c) 101 kPa (e) None of these (b) 100.1 kPa (d) 110 kPa

Explanation / Answer

Problem 9

Given

radius of the spherical ballon with helium is r = 6 m

the volume of the ballon is V = (4/3)pi*6^3 m^3 = 904.78 m^3

densityh of air is rho_air = 1.16 kg/m^3

density of helium is rho _he = (1/7) rho_air= 1/7*1.16 kg /m^3 = 0.1657 kg /m^3

g = 9.8 m/s2

the buoyance force is F_b = rho_air*V*g

m*a = rho_air*V*g

rho_he*V*a = rho_air*V*g

a = rho_air*V*g /rho_he*V

substituting the values

a = 1.16*9.8 /(0.1657) m/s2 = 68.61 m/s2

Problem 10

mass of the piston is m = 10 kg , g = 10 m/s2

weight is F = W = 10*10 N = 100 N

the pressure by definition is P = F/A ==> P = 100*1/10 = 1000 Pa = 1 k Pa

the atmospheric pressure out side is P_a = 100 kPa

the total pressure is P = 100 +1 kPa = 101 kPa

the answer is option c 101 k Pa

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