An empty rubber balloon has a mass of 0.0107 kg . The balloon is ?lled with heli

Question

An empty rubber balloon has a mass of 0.0107 kg . The balloon is ?lled with helium at a density of 0.18 kg/m3 . At this density the balloon has a radius of 0.475 m . If the ?lled balloon is fastened to a vertical line, what is the tension in the line? The acceleration of gravity is 9.8 m/s . Answer in units of N

Explanation / Answer

lets balance forces acting on the balloon weight downwards = (M+m) g force of bouyancy = V ?(air) g (upwards) Tension = T (downwards) ---------------------- if something is tied by string to an object, tension acts on the object to which it is tied >> direction balloon to vertical line ------------------------ we can write (M+m) g + T = V ?(air) g here M = mass of ballon = 0.0120 V = volume of ballon = (4pi/3) R^3 = 0.52333 m^3 m = mass of helium = ?(He) V ?(air) = 1.29 kg/m^3>>>> see link below **** this worked with this air density. normally we take density -air =1.2 http://www.mcrel.org/whelmers/whelm33.as… search density of air in this link ============ T = V ?(air) g - Mg - mg T = V ?(air) g - Mg - ?(He) V g T = V g [?(air) - ?(He)] - Mg T = 0.52333*9.8 [1.29 - 0.181] - 0.0120*9.8 T = 5.688 - 0.118 T = 5.569 N = 5.57 N

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