b) Buoyant force, Fb = 3822 N c) Net force on the balloon = 1.037 * 10³ N d) Additional mass of 105 kg can be supported by the balloon in equilibrium.
The upward force a fluid exerts on an object is known as buoyant force. Archimedes' Principle is the fact that buoyant force is equal to the weight of displaced fluid.
Given mass, Mb= 226Kg , Volume of helium, v is 325 m^3
Density of helium, 0.179 kg/m3 ρh is and density of air, ρa is 1.29 kg/m3
Force along the y axis, ΣFy = o, at equilibrium.
ΣFy= Fb - Wh - Wb - mg= 0
ΣFy= FN - mg = 0
ΣFN = Fb - Wh - Wb
Fb is buoyant force
Here Wh is weight of helium and Wb is weight of balloon
ρa is density of air and ρh is density of helium
b) Fb = ρa v g
= 1.2 * 325 *9.8
Fb = 3822 N
c) Fh = ρh v g
= 0.179 * 325 * 9.8
= 570 N
Wb= Mb * g
= 226 * 9.8
= 2214.8 N
ΣFn= 3822- 570 - 2214.8
= 1037 N
Net force on the balloon = 1.037 * 10³ N
ΣFy = 1037 - mg= 0
m= 105 kg
Additional mass of 105 kg can be supported by the balloon in equilibrium.
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