a hot air balloon weighing 30N is tied to the ground by a string to prevent from floating off the ground. The volume of the balloon is 20m³ and the density of air is 1.3kgm-³. find fhe force exerted by the rope on the balloon

The force exerted by the rope is FT = 225.06 [N]

Explanation:

In order to solve this problem we must use a static analysis, since Globe does not move. For a better understanding in solving this problem, a free body diagram with the forces acting on the globe is attached.

The buoyant force acts upward as it causes the balloon to tend to float, the weight of the balloon tends to lower the balloon and the downward tension force does not allow the balloon to float

The buoyant force is defined by the following equation:

FB = Ro*V*g

where:

FB = Buoyant force [N]

Ro = density of the air = 1.3 [kg/m^3]

V = volume of the balloon = 20 [m^3]

g = gravity acceleration = 9.81 [m/s^2]

FB = 1.3*20*9.81 = 255.06 [N]

Now we do a sum of forces equal to zero in the y-axis

FB - 30 - FT = 0

255.06 -30 = FT

FT = 225.06 [N]

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