A lighter-than-air balloon and its load of passengers and ballast are floating stationary above the earth. ballast is weight (of negligible volume) that can be dropped overboard to make the balloon rise. the radius of this balloon is 6.52 m. assuming a constant value of 1.29 kg/m3 for the density of air, determine how much weight must be dropped overboard to make the balloon rise 107 m in 14.4 s.

Question

Physics

Larry Brennan

30 May, 11:14

A lighter-than-air balloon and its load of passengers and ballast are floating stationary above the earth. ballast is weight (of negligible volume) that can be dropped overboard to make the balloon rise. the radius of this balloon is 6.52 m. assuming a constant value of 1.29 kg/m3 for the density of air, determine how much weight must be dropped overboard to make the balloon rise 107 m in 14.4 s.

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Rudy Little · Answer 1

Step 1: Find the upward acceleration.

d = 107 m

a = ?

vi = 0

t = 14.4 sec

d = vi * t + 1/2 at^2

107 = 1/2 a * 14.4^2

a = 214 / (14.4) ^2

a = 1.03 m/s^2

Step 2: Find the Volume of the balloon and from that the mass.

V = 4/3 * pi * r^3

r = 6.52 m

V = 4/3 x pi x 6.52^3

V = 1,161 m^3.

Density of air = m/V 1.29 = m / 1161

M = 1.29 x 1161

m = 1498 kg

Step 3: The force keeping this in equilibrium = F = m * g

F = 1498 * 9.81 = 14692 N

Step 4: Find the mass needed to cause the upward acceleration.

14692 = (1498 - x) * (9.81 + 1.03)

14692 = (1498 - x) * 10.84 Divide both sides by 10.84

1355.35 = 1022 - x

1355.35 - 1022

x = 333.35 kg