Respuesta :
Answer:
a) F_b = 6.62 N
b) F_net = 5.583 N
Explanation:
Given:
- Conditions of He gas: T = 0 C , P = 1 atm , ρ = 0.179 kg/m^3
- The mass of balloon m = 0.012 kg
- The radius of balloon r = 0.5 m
Find:
a)What is the magnitude of the buoyant force acting on the balloon?
b)What is the magnitude of the net force acting on the balloon?
Solution:
- The buoyant force F_b acting on the balloon is equal to the weight of the air it displaces.The mass of the displaced air ρ*V is the volume of the balloon times the density of the. Multiplying that by acceleration due to gravity gives its weight.
F_b = ρ*V*g
F_b = 4*ρ*g*pi*r^3 / 3
F_b = 4*1.29*9.81*pi*.5^3 / 3
F_b = 6.62 N
- The net force will be the difference between the balloon’s weight and the buoyant force. The weight of the balloon is the density of the helium times the volume of the balloon added to the mass of the empty balloon.
F_g = ρ*V*g + m*g
F_g = 4*ρ*g*pi*r^3 / 3 + 0.012*9.81
F_g = 4*0.179*9.81*pi*.5^3 / 3 + 0.012*9.81
F_g = 1.037 N
- The net force is the difference between weight and buoyant force
F_net = F_g - F_b
F_net = 6.62 - 1.037
F_net = 5.583 N
The buoyant force and the net force acting the balloon is required.
The buoyant force is 6.63 N.
The net force is 5.6 N.
[tex]\rho_a[/tex] = Density of air = [tex]1.29\ \text{kg/m}^3[/tex]
[tex]\rho_h[/tex] = Density of helium = [tex]0.179\ \text{kg/m}^3[/tex]
[tex]m_b[/tex] = Mass of balloon = 0.012 kg
V = Volume of balloon = [tex]\dfrac{4}{3}\pi r^3[/tex]
r = Radius of balloon = 0.5 m
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
The buoyant force is
[tex]F_B=\rho_aVg\\\Rightarrow F_B=1.29\times \dfrac{4}{3}\pi (0.5)^3\times 9.81\\\Rightarrow F_B=6.63\ \text{N}[/tex]
Net force is given by
[tex]F=F_B-m_bg-\rho_hgV\\ =6.63-0.012\times 9.81-0.179\times 9.81\times \dfrac{4}{3}\pi (0.5)^3\\ =5.6\ \text{N}[/tex]
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