Consider a balloon of mass 0.030kg being inflated with a gas of density 0.54kgm_3 what will be the volume of balloom when it just begins to rise in air of density 1.2kg per m_3
i wish i could help but i do not know what that is
it will rise when the weight of air displaced is the same as the gas plus the balloon. Since mass = density * volume,
Filled balloon weight: 9.81(0.030 + 0.54v)
displaced air weight: 9.81*1.2v
so, when they are equal,
0.030 + 0.54v = 1.2v
v = 0.030/0.66 = 0.045 m^3
To find the volume of the balloon when it just begins to rise in air, we need to compare the buoyant force acting on the balloon to its weight.
The buoyant force (F_b) is given by the formula:
F_b = (density of fluid) * g * V
where:
- (density of fluid) is the density of the fluid displaced (in this case, the density of air)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- V is the volume of the fluid displaced
The weight (F_g) of the balloon is given by the formula:
F_g = m * g
where:
- m is the mass of the balloon
- g is the acceleration due to gravity
For the balloon to just begin to rise, the buoyant force must be equal to the weight of the balloon:
F_b = F_g
Now let's plug in the values given in the problem:
m = mass of balloon = 0.030 kg
(density of fluid) = density of air = 1.2 kg/m^3
g = acceleration due to gravity = 9.8 m/s^2
F_g = m * g = 0.030 kg * 9.8 m/s^2 = 0.294 N
Now we can equate the two forces and solve for the volume (V):
F_b = F_g
(density of fluid) * g * V = m * g
1.2 kg/m^3 * 9.8 m/s^2 * V = 0.030 kg * 9.8 m/s^2
1.2 * V = 0.030
V = 0.030 / 1.2
V = 0.025 m^3
Therefore, the volume of the balloon when it just begins to rise in air is 0.025 m^3.