Consider a balloon of mass 0.030kg being inflated with a gas of density 0.54kg/m³.
What will be the volume of the balloon when it just begins to rise in air of 1.29kg/m³.
Take g=10m/s²
the weight of the balloon is .030 * 10 = 0.3 N
the weight of the gas of volume v is 0.54*10 N
The lifting force of a volume of v m³ of displaced air is 1.29v N
so, we need
1.29*10*v = 0.3 + 0.54*10*v
or
1.29v = 0.03+0.54v
...
Jeriq
To calculate the volume of the balloon when it just begins to rise, we need to equate the weight of the balloon to the buoyant force exerted on it.
Step 1: Calculate the weight of the balloon:
Weight = mass x acceleration due to gravity
Weight = 0.030 kg x 10 m/s²
Weight = 0.3 N
Step 2: Calculate the buoyant force:
Buoyant force = weight of the air displaced by the balloon
Buoyant force = density of air x volume of air displaced x acceleration due to gravity
Let the volume of the balloon when it starts to rise be V m³.
Buoyant force = (density of air) x V x (acceleration due to gravity)
0.3 N = (1.29 kg/m³) x V x (10 m/s²)
Step 3: Rearrange the equation to solve for V:
V = 0.3 N / [(1.29 kg/m³) x (10 m/s²)]
V = 0.3 N / (12.9 kg/(m²s²))
V ≈ 0.02326 m³
Therefore, the volume of the balloon when it just begins to rise is approximately 0.02326 cubic meters.
To find the volume of the balloon when it just begins to rise in air, we need to equate the buoyant force on the balloon to its weight.
The buoyant force acting on the balloon is given by the formula:
Buoyant force = (Density of fluid) * (Volume displaced) * (Acceleration due to gravity)
In this case, the fluid is air, and its density is 1.29 kg/m³, and the acceleration due to gravity is given as 10 m/s².
Let's assume that the volume of the balloon when it begins to rise is V (m³).
The weight of the balloon is given by:
Weight = (Mass of balloon) * (Acceleration due to gravity)
The mass of the balloon is given as 0.030 kg, and the acceleration due to gravity is 10 m/s².
Now, we can equate the buoyant force to the weight of the balloon:
(Density of fluid) * V * (Acceleration due to gravity) = (Mass of balloon) * (Acceleration due to gravity)
Plugging in the values:
1.29 kg/m³ * V * 10 m/s² = 0.030 kg * 10 m/s²
Simplifying the equation:
V = (0.030 kg * 10 m/s²) / (1.29 kg/m³ * 10 m/s²)
Canceling out the units and calculating:
V = 0.030 / 1.29 = 0.0233 m³
Therefore, the volume of the balloon when it just begins to rise in air is approximately 0.0233 m³.