An empty rubber balloon has a mass of
0.01 kg . The balloon is filled with helium
at a density of 0.181 kg/m3
. At this density
the balloon has a radius of 0.493 m .
If the filled balloon is fastened to a vertical
line, what is the tension in the line? The
acceleration of gravity is 9.8 m/s
2
.
Answer in units of N
To find the tension in the line, we need to consider the buoyant force acting on the balloon and the weight of the balloon.
The buoyant force is given by the formula:
Buoyant force = density * volume * acceleration due to gravity
The volume of a balloon can be calculated using the formula for the volume of a sphere:
Volume = (4/3) * pi * radius^3
Substituting the given values, we can calculate the volume of the balloon:
Volume = (4/3) * pi * (0.493 m)^3
Next, we can calculate the buoyant force:
Buoyant force = (density of helium) * (volume) * (acceleration due to gravity)
= 0.181 kg/m^3 * [(4/3) * pi * (0.493 m)^3] * 9.8 m/s^2
Next, let's calculate the weight of the balloon:
Weight = mass * acceleration due to gravity
= 0.01 kg * 9.8 m/s^2
Finally, the tension in the line is equal to the difference between the buoyant force and the weight:
Tension in the line = Buoyant force - Weight
Now, plug in the values and calculate the tension:
Tension in the line = (0.181 kg/m^3 * [(4/3) * pi * (0.493 m)^3] * 9.8 m/s^2) - (0.01 kg * 9.8 m/s^2)
Calculate the expression within the parentheses first, then subtract the weight.
The answer will be in units of Newtons (N).