On October 21, 2001, Ian Ashpole of the United Kingdom achieved a record altitude of 3.35 km (11,000 ft) powered by 600 toy balloons filled with helium. Each filled balloon had a radius of about 0.45 m and an estimated mass of 0.27 kg.
(a) Estimate the total buoyant force on the 600 balloons. (Enter your answer to at least two decimal places.)
To estimate the total buoyant force on the 600 balloons, we can use the principle of buoyancy, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
To start, we need to find the volume of each balloon. Since the balloons are spherical, the volume can be calculated using the formula:
V = (4/3) * π * r^3
Where:
V = volume of the balloon
r = radius of the balloon
Using this formula, we can calculate the volume of one balloon:
V = (4/3) * π * (0.45)^3
V ≈ 0.381 m^3
Next, we need to calculate the total volume of the 600 balloons:
Total Volume = 600 * 0.381
Total Volume ≈ 228.6 m^3
Now, we can calculate the buoyant force using the density of the surrounding air. The density of air at sea level is approximately 1.225 kg/m^3.
The formula for buoyant force is:
Buoyant Force = Density of Fluid * Volume Displaced * Acceleration due to Gravity
Buoyant Force = 1.225 kg/m^3 * 228.6 m^3 * 9.8 m/s^2
Buoyant Force ≈ 2,703.65 N
Therefore, the estimated total buoyant force on the 600 balloons is approximately 2,703.65 Newtons.
To estimate the total buoyant force on the 600 balloons, we need to calculate the buoyant force on a single balloon and then multiply it by the number of balloons.
To calculate the buoyant force on a single balloon, we'll use the formula:
Buoyant force = Weight of the fluid displaced by the balloon
Since the balloon is filled with helium, it will displace an equal volume of air. The weight of the air displaced is equal to the mass of the air multiplied by the acceleration due to gravity (9.8 m/s^2). The mass of the air is calculated by multiplying its density by the volume of the air displaced.
Let's assume the density of air is approximately 1.2 kg/m^3 (at sea level and standard conditions). The volume of the air displaced by a balloon can be calculated using the formula for the volume of a sphere:
Volume = (4/3) * π * (radius)^3
Substituting the given values:
radius = 0.45 m,
density of air = 1.2 kg/m^3,
Volume = (4/3) * 3.14 * (0.45)^3 = 0.381 m^3
Now, we can calculate the mass of the air displaced:
Mass = density * volume = 1.2 kg/m^3 * 0.381 m^3 = 0.4572 kg
Finally, we can calculate the buoyant force on a single balloon:
Buoyant force = Weight of the air displaced = mass * gravity = 0.4572 kg * 9.8 m/s^2 = 4.48296 N
Since there are 600 balloons, the total buoyant force can be found by multiplying the buoyant force on a single balloon by 600:
Total buoyant force = 4.48296 N * 600 = 2,689.78 N
Therefore, the estimated total buoyant force on the 600 balloons is approximately 2,689.78 Newtons.
first, figure the total mass of the balloons, and then their weight
next, figure the total volume of the balloons
next, find the density of air at the given altitude
then, the lifting force of the displaced air is volume * density (in units of weight/m^2)
subtract the weight from the lifting force to find how much weight can be lifted