A mountain climber friend with a mass of 80kg ponders the idea of attaching a helium-filled balloon to himself to effectively reduce his weight by 25% when he climbs. He wonders what the approximate size of such baloon would be.
Buoyancy force
= Volume*(air density - helium density)- (balloon fabric mass)
= desired mass reduction = 20 kg
Solve for the volume.
You will have to assume a gas pressure and temperature. You should also take into account the mass of the material of the ballon, but they probably expect you to ignore it.
To determine the approximate size of the helium-filled balloon needed to reduce the mountain climber's weight by 25%, we can use the concept of buoyancy.
Buoyancy is the upward force exerted on an object immersed in a fluid, in this case, the helium-filled balloon in the air. This force is equal to the weight of the fluid displaced by the object.
Here's how we can calculate the approximate size of the balloon:
Step 1: Calculate the weight of the mountain climber without the balloon.
- Given that the climber's mass is 80kg and the acceleration due to gravity is approximately 9.8 m/s², we calculate the weight:
Weight = mass × acceleration due to gravity
Weight = 80kg × 9.8 m/s²
Step 2: Calculate the reduced weight with the balloon.
- The climber wants to reduce his weight by 25%. To do this, we calculate 25% of his weight and subtract it from his original weight:
Reduced Weight = Weight - 25% of Weight
Reduced Weight = Weight - (0.25 × Weight)
Step 3: Calculate the volume of helium needed.
- The volume of the balloon can be determined using the equation:
Buoyant Force = Weight of Displaced Air
Buoyant Force = Weight of Helium
Weight of Helium = Volume of Helium × Density of Air × acceleration due to gravity
Since the climber wants to reduce his weight by 25%, the buoyant force needs to equal 25% of his weight without the balloon. Therefore:
Buoyant Force = 0.25 × Reduced Weight
We set the weight of the helium equal to the buoyant force:
Volume of Helium × Density of Air × acceleration due to gravity = Buoyant Force
Step 4: Convert the volume of helium to the balloon's size.
- Given that helium has a density of approximately 0.18 kg/m³, we can solve for the volume of helium:
Volume of Helium = Buoyant Force / (Density of Air × acceleration due to gravity)
Once you have the volume of helium, consider factors such as the shape and material of the balloon to determine an appropriate size for practical use.
By following these steps, you can calculate the approximate size of the helium-filled balloon that the mountain climber may need to effectively reduce his weight by 25%.
To find the approximate size of the helium-filled balloon, we can use the concept of buoyancy. The buoyant force on an object submerged in a fluid (in this case, air) is equal to the weight of the fluid displaced by the object. In this case, the object is the balloon.
Let's assume that the density of air is approximately 1.2 kg/m^3 and the density of helium is approximately 0.18 kg/m^3. We can use these values to calculate the volume of helium needed to offset 25% of the climber's weight.
First, let's find the climber's weight:
Weight = mass * gravity
Weight = 80 kg * 9.8 m/s^2 ≈ 784 N
Since the climber wants to reduce their weight by 25%, the new weight that the balloon needs to offset would be:
New weight = 0.75 * Weight
New weight = 0.75 * 784 N ≈ 588 N
Now, let's calculate the volume of helium needed to generate this buoyant force:
Buoyant force = Weight of displaced air
Buoyant force = Weight of helium
Weight of helium = density of helium * volume of helium * gravity
Using the equation Weight of helium = Buoyant force = 588 N:
588 N = 0.18 kg/m^3 * volume of helium * 9.8 m/s^2
Rearranging the equation to solve for the volume of helium:
volume of helium = 588 N / (0.18 kg/m^3 * 9.8 m/s^2)
volume of helium ≈ 3339.51 m^3
So, the approximate size of the helium-filled balloon needed to effectively reduce the climber's weight by 25% would be around 3339.51 cubic meters.