A mountain-climber friend with a mass of 82 kg 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 a balloon would be. Hearing of your physics skills, he asks you. Share with him your calculations that find the volume of the balloon.
To calculate the approximate size of the balloon required to reduce your friend's weight by 25%, we'll take the following steps:
1. Determine the weight reduction percentage: The weight reduction percentage is given as 25%.
2. Calculate the weight reduction: The weight reduction is equal to the percentage reduction multiplied by the weight of the climber. In this case, the weight reduction would be 0.25 (25% expressed as a decimal) multiplied by 82 kg (the climber's mass). The weight reduction is equal to 20.5 kg.
3. Convert weight to the mass of the displaced air: Since the climber plans to achieve weight reduction through buoyancy, we need to calculate the mass of the air that the balloon must displace to counteract 20.5 kg of weight. We can use the density of air, which is approximately 1.225 kg/m³.
- Mass = Weight / acceleration due to gravity = 20.5 kg
- Volume of the displaced air = Mass / Density = 20.5 kg / 1.225 kg/m³
- Volume of the displaced air ≈ 16.7 m³
4. Calculate the volume of the balloon: The volume of the balloon should be equal to the volume of the displaced air. This will ensure that when the balloon is filled with helium, it can displace the equivalent amount of air to counterbalance the weight.
Therefore, the approximate size of the balloon would be 16.7 m³.
Keep in mind that this calculation assumes ideal conditions and doesn't account for various factors such as the density of helium, the climber's body position, atmospheric conditions, and the load-bearing capacity of the climber's equipment. It is important for your friend to consult with mountain climbing experts and follow standard safety practices if they intend to pursue this idea further.