Final answer:
To find the size of a helium balloon needed to lift a 75kg physics teacher, the weight of the teacher in Newtons must be equated with the buoyant force from the displaced air using the density of air and helium. Exact calculations require the ideal gas law and specific environmental data, but a rough estimation can be made using average values.
Step-by-step explanation:
Calculating Required Helium Balloon Size To determine what size of a helium baloon would be needed to lift a 75kg physics teacher, we should consider the lifting force required, which is the weight of the teacher. The buoyant force exerted by the helium inside the balloon must be equal to the weight of the displaced air. The weight of the teacher (including the balloon) in Newtons can be calculated by multiplying their mass by the acceleration due to gravity (75 kg × 9.81 m/s²).
The volume of helium needed to lift the teacher can be found using the density of air and helium, as well as the buoyancy equation. Since helium is less dense than air, it provides a lifting force that is proportional to the difference in densities multiplied by the volume of the helium and the acceleration due to gravity.
To calculate the exact volume, we must use the ideal gas law, taking into account the pressure and temperature of the helium, which affects its density. Considering standard atmospheric pressure and typical balloon expansion properties, a sufficiently accurate estimation can be derived. However, exact calculations require specific environmental data.
An example used in understanding these calculations is the Charles's law experiment with a balloon volume of 31,150 L, which uses the ideal gas law to find the moles of hydrogen gas needed. This demonstrates how the volume of a balloon at a certain temperature and pressure can be related to the amount of gas it contains