Consider a children’s cartoon illustrating a child holding the strings of several helium balloons and being lifted into the sky. a. Estimate the minimum number of 10.-L balloons it would take to lift a 50.-lb child. Assume air has an average molar mass of 29 g/mol, and assume the masses of the balloons and strings are negligible. b. Explain why the balloons can lift the child.

First, we need to convert the weight of the child to mass since we're given the weight in pounds. Since 1 kg equals approximately 2.205 lbs, we can find the mass by dividing the child's weight by 2.205. Mass of child = 50 lbs / 2.205 = 22.68 kg Now we can calculate the force required to lift the child. The formula for force is F = m * g, where F is the force, m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²). F = 22.68 kg * 9.8 m/s² = 222.25 N The force required to lift the child is 222.25 Newtons.

To find the buoyant force exerted by one helium balloon, we first determine the difference in densities of air and helium. The density of a gas can be calculated using the formula: density = (mass * molar mass) / (volume * gas constant * temperature). We are given that the molar mass of air is 29 g/mol, which is equal to 0.029 kg/mol. The molar mass of helium is 4 g/mol, which is equal to 0.004 kg/mol. Assume the temperature to be 298 K and the gas constant to be 8.314 J/(K*mol). Assume volume of each balloon to be 10 L, equal to 0.01 m³. Density of air: ρ_air = (1 atm * 0.029 kg/mol) / (0.01 m³ * 8.314 J/(K*mol) * 298 K) = 1.184 kg/m³ Density of helium: ρ_helium = (1 atm * 0.004 kg/mol) / (0.01 m³ * 8.314 J/(K*mol) * 298 K) = 0.165 kg/m³ Now we can find the buoyant force exerted by one helium balloon using Archimedes' principle: buoyant force = volume * (density of air - density of helium) * g. Buoyant force = 0.01 m³ * (1.184 kg/m³ - 0.165 kg/m³) * 9.8 m/s² = 0.0998 N The buoyant force exerted by one helium balloon is 0.0998 Newtons.

To find the minimum number of balloons needed, we will divide the force required to lift the child by the buoyant force exerted by one helium balloon. Minimum number of balloons = force required to lift the child / buoyant force exerted by one helium balloon Minimum number of balloons = 222.25 N / 0.0998 N ≈ 2228 We will need approximately 2228 10-L helium balloons to lift a 50-lb child into the sky.

Helium balloons can lift the child because of the buoyant force resulting from the difference in densities between helium and air. Helium has a lower density than air, and when enclosed in a balloon, it displaces a volume of air that is heavier than the helium itself. This difference in weight creates an upward force called buoyant force, which acts against the force of gravity acting on the child's weight. When the buoyant force exerted by a certain number of helium balloons is greater than or equal to the total weight of the child, the child is lifted into the sky.