A party balloon with a radius of 12.5 cm is filled with helium. How much weight can this balloon lift? Neglect the weight of an empty balloon. (density of air = 1.29 kg/m3, density of helium = 0.178 kg/m3)
volume of air displaced is v = 4/3 πr^3
weight = mg = volume*density * g
now subtract the weight of the balloon from that of the displaced air.
To calculate the weight that the balloon can lift, we need to consider the buoyant force acting on it. The buoyant force is the upward force exerted on an object immersed in a fluid, in this case, air.
First, let's find the volume of the balloon. The volume of a sphere can be calculated using the formula:
V = (4/3) * π * r^3
Where V is the volume and r is the radius of the balloon.
V = (4/3) * π * (12.5 cm)^3 = 9165.625 cm^3
Next, we need to convert the volume to cubic meters, as the provided densities are given in kg/m^3. There are 1,000,000 cm^3 in a m^3, so:
V = 9165.625 cm^3 * (1 m^3 / 1,000,000 cm^3) = 0.009165625 m^3
The buoyant force is given by the equation:
Buoyant Force = (density of fluid) * g * V
Where g is the acceleration due to gravity. In this case, the density of the fluid is the density of air.
Buoyant Force = (1.29 kg/m^3 - 0.178 kg/m^3) * 9.8 m/s^2 * 0.009165625 m^3
Buoyant Force = 1.1124766875 N
Therefore, the balloon can lift a weight of 1.1124766875 N (neglecting the weight of the empty balloon).