A 0.11-kg balloon is filled with helium (density = 0.179 kg/m3). If the balloon is a sphere with a radius of 5.4 m, what is the maximum weight it can lift?
If you multiply the density of the air with the radius of the balloon, and then set that equal to how much the balloon weighs and then shove it up your butt!
To find the maximum weight that the balloon can lift, we need to consider buoyancy, which is the force exerted by a fluid on an object immersed in it.
1. Determine the volume of the balloon:
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
Plugging in the given radius, we get: V = (4/3)π(5.4 m)^3.
Calculate the volume to find the exact value.
2. Calculate the weight of the displaced air:
The weight of the displaced air is equal to the buoyant force acting on the balloon.
The buoyant force is given by the formula F_buoyant = density * volume * gravity, where density is the density of the fluid (in this case, air), volume is the volume of the fluid displaced, and gravity is the acceleration due to gravity (approximately 9.8 m/s^2).
Multiply the density of air (0.179 kg/m^3) by the volume calculated in step 1.
3. Determine the maximum weight the balloon can lift:
The maximum weight the balloon can lift is equal to the weight of the displaced air.
Use the weight of the displaced air calculated in step 2 as the maximum weight.
Note: This calculation assumes that the mass of the balloon itself is negligible compared to the displaced air. If the mass of the balloon is significant, it should also be taken into account while calculating the maximum weight it can lift.