How Do You Calculate Buoyant and Net Force on a Helium Balloon?

[kahl]

Homework Statement

An empty rubber balloon has a mass of .0111 kg. The balloon is filled with helium at 0degrees C, 1atm pressure, and a density of .179 kg/m^3. The filled balloon has a radius of .154 m.
What is the magnitude of the buoyant force acting on the balloon? Answer in units of N.
and
What is the magnitude of the net force acting on the balloon? Answer in uts of N.

Homework Equations

Buoyant Force= (density of fluid)(g)(A)(change in h)

The Attempt at a Solution

don't know what Area to use, is it the area of the circle? and how do I integrate the mass of the empty balloon?

Thanks

 

[turdferguson]

First you need to find the boyant force when the balloon is full of helium. Then factor in the weight of the balloon and the weight of the helium (ideal gas law) to get the net force

 

[m2003]

for the question! I can provide some insights on the buoyant force acting on a balloon. The buoyant force is the upward force exerted by a fluid on an object that is partially or fully immersed in it. In this case, the fluid is helium and the object is the balloon.

To answer the first question, we can use the formula for buoyant force which is given by:

Buoyant Force = (density of fluid) x (gravitational acceleration) x (volume of the object)

In this case, the density of the fluid is given to be 0.179 kg/m^3, the gravitational acceleration is 9.8 m/s^2, and the volume of the balloon can be calculated using the formula for the volume of a sphere:

Volume = (4/3) x π x (radius)^3

Substituting the given values, we get:

Volume = (4/3) x π x (0.154 m)^3 = 0.0059 m^3

Therefore, the buoyant force on the balloon is:

Buoyant Force = (0.179 kg/m^3) x (9.8 m/s^2) x (0.0059 m^3) = 0.099 N

For the second question, the net force acting on the balloon can be calculated by taking into account the weight of the balloon and the buoyant force. The weight of the balloon can be calculated using the formula:

Weight = mass x gravitational acceleration

In this case, the mass of the balloon is given to be 0.0111 kg. Therefore, the weight of the balloon is:

Weight = (0.0111 kg) x (9.8 m/s^2) = 0.109 N

Since the buoyant force is acting in the opposite direction to the weight, the net force on the balloon is:

Net Force = Weight - Buoyant Force = 0.109 N - 0.099 N = 0.01 N

Therefore, the magnitude of the net force acting on the balloon is 0.01 N.

To answer your question about the area to use, yes, it is the area of the circle since we are dealing with a spherical balloon. I hope this helps in your understanding of the buoyant force on a balloon. Keep up the good work in your studies!