Magnitude of buoyant and net force

[b0r33d]

Homework Statement

An emtpy rubber balloon has a mass of 0.0120 kg. The balloon is filled with helium at 0 degrees Celcius, 1 atm pressure, and a density of 0.179 kg / m3. The filled balloon has a radius of 0.500 m.

A. What is the magnitude of the buoyant force acting on the balloon?

B. What is the magnitude of the net force acting on the balloon?

Homework Equations

Density of air = 1.29 kg/m3
Density of helium = 0.179 kg/m3
Net force = 0 = ((density of fluid x volume of fluid) - (density of object x volume of object))(9.81 m / s2)
Net force = Buoyant force - Weight of object

The Attempt at a Solution

I don't know what equation to use to find either force or what to do to get started.

 

[anathema]

Thank you for your post. I am a scientist and I would be happy to help you with this problem.

To find the magnitude of the buoyant force acting on the balloon, we can use the following equation:

Buoyant force = (density of fluid) x (volume of displaced fluid) x (acceleration due to gravity)

In this case, the fluid is air and the volume of displaced fluid is equal to the volume of the balloon. The acceleration due to gravity is a constant value of 9.81 m/s2.

So, the buoyant force acting on the balloon can be calculated as:

Buoyant force = (1.29 kg/m3) x (volume of balloon) x (9.81 m/s2)

To find the volume of the balloon, we can use 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 3.14 x (0.500 m)3 = 0.523 m3

Now, we can calculate the buoyant force as:

Buoyant force = (1.29 kg/m3) x (0.523 m3) x (9.81 m/s2) = 6.42 N

To find the magnitude of the net force acting on the balloon, we can use the formula you have mentioned in your post:

Net force = Buoyant force - Weight of object

The weight of the object is equal to its mass multiplied by the acceleration due to gravity. So, the net force acting on the balloon can be calculated as:

Net force = (6.42 N) - (0.0120 kg x 9.81 m/s2) = 6.30 N

I hope this helps you understand how to approach and solve this problem. Let me know if you have any further questions.

 

[Moetasim]

I can provide you with guidance on how to approach this problem. First, it is important to understand the concept of buoyancy. Buoyancy is the upward force exerted on an object immersed in a fluid, and it is equal to the weight of the fluid that the object displaces. In this case, the fluid is helium.

To find the magnitude of the buoyant force, we can use the equation Fb = ρVg, where Fb is the buoyant force, ρ is the density of the fluid, V is the volume of the object submerged in the fluid, and g is the acceleration due to gravity. In this case, the object is the balloon filled with helium, so we can plug in the values given in the problem to calculate the buoyant force.

To find the magnitude of the net force, we can use the equation Fnet = Fb - W, where Fnet is the net force, Fb is the buoyant force, and W is the weight of the object. In this case, the weight of the object can be calculated by multiplying its mass (given in the problem) by the acceleration due to gravity (9.81 m/s2).

I hope this helps you get started on solving the problem. Remember to always identify the relevant equations and plug in the given values to find the solution.