Finding the acceleration of a balloon

In summary, The question is trying to find the acceleration of a weather balloon with a mass of 5 kg and a radius of 2.879 m when carrying a load of 10 kg. The densities of air and helium are 1.16 kg/m^3, and the equations being used are a= v^2/r and Bernoulli's equation P1+.5(pv1^2+pgy1)=P2+.5(pv2^2+pgy2). The person discussing the problem is trying to manipulate Bernoulli's equation to solve for v, but is struggling and also considered using the escape speed equation. It is also mentioned that the balloon has no velocity immediately after release.
  • #1
kelsif
3
0
1. An empty spherical weather balloon with a mass of 5 kg has a radius of 2.879 m when fully inflated with helium. It is supposed to carry a small load of instruments having a mass of 10 kg. Taking air and helium to have densities of 1.16 kg/m^3, respectively, what will be the acceleration of the balloon and load immediately after it is released?



2. i have a= v^2/r and Bernoulli's equation P1+.5(pv1^2+pgy1)=P2+.5(pv2^2+pgy2)



3. I keep trying to figure a way to manipulate Bernoulli's equation to solve for v to plug into the first equation but can't get it to work. I also tried solving for escape speed (vesc=the square root of 2GM/R). But that doesn't use the densities. I'm extremely confused at this point.
 
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  • #2
Do you need Bernoulli's equation?
Isn't it simply bouyant force upward and weight down.

Remember immediately after release it has no velocity
 
  • #3
no i have bernoulli's equation but i don't know how to solve for the acceleration immediately after release...
 

Related to Finding the acceleration of a balloon

1. What is the acceleration of a balloon?

The acceleration of a balloon is the rate at which its velocity changes over time. It is typically measured in meters per second squared (m/s²).

2. How do you find the acceleration of a balloon?

The acceleration of a balloon can be found by using the formula a = (vf - vi) / t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time.

3. What factors affect the acceleration of a balloon?

The acceleration of a balloon can be affected by several factors, including the force of gravity, the weight of the balloon, the density of the surrounding air, and any external forces acting on the balloon.

4. Can the acceleration of a balloon change?

Yes, the acceleration of a balloon can change depending on the circumstances. For example, if the balloon is rising against the force of gravity, its acceleration will decrease over time until it reaches a constant velocity. However, if the balloon is being pushed or pulled by external forces, its acceleration may change constantly.

5. How is the acceleration of a balloon related to its motion?

The acceleration of a balloon is directly related to its motion. If the acceleration is positive, the balloon is speeding up in the direction of its motion. If the acceleration is negative, the balloon is slowing down in the direction of its motion. A balloon with a constant acceleration will have a linear change in velocity over time, resulting in a curved path of motion.

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