Acceleration of a Hot Air Balloon

Click For Summary
SUMMARY

The acceleration of a rising hot-air balloon can be determined using the relationship between the densities of the air inside and outside the balloon. Given that the outside air density (ρo) is 1.25 times the inside air density (ρi), with ρo at 1.2 kg/m³, the inside density (ρi) is calculated as 0.96 kg/m³. The pressure exerted by the air (P) can be analyzed using the equation P = F/A, where the net force leads to the balloon's acceleration. A force diagram is essential for visualizing the forces acting on the balloon to solve for acceleration.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly buoyancy.
  • Familiarity with the ideal gas law and pressure equations.
  • Basic knowledge of force diagrams and free-body diagrams.
  • Ability to manipulate equations involving density and pressure.
NEXT STEPS
  • Study buoyancy forces in fluid mechanics.
  • Learn how to apply the ideal gas law in practical scenarios.
  • Explore the derivation of the equations of motion for objects in fluid mediums.
  • Review examples of force diagrams in physics problems.
USEFUL FOR

Students studying physics, particularly those focusing on fluid dynamics and buoyancy, as well as educators looking for practical examples of applying theoretical concepts in real-world scenarios.

Shepherd7
Messages
7
Reaction score
0

Homework Statement


What is the magnitude of the acceleration of a rising hot-air balloon if the ratio of the air density outside the balloon to that inside is 1.25? Neglect the mass of the balloon fabric, the basket and it contents.

I don't know how to do a rho so "p" will be rho for density and P will be for pressure
o = outside of balloon
i=inside of balloon

po = 1.25pi
po (of air) = 1.2 kg/m^3
Po = 1atm = 101.3 kPa

Homework Equations



P+1/2pv^2+pgy = P+1/2pv^2+pgy
p = m/v
P=F/A

The Attempt at a Solution



I'm really stuck at the beginning of this problem. I can't seem to find any way to link density and acceleration (without time and a distance or and area). Any suggestions? Also are my assumptions about Po and po right? Seeing at I'm unsure of the elevation/air temp I can't be sure. Also are there other assumptions I should be making? Thanks!
 
Last edited:
Physics news on Phys.org
actually it is easier to draw the force diagram first :)
 

Similar threads

Is Exponential Form Better for Balloon with Inserted Load Calculation?
  • · Replies 170 ·
6
Replies
170
Views
8K
Calculating the Radius of a Hot Air Balloon to Withstand a Load of 300 kg
  • · Replies 2 ·
Replies
2
Views
2K
How Does Changing the Temperature Affect a Hot Air Balloon's Buoyancy?
  • · Replies 17 ·
Replies
17
Views
4K
How Does Temperature Affect the Lifting Capacity of a Hot Air Balloon?
  • · Replies 18 ·
Replies
18
Views
8K
Undergrad How Does the Balloon Analogy Explain the Expansion of the Universe?
  • · Replies 5 ·
Replies
5
Views
2K
Calculating Air Density and Temperature in a Hot Air Balloon
  • · Replies 6 ·
Replies
6
Views
8K
How high will a helium balloon rise?
  • · Replies 10 ·
Replies
10
Views
4K
Calculating Mass Needed to Ground Hot Air Balloon
  • · Replies 3 ·
Replies
3
Views
2K
Hot air balloon - Archimedes Principle
  • · Replies 4 ·
Replies
4
Views
4K
Thermodynamics - Hot-air balloon
  • · Replies 13 ·
Replies
13
Views
8K