Acceleration of a Hot Air Balloon

AI Thread Summary
To determine the acceleration of a rising hot-air balloon with an outside-to-inside air density ratio of 1.25, the relevant equations of fluid dynamics and pressure must be applied. The outside air density is given as 1.2 kg/m^3, leading to an inside density of 0.96 kg/m^3. The pressure inside the balloon is assumed to be 1 atm (101.3 kPa), and the relationship between pressure, density, and force is essential for solving the problem. The discussion highlights the importance of understanding the force diagram and making appropriate assumptions regarding elevation and air temperature. Clarifying these factors is crucial for accurately calculating the balloon's acceleration.
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 :)
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Is Exponential Form Better for Balloon with Inserted Load Calculation?
4
Replies
170
Views
7K
Calculating the Radius of a Hot Air Balloon to Withstand a Load of 300 kg
Replies
2
Views
2K
How Does Changing the Temperature Affect a Hot Air Balloon's Buoyancy?
Replies
17
Views
3K
How Does Temperature Affect the Lifting Capacity of a Hot Air Balloon?
Replies
18
Views
7K
I Big bang balloon?
Replies
5
Views
184
Calculating Air Density and Temperature in a Hot Air Balloon
Replies
6
Views
8K
How high will a helium balloon rise?
Replies
10
Views
3K
Calculating Mass Needed to Ground Hot Air Balloon
Replies
3
Views
2K
Hot air balloon - Archimedes Principle
Replies
4
Views
4K
Thermodynamics - Hot-air balloon
Replies
13
Views
7K

Hot Threads

Recent Insights

Back
Top