A little history of physics .How is physics involved in this?

[graphicer89]

A little history of physics...How is physics involved in this??

Well I was reading over something interesting and something is puzzling me. So it turns out that in 1783 the Montgolfier brothers of France launched what is possibly the first balloon flight carrying passengers which was a Duck, a rooster and a sheep. Their balloon which was a bout 35 feet in diameter and constructed of cloth lined with paper, was launched by filling it with smoke.The flight landed safely about some 8 minutes later. What i am trying to figure out is the physics that is involved with this flight ...for example in terms of its ascent, descenting and the landing this "balloon" made...How would you explain how physics was involved in this experiment??

 

[RoyalCat]

The two main things I can think of as relevant are kinetic gas theory and Archimedes' Principle.
According to Archimedes, if an object of density $$\rho _1$$ is put into a fluid of density $$\rho_2 > \rho_1$$ then the object will experience an upwards lift force.

According to kinetic gas theory, a hotter gas is a less dense gas (A gas is one kind of fluid).

Do note, I only have a rudimentary understanding of both, so you should probably wait for someone to confirm what I've wrote.

 

[minger]

You are correct RoyalCat. Bouyancy in layman's terms says that an object will see an upward force equal the weight of the displaced fluid.

Let's take water as an example. If we were to fill up an infinately thin hollow sphere with water and drop it in more water, what would happen? The principle says that the ball with displace water equal to its own volume, with an associated weight. This weight will exert a force on the ball. In this case, since the densities are equal, the mass equals the force and the ball can remain in equilbrium.

Now, in your case, let's assume that the hot gas, or smoke, or whatever was in the balloon had a density 1/2 that of air. If the volume of the balloon was 100 cubic feet, then the air would exert an upward force of ~8.07 lbf. The smoke itself has mass and weight, which results in net upward force of ~4.04 lbf.

As said previously, there is an ideal gas law which correlates various properties of a fluid. It says that:
$$\frac{P}{\rho} = RT$$
If we keep the pressure and gas constant equal, then we can rewrite:
$$\rho T = \mbox{constant}$$
So, if the temperature goes up, then the density must go down. As we just seen, decreasing the density will decrease the mass the fluid, and thus increase the net upward force.

 

[RoyalCat]

You are correct RoyalCat. Bouyancy in layman's terms says that an object will see an upward force equal the weight of the displaced fluid.

Let's take water as an example. If we were to fill up an infinately thin hollow sphere with water and drop it in more water, what would happen? The principle says that the ball with displace water equal to its own volume, with an associated weight. This weight will exert a force on the ball. In this case, since the densities are equal, the mass equals the force and the ball can remain in equilbrium.

Now, in your case, let's assume that the hot gas, or smoke, or whatever was in the balloon had a density 1/2 that of air. If the volume of the balloon was 100 cubic feet, then the air would exert an upward force of ~8.07 lbf. The smoke itself has mass and weight, which results in net upward force of ~4.04 lbf.

As said previously, there is an ideal gas law which correlates various properties of a fluid. It says that:
$$\frac{P}{\rho} = RT$$
If we keep the pressure and gas constant equal, then we can rewrite:
$$\rho T = \mbox{constant}$$
So, if the temperature goes up, then the density must go down. As we just seen, decreasing the density will decrease the mass the fluid, and thus increase the net upward force.

Just to clarify, depending on the ratio between the densities of the fluid and the object, the upwards force can either be smaller than, greater than, or equal to the weight of the object ($$mg$$) meaning the object can have a net acceleration upwards, downwards, or no net acceleration at all.

This is, of course, ignoring the effect of drag (Which is very significant, mind you). But either way, you get movement.