The density of air near the earth's surface is 1.29 kg?m^3. If a helium balloon with a mass of 1 kg floats in air without rising or falling,what is the minimum volume of helium in the balloon? (presume that the mass of the material making up the balloon is negligible). I am not looking for someone to give me the answer, just explain how to figure it out. like what formula to use?/? Thank you1!

To find the minimum volume of helium in the balloon, we can use the principle of buoyancy. According to Archimedes' principle, an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. In this case, the balloon is floating in air, so the buoyant force is equal to the weight of the air displaced by the balloon.

The buoyant force (F_b) can be calculated using the formula:
F_b = ρ_fluid * V * g
where ρ_fluid is the density of the fluid, V is the volume of the fluid displaced, and g is the acceleration due to gravity.

In this case, the fluid is air and the weight of the air displaced is equal to the weight of the balloon (1 kg) in order to balance the forces and keep the balloon floating without rising or falling.

Thus,
F_b = m_balloon * g
where m_balloon is the mass of the balloon and g is the acceleration due to gravity.

Substituting the values,
ρ_air * V * g = m_balloon * g

From here, we can solve for V, which represents the minimum volume of helium required to balance the forces and keep the balloon floating without rising or falling.

V = m_balloon / ρ_air

Therefore, to find the minimum volume of helium in the balloon, you need to divide the mass of the balloon by the density of air near the Earth's surface, which is given as 1.29 kg/m^3.

To determine the minimum volume of helium in the balloon, we need to consider the buoyant force exerted on the balloon by the air. The buoyant force is the force that opposes the weight of an object in a fluid medium, such as air.

To calculate the buoyant force, we can use Archimedes' principle, which states that the buoyant force on an object submerged or floating in a fluid is equal to the weight of the fluid displaced by the object.

First, we need to calculate the weight of the air displaced by the helium balloon. This is equal to the weight of the air that would occupy the same volume as the balloon. The weight of air can be calculated by multiplying its density by its volume and the acceleration due to gravity (9.8 m/s^2).

Weight of air = density of air * volume of air * acceleration due to gravity

Next, we need to calculate the weight of the balloon itself. Since the mass of the balloon is given as 1 kg and the weight is the mass multiplied by the acceleration due to gravity, we have:

Weight of balloon = mass of balloon * acceleration due to gravity

For the balloon to float without rising or falling, the buoyant force must equal the weight of the balloon. So, we set the weight of air equal to the weight of the balloon:

Weight of air = Weight of balloon

density of air * volume of air * acceleration due to gravity = mass of balloon * acceleration due to gravity

The acceleration due to gravity cancels out on both sides:

density of air * volume of air = mass of balloon

Finally, we can rearrange the equation to solve for the volume of air:

volume of air = mass of balloon / density of air

With the given information that the mass of the balloon is 1 kg and the density of air is 1.29 kg/m^3, we can substitute these into the equation to find the minimum volume of helium in the balloon.