The only things that "float" in air, are things that are lighter than air, and this is because they displace a quantity of air that weighs more than the thing that is floating. This is also true of things that float in water or any other fluid.
As for heavier-than-air things that "float" (fly), these are kept aloft by the motion of air, or by the motion of the thing through the air, which amounts to the same thing. In either case, air is passing the flying thing (for instance, an airplane wing) above and below it, creating low pressure above and high pressure below, thereby lifting the thing off the ground. This works only for things that are aerodynamically correct, and these are called airfoils - an airplane wing, a helicopter rotor and a kite are common examples.
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Air can make things float because of buoyancy. When an object is less dense than the air around it, the air exerts an upward force on the object, known as buoyant force, which counteracts gravity and causes the object to float. This is why objects like balloons or bubbles can float in the air.
Things float in the air when the force of buoyancy (upward force exerted by air or a fluid) is greater than the force of gravity (downward force pulling objects toward the earth). This is known as buoyancy and is what allows objects to float or stay suspended in a fluid or gas like air.
Heat alone does not make things fly. However, heating air can affect the movement of objects in the air. For example, hot air balloons rise because the air inside the balloon is heated, making it less dense than the surrounding air, causing the balloon to float upwards.
Yes, a helium-filled balloon will float in the air because helium is less dense than the surrounding air. When filled with helium, the balloon experiences a buoyant force that causes it to rise and float.
Yes. For every fluid, there are things that float in it ... they just have to be things that are less dense than the fluid. That's how stones float in mercury, logs float in water, and hot balloons float in air.
In a vacuum, there is no air or other medium for objects to displace, so there is no buoyant force to make them float. Objects in a vacuum will simply remain in place if they are not acted upon by any external forces.