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The hot air balloon pushes aside(displaces) air while the fish pushes aside water. The mass of the water and air displaced by the fish and hot air balloon respectively creates a buoyant force pushing upwards against gravity.
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A volume of 16 cubic metres of air is displaced by the balloon. The density of the air at 20^{o}C is 1.21 kg/m^{3} so the mass of the air displaced is
16m^{3} X 1.21kg/m^{3} = 19.36 kg.
So the buoyant force pushing up can support 19.36 kg while the balloon weighs 20 kg. The slight difference means that the balloon is too heavy to be lifted skywards and it will stay grounded.
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On cold mornings the air is more dense than on a hot day. The greater the density of the displaced air the greater the force lifting the balloon skyward.
On
a cold day, at 0^{o}C,
a balloon
with a volume of 200 cubic metres experiences a buoyant force able to support
(1.29 kg/m^{3}
X 200m^{3}
) 258kg.
On a warm day, at 30^{o}C
, the same balloon experiences a buoyant force able to support (1.16 kg/m^{3}
X 200m^{3)}
232kg. The same balloon on a cold day can lift 26kg more mass than on a
warm day.
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The buoyant force acting on the balloons depends on the volume of displaced air. SInce both balloons have the same volume and therefore displace the same amount of air the buoyant force is the same for both balloons.
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The buoyant force equals the weight of 2 litres of water. The weight of 2 litres of water is given by the expression
weight = density X volume
Weight = 1g/cm^{3} X 2,000cm^{3 = 2 kilograms}
The weight of the brick whenit is submerged is therefore (10  2) 8 kilograms.
Does the brick lose mass when it is submerged underwater?
Ofcourse not.
Weight is the force of gravity exerted on an object. Mass is the quantity of matter in an object. So the brick still has the same amount of matter but the force of gravity is less due to the effect of the buoyant force acting upwards.
Buoyancy 

The boat has
a special shape that is designed to push water aside. The more water that
is pushed aside the more force that the water exerts upwards. For example
if the boat pushes aside 300 kilograms of water then the water exerts a
force upwards on the boat able to support 300 kilograms.
Pushing water to one side is called displacement of water. Giant cargo vessels may weigh thousands of tons but they displace thousand of tons of water, which is why they do not sink. 

What keeps both the boat and
the hot air balloon afloat?



Buoyancy is an upward force exerted by a fluid, such as water or air, that opposes the weight of an immersed object. This force increases as the amount of displaced fluid increases. Balloons are objects immersed in a fluid, cold air, and displace this fluid by inflating. Hot air is pumped into the balloon pushing the walls outward to inflate the balloon. 

As the balloon inflates it displaces the fluid it is immersed in, in this case the fluid is air. The weight of this fluid, cold air, is the force (buoyant force) that pushes the balloon upwards against gravity. A cubic metre of air at sea level has a mass of 1.2 kg. So any object that has a volume of 1 cubic metre is buoyed up by a force able to support 1.2 kg. If the mass of the object is more than 1.2 kg it will fall to the ground. If a one cubic metre object has a mass less than 1.2 kg it will rise skyward. 


1) Design
an experiment to test the hypothesis that salt water exerts more of
a buoyant force than freshwater. 

2) A fish and a hot air balloon both hover at a given level for the same reason. What is the reason for this? Solution 


3) A helium filled balloon has a mass of 20kg and a volume of 16 cubic metres. It is released outdoors at sea level when the temperature is 20^{o}C . Will the balloon rise or stay grounded? Explain. Solution 4) The density of air at 0^{o}C is 1.29 kg/m^{3} while at 30^{o}C it is 1.16 kg/m^{3}. Use this information to explain why we see hot air balloons floating in the sky during cold winter mornings rather than on hot summer days. Solution 

5) The density of hydrogen is 0.09 kg/m^{3}. Two balloons are inflated to the same size, one filled with air and the other filled with hydrogen. Which balloon experiences the greatest buoyant force? Solution 

6) A ten kilogram brick is lowered into a tub of water. A volume equal to two litres of water is displaced. If the density of water is 1g/cm^{3} what is the reading of the scale when the brick is fully submerged? Does the brick lose mass when it is placed in water? Solution 
