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Upthrust is a force pushing upwards on an object. We are going to focus on Air Resistance (the air pushing up against something) and Water Resistance (water pushing up against something)

Air Resistance - an explanation (from the Gravity Thinkquest site)

If a piece of paper and a marble are in free fall, they will fall at the same speed, so they should hit the ground at the same time. If you test this by just dropping a marble and a piece of paper you will find it is not true. This is because the objects are not in free fall. To be in free fall, gravity has to be the only force acting on the objects.
When you just drop something, there is also air resistance. Air resistance is a type of friction. Because friction acts in the opposite direction of the object’s motion, air resistance of an object falling downward is an upward force. This is because a falling object is coming down, so the opposite direction is up. If the amount of air resistance was equal for every object falling down, then all objects would still fall at the same speed. Since we know they this doesn't happen, we know air resistance is different for different objects. The amount of air resistance acting on an object depends on the object’s surface area. If an object has a small surface area, it will have little air resistance. Because the piece of paper has a larger surface area than the marble, the marble will have less air resistance than the piece of paper.
Just because an object has more air resistance than another object doesn’t mean it will fall slower. This is because of weight, the force of gravity on an object at the surface of the planet. If the object with the high air resistance had a high weight, it might fall faster than the object that has little air resistance, like if you had a wrecking ball and a piece of paper. Even though the wrecking ball had more air resistance than the piece of paper (as it has a larger surface area), it would fall faster because the wrecking ball weighed more than the paper.

Elephant and feather - air resistance
Upthrust definition
Gravity vs Upthrust
NASA - lift force
Roto Copter - air resistance in action
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Here is an invention from Leonardo da Vinci. How does your force relate to this invention? (Click on the picture to go to the website)
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