A feather is released from rest. As it falls through the air, it is acted upon by two forces – air resistance and its weight. By the time it has reached its terminal velocity, which of the following mathematical statements correctly describes the magnitudes of these two forces?Weight < air resistanceWeight = air resistanceWeight > air resistanceAir resistance < weight
Question
A feather is released from rest. As it falls through the air, it is acted upon by two forces – air resistance and its weight. By the time it has reached its terminal velocity, which of the following mathematical statements correctly describes the magnitudes of these two forces?Weight < air resistanceWeight = air resistanceWeight > air resistanceAir resistance < weight
Solution 1
When an object reaches its terminal velocity, it means that it is no longer accelerating and is falling at a constant speed. This happens when the force due to air resistance equals the force of gravity acting on the object.
So, for a feather falling at terminal velocity, the correct mathematical statement would be:
Weight = Air resistance
Solution 2
The correct mathematical statement is: Weight = air resistance
Here's the step by step explanation:
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When the feather is released, it starts to fall due to the force of gravity, which is its weight.
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As it falls, it experiences air resistance, which is a force that opposes its motion.
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Initially, the weight is greater than the air resistance, so the feather accelerates downwards.
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As the feather's speed increases, the air resistance also increases.
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Eventually, the feather reaches a constant speed, known as the terminal velocity. At this point, it is no longer accelerating.
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When the feather is at terminal velocity, the force of the weight pulling it down is exactly balanced by the air resistance pushing it up. Therefore, at terminal velocity, the weight of the feather equals the air resistance.
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