Gina is driving her car down the street. She has a teddy bear sitting on the back seat. A dog runs in front of Gina's car, so sh
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(a) 0.0147 N
When the filter reaches the terminal speed, it means that its acceleration is now zero, so the net force acting on it is zero.
There are only two forces acting on the filter:
- The weight of the filter, downward: W = mg, where
is the mass of the filter
is the acceleration due to gravity
- The air resistance, upward,
Since the net force is zero, we have
and solving the equation we find the upward force of air resistance:
(b) 0.0441 N
The problem is exactly identical to before, but this time the mass of the stack of filters is 3 times the mass of the single filter, so
And so, the upward force of air resistance is
(c) 28.3 s
We know that the single coffee filter takes t=49 s to reach the ground, travelling at constant terminal speed of v, so the distance covered (the height of the building) is
where t = 49 s.
We also know that the air resistance is proportional to the square of the terminal speed:
which means
For the stack of three filters, we found (b) that the air resistance is 3 times the air resistance for the single filter (a). Therefore, the terminal speed of the stack of filter will be times larger than the terminal speed of the single filter.
Therefore, the time taken will be:
And since t = 49 s, we have