# Terminal Velocity of a Coffee Filter#

In one of the PHYS 111 labs Mateo measured the terminal velocity $$v_T$$ of a coffee filter of mass $$m$$ falling through the air. In equilibrium, the drag force acting on the coffee filter exactly balances the gravitational force on the filter such that:

$$bv_T = mg$$

where $$b$$ is a “drag coefficient” determined by the shape of the filter and the density of the air.

Suppose that the following six measurements of a coffee filter’s terminal velocity were made:

Trial

$$v_T$$ ($$m/s$$)

1

0.76

2

0.9

3

0.85

4

0.71

5

0.86

6

0.88

The standard deviation of this data set is 0.068 $$m/s$$.

## Part 1#

Use the experimental data to determine the uncertainty in the average value of the terminal velocity. State your answer using the appropriate number of significant figures.

Please enter in a numeric value in $$m/s$$.

## Part 2#

Use the experimental data to determine the average value of the terminal velocity. State your answer using the appropriate number of significant figures.

Please enter in a numeric value in $$m/s$$.

## Part 3#

If the coffee filter has a mass of $$m =$$ 2 $$\pm$$ 52 $$g$$, determine the value of the uncertainty in the drag coefficient $$b$$. State your answer using the appropriate number of significant figures. Assume that $$g= 9.81 kg/s$$ and has negligible uncertainty.

Please enter in a numeric value in $$kg/s$$.

## Part 4#

If the coffee filter has a mass of $$m =$$ 2 $$\pm$$ 52 $$g$$, determine the value of the drag coefficient $$b$$. State your answer using the appropriate number of significant figures. Assume that $$g= 9.81 kg/s$$ and has negligible uncertainty.

Please enter in a numeric value in $$kg/s$$.