91影视

The given data can be listed below,

• The mass of a single coffee filter is, $\mathrm{m}=1.7\mathrm{g}\left(\frac{1\mathrm{kg}}{1000\mathrm{g}}\right)=1.7脳{10}^{-3}\mathrm{kg}$.
• The time taken by coffee filter to reach ground is, t = 52 s

The friction is a force that is always against the direction of displacement. In the case of a fluid like air, things do not change, even if the resistance depends on the shape in the hypothesis of perfect (frictionless, inviscid) motion.

When a body attends terminal velocity its resistance force is equal to weight of body and net force is equal to zero.

So, the air resistance force is given by,

$$\begin{gathered} {\mathrm{F}}_{\mathrm{air}}=\mathrm{W} \\ =\mathrm{mg} \end{gathered}$$

Here, m is the mass of the coffee filter and g is the acceleration due to gravity whose value is $9.8m/s^2$.

Substitute values in the above equation.

role="math" $$\begin{gathered} {\mathrm{F}}_{\mathrm{air}}=\left(1.7脳{10}^{-3}\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)\left(\frac{1\mathrm{N}}{1\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2}\right) \\ =0.0166\mathrm{N} \end{gathered}$$

Thus, the air resistance force on the single coffee filter 0.0166 N .

The mass of five coffee filters is given by,

$$\begin{gathered} m_2=5\left(1.7脳{10}^{-3}kg\right) \\ =8.5脳{10}^{-3}kg \end{gathered}$$

The upward air resistance force is given by,

$F_{air}=m_{2}g$

Here, $m_2$is the mass of five coffee filter and g is the acceleration due to gravity.

Substitute values in the above,

$$\begin{gathered} {\mathrm{F}}_{\mathrm{air}}=\left(8.5脳{10}^{-3}\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)\left(\frac{1\mathrm{N}}{1\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2}\right) \\ =0.0833\mathrm{N} \end{gathered}$$

Thus, the air resistance of five coffee filters is$=0.0833\mathrm{N}$ .

The air resistance force is directly proportional to velocity of the object which is given by,

$F_{air}伪v^2$

The air resistance of single coffee filter and five coffee filters is also proportional to the speed of the stick. So, the ratio of these two is given by,

role="math" localid="1657881780900" $$\begin{gathered} \frac{m}{5m}=\frac{v_1^2}{v_2^2} \\ \frac{v_1}{v_2}=\sqrt{\frac{1}{5}} \\ {v}_1=0.45v_2 \end{gathered}$$

Here, is the velocity of single coffee filter and is the velocity of the five coffee filters.

The velocity is given by,

$v=\frac{d}{t}$

Here, d is the distance and t is the time.

From the above equation.

$v伪\frac{1}{t}$

So, the ratio of two velocities can be given by,

$\frac{v_1}{v_2}=\frac{t_2}{t_1}$

Substitute all the values in the above,

$$\begin{gathered} \frac{0.45v_2}{v_2}=\frac{t_2}{52s} \\ {t}_2=23.4s \end{gathered}$$

Thus, the time that the stack of coffee filters to hit the ground is $23.4s$.