Physics, 05.09.2019 17:10 cbonner191

In a pollution control experiment, minute solid particles (typical mass 1×10-13 slug) are dropped in air. the terminal speed of the particles is measured to be 0.2 ft/s. the drag force of these particles is given by fd=kv, where v is the instantaneous particle speed. find the value of the constant k. find the time required to reach 99 percent of terminal speed.

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Answer from: 20Tiglashou

1) $161 \frac{lbf \cdot s}{ft}$

The particle experiences two forces during its fall:

- The force of gravity, , pointing downward, where m is the mass of the particle and g is the acceleration of gravity

- The drag force, , pointing upward, where k is a constant and v is the instantaneous speed of the particle

When the particle reaches its terminal speed, the acceleration becomes zero: this means that the net force is also zero, so the two forces are balanced. Therefore we can write

mg = kv_t

where v_t is the terminal velocity. We have the following data:

$m = 1\cdot 10^{-13} slug= 1\cdot 10^{-13} \frac{lbf \cdot s^2}{ft}$ is the mass

g = 32.2 ft/s^2 is the acceleration

v_t = 0.2 ft/s is the terminal speed

Solving for k, we find

$k=\frac{mg}{v_t}=\frac{(1 \frac{lbf \cdot s^2}{ft})(32.2 \frac{ft}{s^2})}{0.2 \frac{ft}{s}}=161 \frac{lbf \cdot s}{ft}$

2) 28.6 ms

We now want to find the time at which the particle reaches 99 % of the terminal speed, so a speed of

v' = 0.99 v_t = (0.99)(0.2)=0.198 ft/s

The net force acting on the particle is

F=mg-kv

So the acceleration is

$a=\frac{dv}{dt}=g-\frac{k}{m}v$

This differential equation can be rewritten as

$\frac{dv}{g-\frac{k}{m}v}=dt$

And by integrating on both sides and performing the calculation, we can get the final expression for the velocity as

$v=\frac{mg}{k}(1-e^{-\frac{k}{m}t})$

We want to find the time t at which v = 0.198 ft/s, so we now need to re-arrange the formula for t. This gives:

$t = -\frac{m}{k} ln (\frac{g-\frac{k}{m}v}{g})$

And substituting all the values, we find:

$t = -\frac{1}{161} ln (\frac{32.2-\frac{161}{1}(0.198)}{32.2})=0.0286 s = 28.6 ms$

Answer from: Quest

Ibelieve your answer is b.hope this : )

Answer from: Quest

An atom (ours, not carroll's) consists of a positively charged nucleus, surrounded by one or more negatively charged particles called electrons. the positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. although the nucleus is heavy, it is quite small compared with the overall size of an atom. the radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6 nm. * if an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.read more on -

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In a pollution control experiment, minute solid particles (typical mass 1×10-13 slug) are dropped in...

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