💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

View Video Answer

Like

Report

$\bullet$$\bullet$ The drag coefficient for a spherical raindrop with a radius of0.415 $\mathrm{cm}$ falling at its terminal velocity is $2.43 \times 10^{-5} \mathrm{kg} / \mathrm{m}$ .Calculate the raindrop's terminal velocity in $\mathrm{m} / \mathrm{s}$ .

$11.0 \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

Hope College

University of Sheffield

Lectures

04:16

In mathematics, a proof is…

04:48

In mathematics, algebra is…

04:02

Calculate the speed a sph…

04:51

Calculate the velocity a…

03:27

Calculate the speed a sphe…

07:43

According to one model tha…

02:25

(II) The terminal velocity…

02:30

Find the terminal velocity…

03:28

03:19

What is the acceleration o…

04:30

The velocity $v(t)$ of a f…

00:55

What is the terminal speed…

03:07

A spherical particle falli…

01:55

Since raindrops grow as th…

06:22

A raindrop of mass $3.35 \…

01:32

A sphere falls through a f…

03:48

If a rainstorm drops 1 $\m…

02:51

When a raindrop falls, it …

0:00

How does the force of grav…

05:24

(a) Estimate the terminal …

01:15

A raindrop falls from a cl…

01:49

51 states that the drag coefficient for a satirical raindrop with the rays of 510.415 centimeters falling at his terminal velocity is 2.43 times 10 to the negative five kilograms per meter. Calculate the rain jobs terminal velocity in meters per second. Okay, so we're told these two things three days of the spherical raindrop and it's drank coefficient capital D. So, you know an object has reached terminal velocity based on what's presented in textbooks. You know that it's no longer accelerating. An expression for terminal velocity is given by the drag coefficient. Times terminal velocity squared equals m times G. Yeah, exactly. So we're gonna sell for the terminal velocity. Always use Find expression for mass and the drag coefficient over the drag coefficient is getting to us. So racing to find the mass of the raindrop but will allow us to calculate the general velocity. So we're told we approximate in this range on as a sphere with a known radius. Little are so if we're told, Well, let's bring drops on the soon it's perfectly water more that the density, which I'm going to call row here, is approximately one gram per cent of your cute. That's the density. And of course then Steve remember its mass over volume Well, the volume of a sphere simply given this four pi r cubed over three And so therefore we can find the mass of this rain job to simply be the density Rho times are velocity Sorry velocity are brilliant motors here So if you have a density of one gram person were cute Multiply that by the the volume of us here for over three times pi have the radius which I don't need to convert into centimeters because my units will cancel out with the density 0.415 centimeters This whole term is cute Just verifying my centimeters. Cute Kaslow for the centimeters within. A miss wrote of this to be a cube here. So there from units per centimeters cancel Oh, what? And by calculating this for two or three times pi r cubed we find that the mass of this droplet raindrop is 30.299 grams I really had to What our drag coefficient is is the use of Hillary units of kilograms per meter so annual I need to cover this two kilograms. That's 2.99 times 10 native four kilograms. Great sense really only need to solve for this problem. We solve for mess and everything else is campaigning for us. A little check because the question was asked for the velocity in terms of meters per second. Let's check earnings before after Britain calculating to see if we got the great ones. Now we know the mass of our brain. Drop 2.99 I'm sending the native four kilograms Montclair by G 9.8 means per second squared divided by an drag coefficient 2.43 times tend to make it five the grand her meter. So just don't take your units are kilogram cancels out with me here on our numerator and they won over meters on our denominator and maybe one of her second squared in our new Burrier. So this would have units of meter squared per second squared. However, it is under a square root, so that does provide us the proper units of meters per second. So no, Now you have the right units. And so if you were to Catholic this value we would find 23 significant figures that are lost. Never arrange up would be 11.0 unions per second. So this question is based on the idea that once the number has reached terminal velocity, object is falling downward, with weight and the drink force acting up. The acceleration of public in free fall is zero to the balance of these forces as presented here, um must occur and allows us to solve for the terminal velocity there, you know.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, a proof is a sequence of statements given to explain how a c…

In mathematics, algebra is one of the broad parts of mathematics, together w…

Calculate the speed a spherical rain drop would achieve falling from $5.00 …

Calculate the velocity a spherical rain drop would achieve falling from $5…

Calculate the speed a spherical rain drop would achieve falling from 5.00 $\…

According to one model that attempts to account for air resistance, the dist…

(II) The terminal velocity of a $3 \times 10^{-5} \mathrm{kg}$ raindrop is a…

Find the terminal velocity of a spherical bacterium (diameter 2.00$\mu \math…

Find the terminal velocity of a spherical bacterium (diameter $2.00 \mu \mat…

What is the acceleration of a raindrop that has reached half ofits termi…

The velocity $v(t)$ of a falling raindrop at time $t$ is modeledby the e…

What is the terminal speed of a 6.00 kg spherical ball that has a radius of …

A spherical particle falling at a terminal speed in a liquid must have the g…

Since raindrops grow as they fall, their surface area increases and therefor…

A raindrop of mass $3.35 \times 10^{-5} \mathrm{kg}$ falls vertically at con…

A sphere falls through a fluid. Earth exerts a constant down- ward 0.50-N fo…

If a rainstorm drops 1 $\mathrm{cm}$ of rain over an area of 10 $\mathrm{km}…

When a raindrop falls, it increases in size and so its mass at time $t$ is a…

How does the force of gravity on a raindrop compare with the air drag the dr…

(a) Estimate the terminal speed of a wooden sphere (density 0.830 g/cm^{ } )…

A raindrop falls from a cloud $100 \mathrm{m}$ above the ground. Neglect air…

(a) Estimate the terminal speed of a wooden sphere (density 0.830 g/cm^{3} )…

06:11

$\bullet$ $\bullet$ A 350 kg roller coaster starts from rest at point $A$ an…

15:52

A 12.4 $\mu \mathrm{F}$ capacitor is connected through a 0.895 $\mathrm{M\Om…

02:44

Axons. Neurons are the basic units of the nervous system. They contain long …

03:11

$\bullet$ A 5.00 g bullet traveling horizontally at 450 $\mathrm{m} / \mathr…

Energy use of home appliances. An 1800 $\mathrm{W}$ toaster, a 1400 $\mathrm…

01:23

What would be the resulting period of rotation of the space station? You may…

01:45

$\cdot$ A woman with mass 50.0 $\mathrm{kg}$ is standing on the rim of a lar…

03:09

The portion of string between the bridge and upper end of the fingerboard (t…

04:39

$\bullet$ $\bullet$ A 12.0 N package of whole wheat flour is suddenly placed…

$\bullet$ Find the noise level (in dB) of a sound having an intensity of (a)…