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You are using water to dilute small amounts of chemicals in the laboratory, drop by drop. How many drops of water are in a 1.0 bottle? (Hint: Start by estimating the diameter of a drop of water.)

$\approx 2 \cdot 10^{5}$ droplets

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Cornell University

University of Sheffield

McMaster University

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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01:21

You are using water to dil…

03:14

02:34

01:25

01:49

0:00

01:34

Calculate how many water m…

01:51

How many water molecules a…

01:03

When 20 drops of water is …

00:50

A drop of water has a volu…

00:54

Consider water in each gra…

this's Chapter one problem. 28. What we're looking for here is the number of drops of water in a one leader bottle of water. So since we have were given a total volume here in situation of one leader, so if we knew the volume of a single drop of water, then we could divide this total volume by the volume of a drop of water and get the number of drops of water in that bottle. And let's be clear, let's say this is Maybe that's falling on the bottle. So to find the volume of a drop of water, we've seen drops of water. Let's estimate that there, spherical and let's say the diameter is two millimeters. That's going to be a nice, nice, simple number that if we say diameters two meters, then we get the radius of a drop of water is one millimeter or written and standard assault units 10 to the minus three meters. Okay, so now let's do volume of a drop. Let's call this fee sub t. We're saying it's a sphere with that radius, so we're going to do 4/3 pi r cubed 4/3 pi and tend the minus three meters cubed so we can do the math on there and we get this is roughly four times tend to the minus nine meters cubed. And since this is an estimation problem, we only need to keep one significant figure that for there, since we've just kind of made up roughly the diameter of a drop of water, our volume on our final answer are not going to be all that precise. All right, so now we want to know how many drops are in one leader of water. So we're going to take following of the bottle divided by volume of the drop since that's could be one leader divided by four times 10 to the minus nine meter cubed. And here we run into a bit of a problem because our units aren't canceling out because we're in different units. But that's okay. We can convert from leaders two cubic meters, and since the unit conversion, we're gonna multiply by some other fraction. That is evil toe one. And so it turns out that there are 1,000 leaders in one cubic meter, and so we'll dio one meter cubed up here. So now let's look what's going on. These leaders cancel and he's keeping meters cancel. So I left with just a number, which is good. We're looking for the number of drops and so do that division and you get roughly to times 10 to the fifth. But then we're keeping only one significant figures. This is an estimate or 200,000 drops in a one liter bottle.

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