A copper wire (density =8.96 g / cm^3 ) has a diameter of 0.25 mm. If a sample of this copper

A copper wire (density =8.96 g / cm^3 ) has a diameter of...

Key Concepts

Circular Cross-sectional Area

For wire or cylindrical objects, the cross-sectional area is determined by the geometry of a circle. The area is calculated using the formula A = ?*(radius)^2. This allows for the connection of one-dimensional measurements with the three-dimensional volume of the object.

Unit Conversion

Ensuring that all measurements are in consistent units is vital in problem solving. Converting between units, such as from millimeters to centimeters, is necessary to maintain coherence in calculations involving physical formulas.

Mass-Volume Relationship

By using the relationship between mass and density, one can determine the volume of a substance if its mass and density are known. This is done using the formula: volume = mass/density, which is a fundamental concept in understanding the material properties.

Density

Density is a physical property that relates the mass of a material to the volume it occupies. It is calculated by dividing the mass by the volume, providing a conversion factor between these two quantities when one is known.

Transcript

00:01 Okay, so this unit conversion problem is actually throwing in some geometry at us, right? so we have this copper wire that atomic unit, atomic symbol, for copper.

00:15 Right, so we need to figure out how long the wire is.

00:19 So the way that i would approach this problem is i would treat the wire as one long cylinder.

00:26 And if that is the case, so we treat the wire as a cylinder.

00:30 Cylinder, and then because they give us the density and the mass, we're able to get the volume out of that.

00:42 And they're asking what the length of the wire is.

00:49 So if you think about this as some kind of a geometry problem, right, the volume of a cylinder is equal to pi r squared times the height of the cylinder.

01:04 And in this case, the height is what we're going to be looking for, because the height in this case is going to be the length of the cylinder.

01:12 So i'm going to call the answer, the length.

01:15 I'm going to call it h just to stick to what the true equation of the volume of a cylinder is.

01:21 But the way that we're going to do this is we're going to use the density.

01:26 So i'll start off, i guess i'll do this problem in blue.

01:29 I'll start off with the mass of the wire.

01:35 So if we start off with the mass, and we multiply that by the inverse of the density, right? so our grams are going to cancel out.

01:45 So there they go.

01:47 So now we're left with 2 .455 inverse.

01:56 Sorry, cubic centimeters.

01:58 So this is the volume.

02:02 Of the wire based on the mass that we have.

02:07 And this is where it might get a little tricky, right? because our diameter of the wire is given to us in millimeters.

02:16 So going to your textbook and understanding and looking at the prefixes, right, we have to go from milly to centi.

02:23 So one way you can do that is use dimensional analysis, right? and you can go use the scientific notation that's given in that table and go back to meters and then go from meters to centimeters.

02:40 So i'm just going to show that just for fun, right? so for every one millimeter, millie, it has the prefix 10 to the minus three meters, right? so now we're in meters.

02:58 And then if we wanted to go to centimeters, centi has the prefix 10 to the minus second meters.

03:09 So realistically, we just changed by a factor of 10, right? so you could look at the table and say those are only, those millie and centi are only, they're zero away from each other, right? they're adjacent to each other on the table.

03:27 The table moves in factors of 10.

03:29 So there is 10 millimeters for every one centimeter.

03:33 So the diameter, 0 .25 millimeters, is 0 .025 centimeters...

Please give Ace some feedback