Volume and MassVolume and Mass

CPSCPS

Chapter 1Chapter 1

IntroductionIntroduction If I had a stack of gold If I had a stack of gold

coins, how would I coins, how would I count them?count them?

What if I had several What if I had several stacks of gold stacks of gold coins….would I count coins….would I count them all? What could I them all? What could I do differently?do differently?

I might make a scale I might make a scale instead….then if I instead….then if I wanted to know the wanted to know the amount of gold in the amount of gold in the coins, I could just count coins, I could just count the coins.the coins.

Introduction…Introduction…

If I wanted to find out how much gold If I wanted to find out how much gold was in a bar of gold, there are was in a bar of gold, there are several things that I could do. How several things that I could do. How do you think we could measure the do you think we could measure the gold?gold?

What if we took tiny cubes, all the What if we took tiny cubes, all the same size, and used them to fill a same size, and used them to fill a space the same size of the cube? space the same size of the cube? We could count the cubes and know We could count the cubes and know how much gold there was.how much gold there was.

1.2 Volume1.2 Volume

An even easier An even easier solution would be solution would be to count only the to count only the cubes along each cubes along each edge and multiply edge and multiply them them

(#cubes in height)(#cubes in height)

(#cubes in width) (#cubes in width) (#cubes in depth)(#cubes in depth)

Height*width*depthHeight*width*depth

Units of MeasurementUnits of Measurement

MeterMeter = standard unit of measurement = standard unit of measurement CentimeterCentimeter = .01 meters (1/100 of a = .01 meters (1/100 of a

meter)meter) When we multiply the When we multiply the height x width x height x width x

depth (length),depth (length), we cube the centimeter, we cube the centimeter, so the units become so the units become cubic centimetercubic centimeter, , or or cmcm33

When When measuring liquids, we use the measuring liquids, we use the unit unit millilitermilliliter. A . A mLmL is 1/1000 of a liter is 1/1000 of a liter (.001 L(.001 L))

Comparing VolumesComparing Volumes

We use volume to compare different We use volume to compare different amounts of the same substance.amounts of the same substance.

For a solid we can multiply the three sides For a solid we can multiply the three sides of a rectangular solidof a rectangular solid

For a liquid, we can use a graduated For a liquid, we can use a graduated cylinder. Graduated cylinders have unit cylinder. Graduated cylinders have unit measurements along the side, and measurements along the side, and because liquids take the place of their because liquids take the place of their container, we can easily measure the container, we can easily measure the amount.amount.

Volumes of Irregular ShapesVolumes of Irregular Shapes We don’t need to use We don’t need to use

extensive geometry to find extensive geometry to find the volume of an the volume of an irregularly-shaped object. irregularly-shaped object. We can use a method We can use a method called “called “water water displacement.”displacement.” Place some water into a Place some water into a

graduated cylinder and graduated cylinder and measure the amount. measure the amount. (Call it V1)(Call it V1)

Put the object in the Put the object in the graduated cylinder. graduated cylinder.

Measure the new volume. Measure the new volume. (Call it V2)(Call it V2)

Subtract (V2-V1). What Subtract (V2-V1). What you have left is the you have left is the volume of the object.volume of the object.

1.3 Reading Scales1.3 Reading Scales

The smallest divisions on a ruler are 0.1 cm, or 1 mm apart. The smallest divisions on a ruler are 0.1 cm, or 1 mm apart. When you measure something, very rarely is it exactly on a When you measure something, very rarely is it exactly on a

line. Usually it falls between two lines. If you look at the line. Usually it falls between two lines. If you look at the paperclip above, the length falls between 4.7 and 4.8 cm. We paperclip above, the length falls between 4.7 and 4.8 cm. We estimate the last number of the measurement since we do not estimate the last number of the measurement since we do not know exactly what it is. Since it is closer to 4.7, we would know exactly what it is. Since it is closer to 4.7, we would probably say that it is 4.72 cm.probably say that it is 4.72 cm.

More on Reading ScalesMore on Reading Scales

If it fell exactly on the line, we would If it fell exactly on the line, we would report the reading as 4.70 cm. That report the reading as 4.70 cm. That gives us a better idea of exactly how gives us a better idea of exactly how long the paperclip is.long the paperclip is.

1.5 Shortcomings of Volume 1.5 Shortcomings of Volume

When a solid dissolves in a liquid, When a solid dissolves in a liquid, sometimes the volume changes sometimes the volume changes (decreases)(decreases)

Gas is easily compressed (lots of gas Gas is easily compressed (lots of gas can be shoved into the same space-can be shoved into the same space-like pumping a bike tire)like pumping a bike tire)

Difficulty in comparing differences Difficulty in comparing differences between a solid and a liquid, or a between a solid and a liquid, or a liquid and a gas.liquid and a gas.

1.6 Mass1.6 Mass

Mass has been used as a measurement Mass has been used as a measurement tool for thousands of years…tool for thousands of years… Equal arm balances were used early on-Equal arm balances were used early on-

people quickly realized they responded to people quickly realized they responded to MASS. The type of mass did not matterMASS. The type of mass did not matter

A standard mass is necessary in order to A standard mass is necessary in order to compare different types of objectscompare different types of objects

Grams are the standard unit for massGrams are the standard unit for mass 1 kilogram = 1000 grams (1 kg=1000g)1 kilogram = 1000 grams (1 kg=1000g)

More Interesting Units of More Interesting Units of MeasurementMeasurement

1 ml = 1cm1 ml = 1cm33

1 kg = 2.2 lb1 kg = 2.2 lb

1.10 Electronic Balances1.10 Electronic Balances Pan moves slightly Pan moves slightly

when object put on itwhen object put on it The tare button puts The tare button puts

the number (mass) on the number (mass) on the screen back to the screen back to zero.zero.

Be careful to make sure Be careful to make sure the units listed along the units listed along the edge of the screen the edge of the screen are the ones that you are the ones that you are measuring. Ask are measuring. Ask your teacher for your teacher for assistance with this assistance with this feature.feature.