Density Density We know that matter is anything

Density

Density We know that matter is anything that occupies a space and has mass. Mass = the amount of matter in an object Volume = the space an object occupies Density is the amount of matter there is in a given space.

Examples Water vs. Oil Metal vs. Wood Metal Water Wood Oil The amount of particles there are in the metal and water that occupies the space provided is a lot more than the amount of particles present in the oil and wood in the same amount of space. Water and metal are more dense.

What do we use density for? l Density is one of the basic ways to measure and compare the physical properties of different matter

Which one is more dense? l People in a square (popular place vs. not popular place) l How about this: Which square is more dense? • Do they occupy the same volume? • Do the have the same amount of particles? A B

Which one is more dense? l Now which one is more dense? • Do they occupy the same volume? • Do the have the same amount of particles? B A

l A is more dense because for the small volume it holds, it has more matter. l Even though they have the same amount of particles, if A was the same size as B, A would have 4 times as much particles. B A A A

What is density? l. To find density, the amount of mass (a measurement if the particles present) is divided by the volume of the substance. l Density = mass OR volume mass ÷ volume.

Mass is measured in grams and kilograms. Volume is measured in cubic centimeters or milliliters. Mass ALWAYS REMEMBER Grams is represented as a g UNITS! Kilograms is represented as a kg Volume 3 Cubic centimeters = cm, solid Cubic milliliters = m. L, liquid ¡ 1 m. L = 1 cm 3 So if Density = mass , Density = g or g volume cm 3 m. L

SI Units: International System of Units Modern metric system, measurements Mass l Grams = g l Kilograms = kg Length l Meter = m l Millimeter = mm Liquid l Liters = L l Milliliter = m. L ALWAYS REMEMBER UNITS! Time l Seconds = s l Milliseconds = ms Conversions ¡Milli = m __ ¡centi= c __ ¡Kilo = k __

Let’s try a density problem together l Frank has a paper clip. It has a mass of 9 g and a volume of 3 cm 3. What is its density? Given: D= ? m= 9 g V = 3 cm 3 Formula: ALWAYS REMEMBER UNITS! Solve: D= m/V =9 g/3 cm 3 = 3 g/cm 3 Answer: 3 g/cm 3

l Frank also has an eraser. It has a mass of 4 g, and a volume of 2 cm 3. What is its density? Given: D=? m =4 g Solve: ALWAYS REMEMBER =4 g/2 cm 3 UNITS! D= m/v = 2 g/cm 3 V =2 cm 3 Formula Answer: 2 g/cm 3

Work on these problems with your neighbor. l Jack has a rock. The rock has a mass of 6 g and a volume of 3 cm 3. What is the density of the rock? l Jill has a gel pen. The gel pen has a mass of 8 g with a volume of 4 cm 3. What is the density of the rock?

Now, try these on your own. l Alicia has a watch. It has a mass of 4 g and a volume of 2 cm 3. What is the density of the watch? l Mia has a wallet. It has a mass of 15 g and a volume of 5 cm 3. What is the density of the wallet?

• To actually calculate density we need measuring instruments. • To measure the mass, we need to use a balance. • If we use a scale, we measure the weight of the object. The weight is the force due to gravity pulling down. • You weigh less on the moon because gravity is less. But the amount of particles you are made of doesn’t change. • Only mass is measured by the balance because the object’s mass counteract with the weights on the balance.

Measuring the volume of an object can be very tricky as well. Most objects are not regular shapes that we have formulas for to calculate the volume. r Cube or Cubic rectangle l h Cylinder w h

l Frank measured another eraser. He used a balance to measure the mass at 4 g. However Frank is having trouble finding the volume. Can you help him? h = 2 cm l = 5 cm Given: L = 5 cm w = 1 cm h = 2 cm Formula w = 1 cm ALWAYS REMEMBER UNITS! Solve: V = 5 cm x 1 cm x 2 cm = 10 cm 3 Answer: 10 cm 3

l Frank has a cup for soda. He wants to know how much soda the cup could hold so he measures the volume of the cup. What is the volume? d h = 10 cm d = 4 cm Before we attempt this problem here are some clarification: ALWAYS REMEMBER UNITS! l π has a numerical value of 3. 14. l The Formula can be written V = 3. 14 x r 2 x h

d = 4 cm h = 10 cm l What’s the area of a circle? l A=πxr 2 = πxrxr l The volume is just the area of the base times the height. V=πxr 2 xh d l d is twice the radius so: d = 2 x r l r = d/2

l Frank has a cup for soda. He wants to know how much soda the cup could hold so he measures the volume of the cup. What is the volume? d h = 10 cm d = 2 x r, r = d/2 r 2 =r x r d = 4 cm Given: V= ? r = ? Cm d = 4 cm h = 10 cm Formulas: V = 3. 14 x r 2 x h r = d/2 = 3. 14 x r 2 x h Solve: ALWAYS REMEMBER UNITS! r = 4 cm/2 = 2 cm V = 3. 14 x (2 cm)2 x 10 cm = 3. 14 x (2 cm) x 10 cm = 3. 14 x 40 cm 3 = 125. 6637 cm 3 = 125. 66 cm 3 Answer: 125. 66 cm 3

In real life, most objects only resemble these shapes. Most objects are odd shaped. It is almost impossible to accurately calculate the volume of most objects. That’s where volume by displacement comes into play. When you think of displacement, what do you think of?

In volume by displacement, the displacement of water or any other liquid is involved. In a graduated cylinder, we measure the initial volume of water. V 1 Then we drop our object in. The object takes a certain amount of space. The water particles rises to a new final volume. VF The difference in the water levels from before and after will give you the volume of the object.

The equation for volume of displacement Volume of the object = Volume of water after – Volume of water before Vo = Vf-Vi What is the volume of this object? Vo= ? Vf = 9 m. L Vi = 7 m. L Vo = 9 m. L – 7 m. L 2 m. L

Measuring Accuracy l There many type of errors ¡ Instrumental: The balance is not calibrated right ¡ Human Error: mathematical, looking at the ticks on the instruments, eyes play trick on you. l When measuring Volume of liquids: ¡ Meniscus: Bottom arch water of used for measuring volume.

Liquid Layers l If you pour together liquids that don’t mix and have different densities, they will form liquid layers. l When liquids don’t mix that means they’re insoluble _______ l The liquid with the highest density will be on the bottom. l The liquid with the lowest density will be on the top.

Liquid Layers l Which layer has the highest density? l Which layer has the lowest density? l Imagine that the liquids on the left have the following densities: ¡ 10 g/cm 3. ¡ 6 g/cm 3. 3 g/cm 3. 5 g/cm 3. l Which density would go with which layer?

Liquid Layers – Try with your neighbor l Which liquid has the highest density? l Which liquid has the lowest density? l Which liquid has the middle density?

Liquid Layers – Try on your own! l Imagine that the liquids on the right have the following densities: ¡ 15 g/cm 3 ¡ 3 g/cm 3 ¡ 7 g/cm 3 10 g/cm 3 9 g/cm 3 12 g/cm 3 l Match the colors to the correct densities. 3 g/cm 3 7 g/cm 3 9 g/cm 3 10 g/cm 3 12 g/cm 3 15 g/cm 3

Review l What is the formula for density? l What two methods can be used to measure volume? l What is a meniscus? l What happens if you pour together liquids that have different densities? l Will the liquid on the top have the highest or lowest density? l Will the liquid on the bottom have the highest or lowest density?

Super Scientist Question of the Day l Jake has a book, a ruler, and a balance. l How can Jake find the density of the book with the tools he has?

l Practice Volume by displacement and density at: http: //www. sciencejoywagon. com/explrsci/media/density. htm Website is on the Homework page under Friday 6 th.