Displacement and Density

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Displacement and Density

• Section 10.5
• April 12, 2005

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Answers to Homework

• Page 543
• 6. 3456?
• 12. r 9 in.
• 16. The golf ball is 10.6? the volume left in
  the cylinder is 16? so the water will not
  overflow.

Page 547 5. V 256/3 ? ? 85.3 ? 6. S.A.
144 ?.
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Displacement

• What happens when I add ice cubes to a glass of
  soda? What happens when you put a scoop of ice
  cream in some root beer? What happens if you put
  your dog in the tub full of water for a bath?

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• All of these are examples of DISPLACEMENT, which
  means that the water is displaced by an object
  when it is placed in water.

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Displacement

• You can use displacement to find the volume of
  any object, especially objects of irregular size
  that we cannot measure with a formula.
• We just have to put them in an object filled with
  water in a container we can find the volume of!

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DEMONSTRATION
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Find the volume of the rock.

• Volume of water in square prism BEFORE inserting
  rock
• V BH (4 in)(4 in)(____)
• Volume of water AFTER
• V BH (4 in)(4 in)(____)
• What is the volume of the water DISPLACED?
• Vafter Vbefore _____
• What is the volume of the rock? _____

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Find the volume of the object.

• Volume of water in cylindrical container BEFORE
  inserting object
• V BH ?r2H ?(2 in)2(____) _______
• Volume of water AFTER
• V ?r2H ?(2 in)2(____) _______
• What is the volume of the water DISPLACED?
• Vafter Vbefore _____
• What is the volume of the object?
• What is another way to find the displaced volume?
  What changes as you insert the object?

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So to find the volume using displacement

• V BH where B is the area of the base of the
  container (prism or cylinder) and H is the change
  in the height of the water.
• Example When you place a clump of metal into a
  container of water, it raises that water level by
  5 cm. If the container is a rectangular prism
  whose base measures 15 cm by 15 cm, what is the
  volume of the metal?

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Archimedes, Again!

• A king once gave him a difficult task. The king
  had a crown. He had paid for pure gold. He was
  afraid that the crown-maker had mixed silver with
  the gold. He wanted Archimedes to figure out
  whether or not the crown was pure gold or mixed
  with silver. Now, you know that all he had to do
  was to figure out the density of the metal.

Silver's specific gravity is 10.5 and the
specific gravity of gold is 19.3. It should be
easy to detect the difference. The problem was to
determine the volume of the crown. The kind did
not want Archimedes to harm the crown in any way.
How do you calculate the volume of a crown?
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Finding Density

• Density is the mass of matter in a given volume.
• Density is the ratio of the mass of a substance
  to its volume, and it can be calculated by
  dividing the mass by the volume. Density is often
  expressed in units such as grams per cubic
  centimeter (g/cm3) or pounds per cubic foot
  (lb/ft3).
• Density Mass / Volume

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Density Table
Metal Density Metal Density
Aluminum 2.81 g/cm3 Nickel 8.89 g/cm3
Copper 8.97 g/cm3 Platinum 21.40 g/cm3
Gold 19.30 g/cm3 Potassium 0.86 g/cm3
Lead 11.30 g/cm3 Silver 10.50 g/cm3
Lithium 0.54 g/cm3 Sodium 0.97 g/cm3
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Calculating Density

• Archimedes places the crown in a cylindrical
  container full of water of radius 6 cm, and
  notices that the water level rises 1.1 cm. He
  weighs the crown and notices that it weighs
  2401.05 grams. Is the crown made of gold?
• Mass 2401.05 g
• Volume V ?r2H ?(6 cm)2(1.1 cm) _______
• Density Mass / Volume __________

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Homework

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