Archimedes Principle

11 1405 2008a

Materials two 20gram slotted masses 600 ml beakers & 2oz Solo Cups (about 60mL size cup) Triple beam balance Density Set (e.g. aluminum, brass, steel, lead) 50 ml graduated cylinder & Spill Cup Support structure for triple beam balance for weighing hanging objects

Introduction The story is told that the Greek mathematician Archimedes liked to lounge around in his bath all day. He would work out his geometric proofs on his stomach (he was quite fat) writing with bath oil. One day when he was contemplating why things floated, the idea, which has become known as Archimedes' Principle, occurred to him. He became so excited by his discovery that he jumped out of his bath and ran through the streets of his town shouting "Eureka" which is Greek for "I've found it". In this lab we will attempt to grasp some of Archimedes' excitement by rediscovering his principle.

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Part 1 Discovery Activity Procedure a) Fill the spill-cup as shown by your instructor. Place both 20gram masses in the cup. Turn the cup sideways and sink the cup carefully, collecting the water in the cylinder. Water displaced by sunk cup & mass: ______mL. Do you think the cup & mass will displace more or less water if allowed to float instead of sinking? ______Explain your reasoning:

______Carefully retrieve the cup & mass. Fill the spill cup. b) Float the cup & mass, collecting water in the cylinder. Water displaced by floating cup & mass: ______mL.

Which situation displaced more water?______

Was your prediction correct? ______

Draw a force diagram for (a) the mass resting at the bottom of the beaker, and (b) floating at the surface. Label all forces correctly.

(a) (b)

In which situation, (a) or (b), does the mass & cup receive more buoyant force? ______

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Part 2 Determining Archimedes’ Principle Safety : No eating or drinking in the lab while performing this procedure. Wash hands after handling the lead.

The Density Cube Set consists of the following materials  aluminum (light grey color, least dense)  brass (shiny copper color)  steel (grey color, sharp edges)  lead (grey color, soft edges) Procedure 1. Fill the spill cup with water. Slowly lower the first object into the water, collecting the overflow in the cylinder. Record the displaced mass in Column B noting that 1mL of water has a mass of 1 gram. Repeat for all objects. 2. Weigh each of your objects in air and record in Column M1. 3. Weigh each of your objects while completely submerged in water and record in Column M2.

M1 M2 A B Mass in Mass Mass of 2(A – B) Air In Water M1 – M2 Displaced (A + B) Water X100%

(grams) (grams) (grams) (grams) aluminum

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Questions & Analysis Draw a force diagram with correct relative scale for the aluminum cube while it is being weighed submerged. Label each force in your diagram clearly.

How many different types of forces act on the Al cube?

Rank these forces from the smallest to the largest.

______< ______< ______

Calculate the density of each object in grams/cm3 , by dividing the mass in air by the volume of displaced water (note that 1mL = 1cm3).

E A Experimental Reference 2(E – A) Density Density (E + A) (g/cm3) (g/cm3) X100% Aluminum 2.70

Brass 8.50

Steel 7.85

Lead 11.34