Archimedes Principle



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11 1405 2008a


Archimedes Principle

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.

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?______________

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 Air

Mass

In Water

M1 – M2


Mass of Displaced Water


2(A – B) (A + B)

X100%





(grams)

(grams)

(grams)

(grams)



aluminum
















brass
















steel
















lead
















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 Density

(g/cm3)



Reference

Density


(g/cm3)

2(E – A)
(E + A)

X100%


Aluminum





2.70




Brass





8.50




Steel




7.85




Lead





11.34













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