Archimedes Principal

Any object in a fluid experiences an upward buoyant force which tends to cause it to float in the liquid. This buoyancy force will tend to diminish the apparent weight of a body submerged in the fluid Archimedes' principle states that this force is equal to the Weight of the fluid which the object displaces

Objective: To determine the specific gravity of several metal objects

Apparatus: Triple beam balance, metal cylinders wooden cylinder, alcohol cork or Piece of wood and thread

Theory: The density of an object p0 is defined as mass M of the object divided by its volume V that is p0= M/V. The specific gravity SG of an object is the ratio of its Density in air p0 to the density of water pw

at the same temperature that is SG¿ p0pw

.When an object is totally immersed in a fluid, the volume

of the fluid displaced is equal to the volume of the object An object floats if its density is less than the density of the fluid in which it is placed An object will submerge if its density is greater than the density of the fluid in which it is immersed It will sink in the fluid to a depth that is sufficient to displace the weight of the fluid equal to its own weight In this equilibrium condition , the buoyancy force, B, plus the tension in the wire ,W1 is equal to the weight of the object W, as shown in the free body diagram The quantity W1 is also equal to the apparent weight read by the laboratory balance when the object is in the fluid According to Archimedes principle, the buoyant force is equal to the weight of displaced fluid Thisis given by

B = Mw g = pwV w g= pwV 0g

Where Mw mass of the water displaced, V wis volume of water displaced and V0 Is the volume of the object Thus

W1 = W - B = Mg - pwV w g = p0V 0g−pwV 0g

W (W-W1) = Mg/ (Mg –M1g) = p0pw

=Specific Gravity¿ SG

Procedure:

1. The triple beam balance is set up with a fine thread attached to the underside of the pan carrier so that you can weigh bodies by hanging them on the thread rather than placing them in the pan. Check that beam balance balances with no body attached and adjust it accordingly. Then weigh the aluminum cylinder in air by suspending it on the end of the thread. Record this as mass of the cylinder in air as M.

2. Fill the beaker with water and place it on the floor with the metal cylinder submerged in it as shown in figure below. Be sure the cylinder is completely submerged and not touching the sides of the beaker. Record this as mass of the aluminum cylinder in water as M1.

3. Repeat procedures 1—2 for brass, copper and lead cylinders. 4. Calculate the specific gravity of each object. 5. Calculate the % difference of your measurements by comparing your results from the

accepted value of the specific gravity.

Data and Table:

Table 1.

Object Mass in air M

Mass in water M1

Specific gravity SG=M/(M-M1)

% Difference

Copper 57 50.7 9.04 11.05%Aluminum 18.4 11.9 2.83 64.6Gold 54.9 48.2 8.19 12.2Stone 69.3 63 11 9.09

Sample Calculations:

SG¿M /(M−M 1)

% Error¿|E−K|/K ×(100%)

Results, conclusions and error analysis:

Yes Archimedes principal is verified from the above measurements and there is less error with the as calculating the % difference from the expected values.

Questions:

1. Do your data indicate that Archimedes principle is valid? State clearly the evidence for your answer.Answer: Yes the data indicates that Archimedes principal is valid up to nears for most of the objects like cooper, gold, stone.

2. What are the densities of the objects determined from your measurements? Do these measurements agree with the accepted values? The following are the densities of the objects: Copper: 9.04 Aluminum: 2.83 Gold: 8.19Stone: 11

Yes these measurements agree with the accepted values but there is a percentage difference.