# Archimedes’ Principle Lab Report

###### Purpose

To find out whether the force of buoyance experienced by an object is equal to the weight of water displaced. In other words, to proof Archimedes principle.

###### Equipment

Wooden block

Metal cylinder

An irregular object

Water

Beaker

Beam balance

Vernier calipers

###### Introduction

The buoyance forced exerted by a liquid on an object is equal to the weight of the amount of the liquid displaced.

B= ρVg

Where

V is the volume of the liquid displaced

g force of gravity

ρ is the density of the liquid.

later, it was found out that the force of buoyance was equal to the difference between the apparent weight and the actual weight.

B= Wactual Wapparent

###### Experimental procedure

A clamp was attached to the bench and vertical bench rod inserted. The balance was placed in the vertical bench rod so as the pan to hang over the table. Then items to be weighed were hang on the pan suspended on the string.

The mass of the metal cylinder was measured using the balance. The dimensions of the cylinder were taken using Vernier caliper. The data was then used to calculate the volume and the density of the cylinder.

In additional to that, the mass and the dimensions of the wooden block were measured. The data was used to calculate the volume and the density of the wooden block. Volume of an irregular object was determined and recorded. A large beaker of water was placed on the table. The beaker was large enough so the three objects were comfortably accommodated and submerged with touching the bottom of the beaker.

###### measuring weight

The metal cylinder was suspended from the balance and it weight measured while suspended under the water. This is apparent weight of the cylinder. In same way the apparent weight of the irregular object was weighed and recorded. The specific gravity of the metal cylinder was determine and so was that of the irregular object.

It followed that for the wooden block either cylinder or the irregular object was used as the sinker for the wood. The apparent weight of the irregular object was determined and recorded.

Then, the specific gravity of the wooden block was calculated.

###### Data analysis

Mass of the cylinder=60.1g

Height of the cylinder = 2.12cm

Diameter of the cylinder =1.603cm

Apparent weight of the cylinder = 53.8g

Mass of the wooden block= 27.6g

Diameter of the wooden block = 5.2cm

Height of the wooden block = 2.7cm

Apparent weight of the wooden block = 23.5g

Mass of the irregular object = 65g

Apparent weight of the irregular object =57.9g

Initial volume of the water = 98cm3

Volume of the irregular object = 10cm3

Volume of the cylinder

Vcyl=  *r2*h

= 2.12 * 1.6032/4 *

= 4.28cm3

Density of the cylinder

Density ρ = mass/ volume

ρ = 60.1/ 4.28

ρ = 14.05g/cm3

specific gravity of cylinder

s.g =

s.g cyl= 14.05/1

=14.05

Volume of the wooden block

vblock=  *r2*h

=  *2.6*2.6*2.7

= 57.34cm3

Density ρ = mass/ volume

= 27.6/ 57.34

= 0.48g/cm3

Specific gravity of wooden block

s.g block= 0.48/1

=0.48

Density of the irregular object

Density ρ = mass/ volume

= 65/ 10

= 6.5g/cm3

s.girre= 6.5/1

=6.5

###### questions

Question 1

 Weight N Apparent weight g Mass g Volume cm3 Density g/cm3 Specific gravity g/cm3 Cylinder 0.5886 53.8 60.1 4.28 14.05 14.05 Block 0.271 23.5 27.6 57.34 0.48 0.48 Irregular 0.64 57.9 65 10 6.5 6.5

Q1a. Density is the property which is able to describe an object well. It fully describe the object  in reference to mass and volume

Q1b. yes an object weighs less when submerged in water the reason being it experience up thrust force equivalent to weight of the water displaced

Q2a. The apparent weight of Aluminium is lower than that of the iron reason being Aluminium displaced more volume of water than iron

Q2b. the apparent weight in air is higher than that in the water. The reason is that water is denser than the air and therefore 1cm3 of water has more weight compare to that of air.

Q3. Yes the balance will be disturbed. The reason is that finger displaces some water which exerts buoyance force which in turn exert a reaction force downward.

Q4. Yes object weighs less in the air than they actual are. The reason is that air exerts buoyance force which makes the reading to be apparent weight. If an object has a volume of 4cm3, it will displace air of the same volume which in turn will push the object upward

Q5. Yes the density depends on the object, the object expands in higher temperature increasing volume and then reducing density since the mass remains constant.

###### Discussion

In effort to verify Archimedes` principle, there were some percentage error present in the above data in table. The following are the source of the error; improper use of Vernier caliper and also the beam balance could have not been zeroed properly at the beginning of the experiment.  Therefore, errors caused inaccurate values in the measurement of the dimensions hence inaccurate volumes and also the mass of the object was inaccurate. However, this was enough to offset the observation to make them inaccurate.

###### Conclusion

Proving that the the up-thrust force (buoyance) experienced by given body in a liquid is equivalent to the weight of the liquid displaced was the objective main objective of the lab exercise. This was done while using Archimedes` principle. Furthermore, it was shown that the buoyance if different for all liquids since they have different densities.

Read more on Snell`s law here