Archimedes Principle

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1 Archiedes Principle Ojectives- 1- To easure gauge pressure. 2- To veriy Archiedes' Principle. 3- To use this principle to deterine the density o an unknown liquid deterine the density o an irregular solid Speciic gravity o various ojects and luids. Theory:- Part I. The Pressure Depth Relation: A ody, which is less dense than water, placed on a water surace will sink into the liquid until the ody experiences a uoyant orce, B that equals its weight, W. This eans that when the ody loats, its weight and the uoyant orce are the sae in agnitude ut opposite in direction (sound ailiar?). You will use a cylinder (an aluinu can) so that the uoyant orce due to the luid acts only on the otto o the cylinder i the can loats vertically. Once you know the orce which acts on the otto o the can and the area o the otto you can ind the pressure on the otto o the can. This is a gauge pressure ecause it assues that the downward orce is due only to the weight o the can and that the atosphere akes no contriution. Fro the deinition o pressure, we have: Force F W g Pr essure..(1) Area A A A N units: pascal 2 This gauge pressure is the pressure o the water on the cylinder otto at that depth elow the surace. We can also use the pressure-depth relation to calculate the pressure soe distance elow the luid surace: p p 0 gh p p 0 p gh (2) Where ρ is the density o luid and h is the depth in the liquid. gh

2 Part II. Archiedes Principle: A) Veriication o Archiedes Principle: The uoyant orce is descried y Archiedes principle as: an oject, when placed in a luid, is uoyed up y a orce equal to the weight o the luid displaced y the oject. The principle lies to an oject either entirely or partially suerged in the luid. The agnitude o the uoyant orce depends only on the weight o the displaced luid, and not on the oject s weight. I a oject is held at rest y a string (in air), its weight is given y ( W ) g V g (3) Where air,, V are the ass, density and volue o the oject, respectively. I a solid is suerged in a luid, it will e acted upon y three orces. 1. The weight o the ody, W. 2. The uoyant orce, B, on the ody, which can e siilarly expressed using Archiedes Principle: B W g V g, (4) where the suscript reers to the luid. 3. The tension in the string, T = arent weight W. Since the ody is in equiliriu, T ( W.) B W 0. Oviously, we can copute the uoyant orce as B W W... (5) i.e., ro the dierence o the actual weight o the ody in air and the arent weight o the ody in the luid. B) Density o Unknown Liquid Also ro Archiedes principle, we can deduce the density o unknown liquid. Fro equation (5) W W B. Where V o is the volue o the suerged part o the oject. The volue o the suerged part o a cuoid oriented vertically is equal to its cross-sectional area A ultiplied y the height h o the suerged part, so W g ( A g h (6). ) This is a linear relationship etween W. and h, the slope o the plotted straight line will e A ρ g.

3 C) Speciic gravity Speciic gravity (G.) o any sustance is the ratio o the density o a ody to the density o soe standard sustance. Within the liits o accuracy o this exercise, water at roo teperature ρ ay e chosen as the standard G. Since the volue o the water is necessarily equal to the volue o the ody iersed (call the V), then Vg W W G Vg B W W G '. (7) D) Density o irregular Solid You can deterine the density o an unknown solid ro equation.(8) V It s easy to easure the ass o an oject, ut unless it has a regular shape it s not so easy to easure its volue. But Archiedes showed us how to easure volue y easuring weight. This upward orce is equal to the weight o the displaced luid. But the volue o the luid is equal to the volue o the oject. Fro equation (4) and (8) the density o ody given y g g V B W W.. (9) Apparatus:- Balance, container o cork, sand, eaker, graduated cylinder, cuoids, sinker, unknown luid, string, and Venire caliper. Procedure:- Part I. The Pressure Depth Relation: 1. Measure the diensions cork container ase. 2. Load a cork container with sand so that it loats in the water and shake the sand aout until the cork loats upright and level. Tilt the cork to allow any air tred eneath it to escape.

4 3. Measure the depth elow the water surace o the otto o the cork, h. 4. Reove the cork ro the water, dry it o, and easure its ass. Then calculate the gauge pressure at depth h ro equation (1), and the equation (2) 5. Taulate your easureent in tale 1 Part II. Archiedes Principle: A) Veriication o Archiedes Principle: 1-.Use a vernier caliper (and/or) icroeter to easure the diensions o the oject (cuoids). So, calculate the volue o ody V which is the sae volue o luid displaced V.. 2- Mark o the cuoids every 1 c vertically starting ro the otto. 3- Suspend the cuoids y string ro the weigh-elow hook without touching the epty eaker located on plator 4- Deterine the ass o the cuoids using a alance ( ), so (w ). 5- Now pour luid ro another eaker slowly ro the side. Fill the eaker to a level atching the irst o your arks. 6- Record the new weight. Repeat or the next ark. 7- Fill the eaker o luid so that the saple is copletely suerged without touching the container and easure the. and W.. 8- Taulate your easureent in tale Calculate uoyant orce B 1 ro equation (4), and another way B 2 such as equation (5) and copare etween B1 and B 2. B) Density o Unknown Liquid 1. Using the easureent o tale Plot the graph o earance weight W. as vertical axis against h as horizontal axis, then deterine the o the luid y equation (6). C) Speciic gravity 1. Using the easureent o tale Sustitute in equation(7). D) Density o irregular Solid (Density o Rock) 1- Suspend the irregular ody (Rock) in alance y string and easure the( ). 2- But the known luid density (Water is a convenient liquid to use ecause its density equals 998 kg/ 3 ) in the graduated cylinder and read the volue(v ) 3- Iersed oject in the graduated cylinder. Notice luid with rise record the volue (V + ) and ass. 4- Calculate the volue o oject (V ) ro V =V + -V. used equation (8) to calculate the ( ) 1 5- Calculate density o ody ( ) 2 y another ethod, such as equation (9). 6- Record the data in tale 3 and copare etween ( ) 1 and ( ) 2.

5 Measureents and result:- Part I. The Pressure Depth Relation Tale 1 Floating saple Base diensions L*W Base area A ( 2 ) Mass (Kg) Weight W (N) W P1 A (Pa) P2 gh (Pa) %Eror p2 p1 *100 p 1 1 2

6 Part II. Archiedes Principle: Tale 2 = Kg. W = * g = N Base area o cuoids (A) = * =.. 2 Theoretical density o Water ρ = 998 Kg/ 3 Height (h) (). (Kg) W (N) Total suerge(h t ) A) Veriication o Archiedes Principle: V =V =A*h t = 3 B1 V g..n B W W..N 2. B) Density o Unknown Liquid W. g ( A g) h Fro graph W V.I.=..N. Slope=.N/ slope g..kg/ 3 A W (N) C) Speciic gravity Fro tale 2 G '. = =. h()x10

7 D) Density o irregular Solid (Density o Rock) Tale 3 ρ = ρ w = 998 Kg/ 3 (Kg) V ( 3 ) V + ( 3 ) V ( 3 ) ( )1 V (Kg/ 3 ) ( ) 2 (Kg/ 3 )

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