Experiment R: Relative DensitiesAbstractThis report discusses how to find relative densities ofunknown materials using three different methods and includes explanations ofthe results achieved, as well as comparisons to known data. It was found thateach method was better fitted for the physical state of the exercised material.Improvements that may benefit the safety or accuracy of the results for eachmethod used is discussed further into the report. The purpose of this reportwas to compare the three methods to discover which was the most accurate orreliable in determining the density of each sample.IntroductionThe purpose of this report was to compare the methods ofmeasuring density for accuracy and reliability. This can later be used todetermine which method is best, given the physical state of the material. Thishas been based on the assumption that there is no provided access to betterequipment than the ones used in this experiment, which may significantlyincrease accuracy or reliability of data.

These experimental procedures canalso be used to find out what a liquid sample or a solid sample is, this can beregarded as the motivation for this report.TheoryThroughout this subsection, there will be references tomethod numbers 1 to 3, method one is called ‘Hydrostatic Balance’, method 2 iscalled ‘Relative Density Bottle’ and method 3 is called ‘Hare’s Apparatus’.Although similar in name, there is a distinct difference between relativedensity and density. The difference is the following: ‘the relative density isthe ratio of the density of the substance to the density of water’ 2.Therefore, relative density has no unit of measurement, but density does. Asthe relative density requires the density of the substance, the density of thesample must be measured. This is done using one of the three methods mentionedin this report. These methods tend to use the concept of Archimedes’ Principle3, which is when a sample or material (in this case) is completely submergedin water, it tends to feel lighter 3.

This ‘weight lost’ equates to the’buoyant force’ on the object which is the upward force the water is applyingto a floating object for example 3. This principle can also be described as abody in liquid experiences an upward force which equates to the weight of theliquid that this body had displaced 3. Using this principle to find thedensity of an object we can then use the following formulae to work out theRelative density: (Equation1) (Equation2)However, there is an error associated with using Archimedes’Principle. When a body is underwater, air bubbles occur at the surface of thesample 4 which adds extra weight and therefore effects the result of relativedensity. Relative density will appear lower than its most accurate value.

Onceresults have been recorded, they will be compared to Kaye and Laby’s Book ofPhysical Constants 1 to decide on which method is the most reliable oraccurate. This book is used as reference during the experiment which was puttogether by Physicists Kaye and Laby 1. During the procedure there will beerrors occurring, the formula for calculating this error for these proceduresare found below: (Equation3)Where the denominators of each bracket shown above are themean value of each set of data and the numerators are the errors associatedwith them, such as using a ruler with an error of 0.05cm.

Equation 3 will haveto be rearranged to find the value for . (Equation4)Where: = Weight of Water and Bottle, = Weight of Bottle, = Weight of Bottle, Shot and Water and = Weight of Bottle and Shot. For the secondmethod, a Relative Density Bottle is needed. This Bottle allows the same volumeof water to be put in the bottle each time as the lid has a hole which ispushed down inside the bottle, pushing any unwanted water out. This means thatthe bottle must be slightly overfilled to get the same volume each time. Thethird method includes the use of a glass tube called Hare’s apparatus, shapedlike the letter y 4. Method 3 uses the equations below: (Equation5)Where: = Density of Water, = Density of Ethanol, = Height of Ethanol on Hare’s apparatus and = Height of Water on Hare’s apparatus.

In theory,methods: ‘Hydrostatic balance’ and ‘Relative Density Bottle’ would be the mostsuitable for measuring the density of material’s in the solid physical statewhereas method ‘Hare’s Apparatus’ would be most suitable for testing thedensity of Liquids. It is also worth noting that, to work out the mean of a setof data, the following equation was used: (Equation6)Where is the mean, the numerator is the set ofvalues and n is the number of values. To work out the standard error on themean, combine the following equations with equation 6 and equation 3: (Equation7) (Equation8) (Equation9) (Equation10)Throughout this report, the value of 1 g/cm³ will be used as the density of water,this value has been taken from Kaye and Laby’s Book of Physical Constants 1. (Equation11)Where is the relative density of x in salt solution, is the density of salt and is the density of x.Experimental MethodsFirstly, the Hydrostatic Balance requires the followingequipment: an electronic crane scale (for example the one used during thisexperiment is the Kern FOB 500-1S Balance (0.

5kg)) 5, string, metal samplesthat are preferably around 50g-200g, a beaker and a raised platform with abouta 5cm in diameter hole in the middle. To begin the experiment, place theelectronic balance on the raised platform so that the hook on the underside ofthe balance is coming out of the hole. With the hook attached, re-calibrate thedevice so that the digital display shows 0g, this makes sure that the weight ofthe hook is not included in the recorded value of the sample.

Then the stringmust be used to attach the metal sample to the hook but be sure to allow enoughstring so that the metal can be submerged in water in the beaker below. Ensurethat the sample has stopped spinning and record the value that the balanceshows. Fill a beaker with water high enough so that the metal sample can becompletely submerged and place it under the metal sample and into the waterbelow. Check for any air bubbles clinging onto the surface of the sample, ifso, try rubbing the bubbles off with your fingers. If the sample is nottouching the beaker and it has stopped spinning, record that value as well.

Nowrepeat all the above with the rest of the metal samples you have – each 2 moretimes for reliability – take a value for the mean for each set of data and useequation 2 to find the relative density. Rearrange equation 1 to find thedensity of the material and use equations 3, 6, 7, 8 and 9 to find the errorassociated with that value, then compare the recorded value with the value in Kayeand Laby’s Book of Physical Constants 1 to find out what the material is. Theequipment should be set up as Figure 1 below:Figure 1: A sketch of the ‘Hydrostatic Balance’ apparatus with thebeaker included, used to measure the weight of a metal sample when submergedand when not submerged in water.

For the second experimental procedure ‘Relative DensityBottle’, the following equipment is needed: A Relative Density Bottle, Salt(NaCl), Shot Pellets of Lead and the Kern FOB 500-1S Balance (0.5kg) 5.Before starting the procedure, the density of salt solution must be calculated.Ensure that the Relative Density Bottle is rotated on its side while filling itto get rid of any air bubbles which would mean less liquid would get into thebottle than usual. To calculate the density of the salt solution, the apparatusfrom the first method must be reused.

Add about 10g of Sodium Chloride to thebeaker filled with water, then submerge one of the metal samples into thesolution. The system should already be re-calibrated to the hook from the lasttime it was used in this experiment Make sure that all the salt has dissolved,that there are no air bubbles on the surface of the sample and that the metalsample is attached and not touching the beaker before weighing. Record yourdata. Now using data concluded from the past method use equation 11 to work outthe density of the salt solution, repeat two more times. Then use equations 7,8 and 9 to work out the combined error. Now to begin the procedure, fill therelative density bottle with salt solution, add the stopper to the relativedensity bottle and wipe off any excess liquid. Weigh it then record your value.

Now empty the bottle and fill with distilled water, weigh, then record thisvalue down also. Get 50g of the Shot Pellets of Lead and put it into therelative density bottle filled with distilled water make sure to attach thestopper and wipe away any excess liquid each time. Now weigh the relativedensity bottle with the shot pellets and distilled water and record this value.Repeat the above 2 more times to ensure your data is reliable. Use equations 4and 1 to find out the density and relative density for the shot pellets, thenuse equation 3, 6, 7, 8, 9 and 10 to work out the combined error on your valuefor the density and relative density of the shot pellets. Finally, for thismethod, compare your data to Kaye and Laby’s Book of Physical Constants 1 tofind out whether this method is reliable and/or accurate. Set up the equipmentfor this procedure as illustrated below in Figure 2:Figure 2: A sketch of the ‘Relative Density Bottle’ apparatus, usedto measure the weight of water that is displaced due to the addition of Leadshot pellets.

The third and final method ‘Hare’s apparatus’, you will needHare’s Apparatus, two beakers, a boss, a clamp and a ruler. Get two beakers andfill them both, one with ethanol and one with distilled water. Attach Hare’sapparatus onto a boss and clamp low enough so that the two ends of the y-shapedtube can be lowered into the liquid. Suck on the only end that isn’t submergedinto either liquid until the liquid stops at a reasonable height within theHare’s Apparatus. Place your thumb over that tube so that the liquid does notrun down the tube back into the beaker and record the heights: and .

Note that and is measured from the surface of the liquid ineach beaker, to where it reaches in the Hare’s Apparatus. Record the values for and using the ruler and repeat 2 more times forreliability, then rearrange equation 5 to find your density of ethanol. Afterthis is done, use equation 1 to find the relative density. To work out thecombined errors, use propagation error equations 3, 6, 7, 8 and 10. Theequipment should be set up like the following in Figure 3 below:Figure 3: A sketch of the ‘Hare’s Apparatus’ set up, used tomeasure the density of Ethanol.

ResultsHere are the results that were concluded from when theexperimental procedure was carried out:Figure 4: A Graph showing the recorded relative density of theunknown metal samples labelled 1 to 4 using method 1 ‘Hydrostatic Balance’In reference to Figure 4, when comparing the relativedensities of objects 1 to 4 with Kaye and Laby’s Book of Physical constants 1,it was concluded that object number 1 was Lead, object number 2 was Copper,object number 3 was Silver and object number 4 was Titanium. Sample Relative Density Lead (Method 2) (10.540.2) Ethanol (Method 3) (1.30.2) Figure 5: A tableshowing the recorded relative density of Ethanol and Lead.

The relative densityfor Lead was acquired by using the ‘Relative Density Bottle’ method whereas theEthanol value was found using the ‘Hare’s Apparatus’ method.The errors included in the results were calculated usingequations 3, 6, 7, 8, 9 and 10 under the ‘Theory’ subsection.DiscussionThe value for the relative density of ethanol was slightlyoff when compared with Kaye and Laby’s Book of Physical Constants 1. Thevalue referred to in Kaye and Laby’s Physical Book of Constants 1 did not liewithin the range of the error calculated within this report either.

This couldhave been because of the parallax error on the ruler from the surface of theliquid to the top of where the liquid had stopped in Hare’s apparatus. It wasdifficult to tell the height of the ethanol or water as the ruler was held freehand against the apparatus during the procedure. This left the data for method3 unreliable when compared to universal data 1.

Kaye and Laby’s 1 value forthe density Lead also did not lie within the range that was calculated however,it wasn’t far off from it. Kaye and Laby 1 reported 11.43 g/cm³ for Lead and0.79 g/cm³ for Ethanol. Method 1 is the only procedure where all valuesreferred to was within the range of Kaye and Laby’s 1 data.

Therefore, forthis experiment Method 1 ‘Hydrostatic Balance’ is the most reliable.ConclusionThe most reliable and accurate method out of the three tofind Density and Relative Density of a material is method 1 ‘HydrostaticBalance’. However, this method can only be used when testing the density of asolid, not a liquid or gas phase material.References1 Kaye and Laby, Book of Physical and Chemical Constantsand Some Mathematical Functions “Densities and Relative Densities of knownmaterials” (1911)2 https://en.wikipedia.org/wiki/Relative_density(2018)3 https://en.wikipedia.org/wiki/Archimedes%27_principle(2018)4 Christian McQueen, Physics Labs Foundations of PhysicsLaboratory Book (2017)5 https://scales-measuring.com/bench-scales/369-kern-fob-500-1s-stainless-steel-bench-scale.html