Physics Lab 7 copy

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Laboratory Manual for Physics 2750 2022-23 ARCHIMEDES' PRINCIPLE LAB: DATA AND ANALYSIS SECTION Part I: Find the density of a floating object 1. A block of unknown density is floating In a fluid. The block has a height H, mass m, and the height of the block below the water llne is h1 , as shown below. Consider that the block has a bottom area A. Using the picture on the right below , draw and label all the forces acting on the block. 2. Write Newton's second law for the block. This is equation 1. b - V\"\j (,, ~b v \J3 3. Write the equation that allows you to calculate the buoyant force acting on an object. Write the volume of the fluid displaced using the bottom area of the block and the height of the submerged part of the block. Replace this in the equation for the buoyant force. This is equation 2. v'Y\8 :: Vo~ (4-h~) 4. Write the equation that allows you to calculate the mass of the block as a function of its volume and density . Then write the volume using its bottom area A and height H. Replace in the equation for the mass m. This is equation 3. 5. Using equation 1, 2, and 3, find the density of the block as a function of the height of the block, fluid density , height of block below the water surface, and any other constants (if any). This is equation 4. Vn ( A· \\ )8:: Vf lA · \"1~1, ?b -: \J ~ l~') 63

Laboratory Manual for Physics 2750 2022-23 6. Use the wooden blocks on your table and measure the total height of each block, H. Record the measured heights in the table below. 7. Place the block in the water. Use the ruler on the block to measure the submerged depth of the block , ht, while the block is floating in equilibrium. Record your measurement in the table. Repeat for each block. 8. Using equation 4 and the measurements taken, calculate the density of each block. Remember that the density of water is 1000 kg/m 3 • Fill out the results in the table below. Block number Submerged depth, h1 Height of block, H ,., calculated density of the M block t.tJt v,,,,3 I D .o 1 is O.O Z-16 767, 2- 3 2- 0 . Otvi 0 . 0l 2-"t bq2. q<[ " 0 .O l ?D 0.0 240 7W s o. 0 Z-\0 o .o z2)s BC\3,bl b 0 . 020 0 0 . 02 '60 tbq . s7 9. What are the primary sources of error in finding the density of the blocks? \-\ u V\I\CA.,V\ e,;\f' v' O Y' w h e<f\ VV\ ~ur"1 Vl3 t D \ D cJ: e\9 vi t CLv\,cl S VDVY\. ~ oLQ..,, () t V\ 0-,V'e.,f ~ p r-° 1M CCV'\J Souv'Ce.S Part II: Find the density of an object that sinks The metal rods given to you for this activity have the following labels: S or SS = steel Lor Pb= lead Zn= Zinc Torn = titanium A or Al= aluminum W= Tungsten N or Ni = nickel Sn= Tin The yellow rod is brass; the reddish brown one is copper Note: you may not have been given all these rods. 1. A pendant of mass m has an unknown density. The pendant is su spended from a mass balance . Draw all the forces acting on the pendant in the air on the picture provided. 2. What is the force that the balanc e reads when the pendant is in the air? (hint: use Newton's 2 nd law for an object in equilibrium). T his is equation 1. \ ~ \'Y\3 : 0 ptad aat s 11.1 pca d ed from ba lance 64

i i i i ' ' ' t t t • Laboratory Manual for Physics 2750 2022-23 3. The pendant, still hanging from the mass balance, Is submerged fully in water. Draw all the forces acting on the pendant on the figure provided. 4. What is the force that the balance reads when the pendant Is fully submerged? This is equation 2. pu d an t l mm tned ht •• ftr 5. Write the equation that allows you to calculate the buoyant force on the pendant from Archimedes principle. This is equation 3. 6. What you know are the forces read by the balance, and the density of the fluid. Combine equations 1- 3 to find an equation that will allow you to calculate the volume of the pendant as a function of the forces read by the balance, fluid density, and any other constants (if any). This is equation 4. \J -: ~81- V\'\8 L ?~3 65

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Laboratory Manual for Physics 2750 2022-23 7. Now start your measurements. Determine the mass of the pendant in air and the force read by the scate and record it in the table below. 8. With the pendant still suspended from the balance, hold up a beaker with water such that the pendant is fully immersed. The pendant should not touch the sides or the bottom of the beaker. Record the mass of the pendant when fully submerged in the table and then calculate the force read by the scale. The mass read is called "apparent mass" and the force read represents the force of gravity for the "apparent mass". 9. Calculate the volume of the pendant using equation 4 and the fact that the density of water is 1000 kg/m 3 • Record it in the table. 10. Calculate the density of the pendant using the definition of density and record it in the table. .... 3,. Mjt Apparent Mass Mass in air Force in air ...i Force in water Pendant volume Pendant densify ~'1 In water t"c. ...i W\ ~ tutv>i, - -s / O. l64-qS \ .6 \ i2- O.l4-2>3 \ .4 VS7 7 z. Z. \ )< 10 bC\ 7 3.Cffs 11. To determine the composition of the pendant, you need to measure the densities of the other metals provided and compare the density values obtained with that for the pendant. Fill out the table below . Measure the volume of each rod using the graduated cylinder. Note: Not all rods will be given to you. Fill in the rows for the rods given. Name of metal Mass of rod in air t-,_. Volume of the rod t'Yl 3 Densify of the rod f:j n, '-J \ OC\oO Steel 0-04-'bt 4 -x ,o-~ Titanium Nickel Lead Aluminum o.o,w to x ,o-" ~('.)C) CJ Tin 0.0409 Sxio-(:, 6l f;O Zinc ('.).D396 6 )( 10- 6 b6CXJ Tungsten 12. What is the composition of the pendant? ~CA>~ C?V) CJUI' vv,e.ct.Wr"~ts, t\t,, cowi, po~, liO V\ ,, s 2; vie 'Y v e...,, , a e.v'v'o v\ w V' ca\ cu I (A, no V\ s lv-V1 e, o flf CLl.r\ t lQ_ t,vwq)c,s ·, t ,CJV\ -,s cxct-vC,L-l \,/ ~t-e.- e.,\ . 13. What are some sources of error in your lab? \-\ \JVY'(:A.,V\ eA'if'OV' LVOUlcA be,, t~ VY\U, \ v\ &:Ju{'C <L Di 1 eA'v'<:J f' clue.,, -\ -o V\CA;\J \V\,& to clo cc lot of m eo.su r'VV\L Vl t_s 1 D~ ~Q\.,V\~. I 66 C 4 -4 4 -

Conclusions: The conclusions should include the following parts: a') What is the purpose/goal of this lab? Laboratory Ma nu al for Physics 2750 2022-23 b) Summarize important results, methods used to obtain them, and draw conclusions supported by your results . c) Specify one or two interesting things that you learned from this lab . 0-.) l ~L "i b , O wi· 1 V\Q/ tw.- CAtJ/1. s 'i C? \J C,U" i OU:. o b~ e.c., \ s us ·1 n9 A vt,Y\ h,Y\e,cJ..L,, -::, ' P" ·, f'\C1 p ,e . b) uje,, tO UVlO \- I.e.,, \' e,,vlDlCLVl t <Ae.Y1 5i tv [)Si~ Vvl C{..8, S, fov1c...e/ D.Ytcl v-olu llht-. Lt \~ 69 7 '6 _q &' R'iJ / .--n s . U 'b ,vtf; tvi ,s clo.-:\-o-, tlQ., ~e,v,"& ,t'--{ Ts {., \ ~csf- to 1 ll- c).Q,Vl~, t-'-1 o -z-, "'c, t VI w vi e,, \vs ~o V\ , t w.__ co Vv1 p os ( -H C? V\ l,U .e.. Sc,+ l)~ 1. vt3 ouv1 C.QlC, ul c 1 .... ,,t1 c>v1S wcc.s, w r0vg , b Q. CO-- U t lL W M f>CJS. t, OVl bUCl.S 0 UPPO ~~ iC'.) bv 2> t ¤ -,Q_\. s) I t()UV\cA \ t- ) r\ '-\Q, v'f2S t} to VVI QU-&Ur1 -e..., t(z VV10l~S of- \-UL \7Q, V1cl D--- n t u s, Y15' {)._, bGl-lvlV1C fl , (Jy1 CA \ t- \A.J OL::, 1 V\,-he.,, V' ..Q.. 't) T\- v19 tu VVkQ_,C{ v" V"-e__ Kt,,, GU-,Vl ~, ~, e_ ss o t\G vYi.e.,,f evl V'U o{ S . 67

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