Question

Error Propagation and Density of Materials

I need you to finish the two columns(Don't worry about the third) in the table using the formulas in page one. Please show work

3) Use the Vernier caliper to measure the height, h, and the diameter, D, of the cylinder. Record h and D and their uncertainties, Ah and AD. 4) the graduated cylinder Use metal. the determine of to the volume how would you do this? Analysis The density of a sample of material is given by (1), that is, (1) where m is the mass of the sample and V is the volume. The volume of a cylinder is _ TDh V= (7) 4 where D is the diameter and h is the height of the cylinder. The density can then be written as 4m (8) Dh and the uncertainty in the density as Am Ap p AD (9) m A) Use (8) and (9) and the meter stick measurements to calculate the density of the sample and its uncertainty. P±Ap= B) Use (8) and (9) and the Vernier caliper measurements to calculate the density and p+Ap= its uncertainty. C) Use the graduated cylinder measurements to calculate the density and its uncertainty. P ±Ap = D) Identify your metal by comparing your results to the known values: 2.70 g/cm 8.5 g/cm 8.9 g/cm3 11.34 g/cm 7.7 g/cm Aluminum Brass Copper Lead Stainless steel 2 Ruler value + error Vernier Caliper value+error Gra cylin Mass of cylinder 18.49- 599118,49-5.99 ( Diameter of Cylinder ) Radius of Cylinder ) Height of cylinder ) of cylinder's 1.27am.05en20005m .64cm 05n038cmto.0 5 ( 4.81cm t,OGan5.1tocn1o.05. ( Area base ( Volume of cylinder Density of cylinder Sample calculations:

Answer 1

Area of Cy inder 's Ba se:- A AR2 Ruler Nalue R- R= 0.64Cm AR=0.05 cm 2. T (0.64) 2 Ab= Base Area -1.29 Cm 2 2AR RAb A Ab= 2x0.05 A O.16Cm XAL o.16.29 Ab G.64 O.20CA2 Area of Cy inder 's Base ABt DAL 1.29 cm 2 a.16 c Ab= TR2 AA 2AR AAL= A2AR 1.29 Cm22x0.05 Ch A 0.L4 cm DAb= 0.20 Cm 2 Area of Cylinderis Base Ab t AAb 1.2-2 cm2 t 0.20 chm 1 Ars vern'ier Cali ber value- R-O.638cm AR O.O5 Cm 22 Ab = -1.279 Cm2 2x0.05 DAL-1.279 0.200 Cm2 O.638 Area of Cy Linderls Base =( 1.279 t a.200 ) Cm As 2 Nolumeof Cy inder R2H N= Rulervale (0.04 to.05)cm R =0.64 cm DR- 0.65h Radius H=4.81 cm DH:0.05ch (4.81 t0.05Jcm Height 1

(0.4)2 22 6.19 cm3 X 4.81 =6-19 cm3 /2x0.os O.64 O.os ) AV 14 AH 2AR DH + 2AR 4-81 H V R 3 ご.03 Cm (6-19 t 63 V+ΔV Nolume Nernier Caliper Value Cm (0.633 t 0.0s (5-170 ±0.05)cmヲH-5.70Cm, DH=0.65ch )CmうR-0.633, ARニ0.05 Ch Radius 急 - Height 11 *(0.633)2 3 6.614 cm 22 X 5.176 2x 0.05 S.OS .1o Cm 6.614 AV- .C38 5.170 Volume ニ 4 t.1o1) Cm (6.61