Lab 3

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School

East Carolina University *

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Course

1260

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Mechanical Engineering

Date

Oct 30, 2023

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docx

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2

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ELAR A2 EXERCISES 1-6 Complete these calculations of uncertainty propagation and submit them for the pre lab assignment. You must show your work in your submission. Your video analysis of the motion of a marble gives it position in frame 23 as (X23, 423) = (0134 m, 0.120 m) and its position in frame 24 as (X24, 324) = (0.122 m, 0.112 m). You estimate that you can measure the x and v positions with uncertainty #0.003 m. The frame rate of the video is 30 frames/s, which means the time interval between frames is At = 0,033 33%. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this problem, use S(A) = 1 x 10-6s. The mass of the marble is (2.031 # 0.001) x 10-2 kg, Calculate the following quantities: ie = Xi || The value of the velocity component Vx = X A\+ and ite uncertainty, \d&x\ \ om&zzse. » 30s™/m )\ _ I e © 1086 2/m Dux = (30507 0.603w) +(10:3 £ % + (00333332 ) Nux 2 0.00 s +0326m/ 52 095 % 2. | The value of the velocity component ~/, = X=1-Y1. “A;\/ ~ and ite uncertainty, Yi=0.10m Virl=0.\12m A} =0.033338s Ay =Yi¥1-$1 201 =0 A 10m =~ 0.008m 0% ogaizss ¥ T O-W s Vy =B¥=: < CvyEmd s \_L“J—|_ Seany < 30s/m 0.00%™ ~ VM= Gommax 725" m Dvy= (305"/m"0.008m)+ (7.25Ym + (0.0333339) DNvy= 0.0 /s + 0.20ms 2 0.3 Ws
and ite uncertainty, 0.43 v/s lve Juik vyt av =20 (vi+vyY) [BY. = 2 (vx Bvx+VyAvy) [ 2w [ Av =0.36 x0.8+024 x0\8 0.36°+024* AV 0.25m/5 The value of the momentum component ©x =(nv and ite uncertainty [ | M (mass of $re mosble) 2.031 X 1D "% ¥, [Vx (velocity comprent indhe X-ditectio) = -0.36 m/s> [Py =MV = (2,031 x10% kg) * (0% /) Px:'Om‘737.V\3-m/5 rooomszxgevs W The value of the momentum component Py=vivy and ite uncertainty, 1 The value of the kinetic energy W=z ow t=F (v %) and its uncertainty X | b= 05 % 2.0 1072 x 0.49% {IRERI0 20" AW _ Aw gAv - v T [ AW _ ooo1x10 0.25 1.88x10° ~ 2.03(x0"" i 0u3 | Ak=213x10° T
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