Physics lab report

labreport1volumes-errorpropagation1.pdf

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Experimental Data

Rectangular Measurements

Height (cm) Length (cm) Width (cm) 1 7.41 7.60 3.60 2 7.40 7.60 3.70 3 7.42 7.60 3.65 4 7.41 7.60 3.70 5 7.40 7.60 3.66 Mean 7.41 7.60 3.66 Std. Dev. .0084 0 .041 Uncertainty .0038 0 .018

Triangular Prism Measurements

Height (cm) Length (cm) Normal (cm) 1 4.88 2.44 4.99 2 4.83 2.44 4.94 3 4.83 2.40 5.00 4 4.83 2.40 499 5 4.83 2.44 4.99 Mean 4.84 2.42 4.98 Std. Dev. .0224 .0219 .0239 Uncertainty .01 .0098 .0106

Hollow Cylinder Measurements

Height (cm) Length (cm) Normal (cm) 1 12.71 .49 7.60 2 12.71 .50 7.62 3 12.71 .50 7.62 4 12.72 .50 7.60 5 12.72 .50 7.60 Mean 12.71 .50 7.61 Std. Dev. .0055 .0045 .011 Uncertainty .0025 .0020 .0049

Bullet Measurements

Height (cm) Length (cm) 1 7.00 3.50 Uncertainty .05 mm

Cup Measurements

Height (cm) Length (cm) Normal (cm) 1 10.14 5.40 5.40 2 10.00 5.40 5.40 3 10.02 5.44 5.41 4 10.01 5.42 5.41 5 9.91 5.39 5.40 Mean 10.02 5.41 5.40 Std. Dev. .0820 .020 .0055 Uncertainty .0367 .0090 .0025 Data Analysis Mean of Rectangular Height:

( xi) / n = Mean∑ n

i = 1

(7.41 + 7.40 +7.42 + 7.41 + 7.40) / 5 = Mean 7.41 cm = Mean Standard Deviation of Rectangular height:

Std. Dev. = √ ( (xi x) ]n1 * ∑ n

i = 1 − 2

√ (.002 008 012 002 008 ) / 52 +. 2 +. 2 +. 2 +. 2 Std. Dev. = .0074 Volume of Rectangular: V = l * w * h V = 7.41 * 7.60 * 3.66 V = 206 cm3 Error Propagation of Rectangular:

= (dV/dl * )2 + (dV/dw) * )2 + (dV/dh * )2V Δ 2 lΔ wΔ hΔ = (wh * )2 + (lh * )2 + (lw * )2V Δ 2 lΔ wΔ hΔ = (3.66 * 7.41 * 0)2 + (7.60 * 7.41 * .041)2 + (7.60 * 3.66 * .0074)2V Δ 2

= 1.019 cm3VΔ Volume of Hollow Cylinder: V = π(d/2 + t)2 * h - π(d/2)2 * h V = π(7.61/2 + .5)2 * 12.71 - π(7.61/2)2 * 12.71 V = 162 cm3 Error Propagation of Hollow Cylinder:

= (dV/dd) * )2 + (dV/dt * )2 + (dV/dh * )2V Δ 2 dΔ tΔ hΔ

= π[((2(d/2 + t)(½) - ½*d*h) * .0049)2 + (2(d/2 + t) * .002)2 + ((d/2 + t)2 - (d/2)2 *V Δ 2 .0025]

= π[((7.61/2 + .5)-½*7.61*12.71) * .0049)2 + (2(7.61/2 + .5) * .002)2 + ((7.61/2 +V Δ 2 .5)2 - (7.61/2)2 * .0025)2]

= .217 cm3VΔ