Posted: September 13th, 2017

Introduction to Chemical Engineering: Describing Physical Quantities

Introduction to Chemical Engineering

Describing Physical Quantities Assignment

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Assignment pdf
Describing_physical_quantities_2

sample solutions

Moment of inertia

i=τ/α
From the figure, value of h = hsinθ where θ is the angle the rod makes with the vertical,
Hence, T = 2 π√(I support)/mghsinθ (1)
For a simple pendulum with frequency ω = √g/I , and length 2/3 L, T = 2 π√(3I support)/2ghsinθ (2)
For a small angle, sinθ= θ and hence the equation 1 above is an equivalent from of equation 2.
Results analysis
The Slider position where periods T1 and T2 are equal = 24 meters
Value for equal period T = 0.9975 seconds, from the graph.
Plugging this value of T in equation
Force of gravity g= 4π2 d / T2 , for our pendulum the distance d was 0.24810 meters.
Hence, g = (4 x 3.142 x 3.142 x 0.2481)/ 0.99752
Acceleration due to gravity = 9.84375 m/s2 .
Finding the uncertainty in g.
From the data in excel spreadsheet, ∆ Tavg = 0.0047612
Fractional Uncertainty in T = ∆ T/ Tavg = 0.004738/0.995127 = 0.0047612
Fractional Uncertainty in calculating g = ∆g/g = [( ∆d)/d + 2 ∆T/T] = 10-4 + 2(0.0047612) = 0.0096224.
Uncertainty in g = ∆g/g x g = (9.84375-9.82)/ 9.82 x 9.82 = 0.0235.

Hence, ∆g = ± 0.0235