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SolutionsSet01

# SolutionsSet01 - Homework Solutions Set 01 Problem 1...

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Homework Solutions Physics 121 Set 01 Spring 2008 - 1 - Problem 1 The data shown in the figure are summarized in the following table. t (s) v (m/s) a (m/s 2 ) σ a (m/s 2 ) Weight (s 4 /m 2 ) 1 -1 -1.00 1.11 0.8 2 -5 -2.50 0.80 1.6 3 -5 -1.67 0.43 5.3 4 -9 -2.25 0.38 7.1 5 -9 -1.80 0.26 13.8 The calculated acceleration is equal to v / t . The error in the acceleration is equal to ! a = " a " t # \$ % & ( 2 ! t 2 + " a " v # \$ % & ( 2 ! v 2 = v t 2 # \$ % & ( 2 ! t 2 + 1 t # \$ % & ( 2 ! v 2 = a ! t t # \$ % & ( 2 + ! v v # \$ % & ( 2 Looking at the figure you see that the error in the t is 0.5 s and the error in v is 1 m/s and these errors have been used to determine the errors in a shown in the Table. In order to estimate the acceleration, we take the weighted average of the 5 values shown in the table (note: you need to use the weighted average since the error in each data point, and thus its weight, differs):

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Homework Solutions Physics 121 Set 01 Spring 2008 - 2 - a = w i a i i = 1 n ! w i i = 1 n ! where w i = 1 ! i 2 The weighted average is –1.9 m/s 2 . The error in the weighted average is ! = 1 w i i = 1 N " which for the data shown in the table is equal to 0.19 m/s 2 .
Homework Solutions Physics 121 Set 01 Spring 2008 - 3 - Problem 2 In order to find the fractional error in Y we have to first calculate the error in Y . Since E and I are known with great precision, we can ignore the error in Y due to errors in E and I . The error in Y is equal to ! Y = " Y " W # \$ % & ( 2 ! W 2 + " Y " L # \$ % & ( 2 ! L 2 = L 3 48 EI # \$ % & ( 2 ! W 2 + 3 WL 2 48 EI # \$ % & ( 2 ! L 2 The fractional error in Y is equal to ! Y Y = L 3 48 EI " # \$ % & 2 ! W 2 + 3 WL 2 48 EI " # \$ % & 2 ! L 2 WL 3 48 EI = ! W W " # \$ % & 2 + 3 ! L L " # \$ % & 2

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Homework Solutions Physics 121 Set 01 Spring 2008 - 4 - Problem 3 Consider a raindrop falling with a vertical velocity v y . An observer in the bus, moving with velocity v x , observes the raindrop during a period t . During this time, the displacement of the raindrop is v x t and v y t in the horizontal and vertical direction, respectively. To the observer the raindrop appears to be falling at angle θ equal to tan ! = v x v y In this problem, the angle of the rain is given.
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