hw8 - TAM212 Introductory Dynamics Spring 2005 S....

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TAM212 Introductory Dynamics Spring 2005 S. Balachandar Homework 8 (1.135, 1.141) 1.135 We are given v = - 2 ˆ i m / s a = - 4 ˆ i + 3 ˆ j - 2 ˆ k m / s 2 ˆ e t = v p | v p | = - ˆ i (a) d | v | dt = a · ˆ e t = ( - 4) · ( - 1) = 4 m / s 2 (b) a = a t + a n a n = 3 ˆ j - 2 ˆ k (since we saw from (a) that a t = - 4 ˆ i ) Now, we know that v 2 ρ = | a n | 2 2 ρ = 3 2 + 2 2 ρ = 1 . 11 m 1.141 From (1.105), we have v p = - aK ( ˆ i + ˆ j ) ˆ e t = - ˆ i 2 - ˆ j 2 1
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From (1.106), we have a p = aK 2 ( 2 ˆ i - ˆ j ) | a t | = a p · ˆ e t = aK 2 ± 2 ² - 1 2 ³ + ( - 1) ² - 1 2 ³´ = - aK 2 2 a t = aK 2 2 µ ˆ i 2 + ˆ
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hw8 - TAM212 Introductory Dynamics Spring 2005 S....

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