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Unformatted text preview: Alvarado, Patrick – Homework 5 – Due: Oct 12 2006, 10:00 am – Inst: Andrei Sirenko 1 This printout should have 17 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 2) 10 points Consider the two vectors ~ M = ( a, b ) = a ˆ ı + b ˆ and ~ N = ( c, d ) = c ˆ ı + d ˆ , where a = 4, b = 4, c = 1, and d = 1. a and c represent the xdisplacement and b and d represent the y displacement in a Cartesian xy coordinate system. Note: ˆ ı and ˆ represent unit vectors ( i.e. vectors of length 1) in the x and y directions, respectively. What is the value of the scalar product ~ N · ~ N ? Correct answer: 2 . Explanation: Take the scalar products of the x and y displacement of ~ N and ~ N individually ~ N · ~ N = ( c ˆ ı + d ˆ ) · ( c ˆ ı + d ˆ ) = c 2 (ˆ ı · ˆ ı ) + d c (ˆ · ˆ ı ) + c d (ˆ ı · ˆ ) + d 2 (ˆ · ˆ ) = c 2 + d 2 = (1) 2 + ( 1) 2 = 2 . since ˆ ı ⊥ ˆ , we have ˆ ı · ˆ ı = 1, ˆ · ˆ ı = 0, ˆ ı · ˆ = 0, and ˆ · ˆ = 1. Note: cos 0 ◦ = 1 and cos 90 ◦ = 0. 002 (part 2 of 2) 10 points What is the value of the scalar product ~ M · ~ N ? Correct answer: 0 . Explanation: Take the scalar products of the x and y displacement of ~ M and ~ N individually ~ M · ~ N = ( a ˆ ı + b ˆ ) · ( c ˆ ı + d ˆ ) = a c (ˆ ı · ˆ ı ) + b c (ˆ · ˆ ı ) + a d (ˆ ı · ˆ ) + b d (ˆ · ˆ ) = a c + b d = (4) (1) + (4) ( 1) = 0 . since ˆ ı ⊥ ˆ , we have ˆ ı · ˆ ı = 1, ˆ · ˆ ı = 0, ˆ ı · ˆ = 0, and ˆ · ˆ = 1. Note: cos 0 ◦ = 1 and cos 90 ◦ = 0. keywords: 003 (part 1 of 2) 10 points A particle is located at the vector position ~r = (1 . 4 m)ˆ ı + (3 . 5 m)ˆ and the force acting on it is ~ F = (3 . 8 N)ˆ ı + (4 N)ˆ . What is the magnitude of the torque about the origin? Correct answer: 7 . 7 Nm. Explanation: Basic Concept: ~ τ = ~r × ~ F Solution: Since neither position of the par ticle, nor the force acting on the particle have the zcomponents, the torque acting on the particle has only zcomponent: ~ τ = [ x F y y F x ] ˆ k = [(1 . 4 m) (4 N) (3 . 5 m) (3 . 8 N)] ˆ k = [ 7 . 7 Nm] ˆ k ....
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This note was uploaded on 09/04/2008 for the course PHYS 106 taught by Professor Opyt during the Spring '08 term at NJIT.
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