Quiz#1-W09-Solutions

Quiz#1-W09-Solutions - MECHANICAL & AEROSPACE...

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MECHANICAL & AEROSPACE ENGINEERING DEPARTMENT UNIVERSITY OF CALIFORNIA, LOS ANGELES MAE 102 Mechanics of Particles and Rigid Bodies Winter, 2009 INSTRUCTOR CHATTERJEE, A. K. SOLUTIONS QUIZ January 23, 2009
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MAE-102 Quiz #1: Solutions Winter ‘09 v v 1 P 3 P 2 P θ ϕ a radius radius b x y Problem 1 (10+10) 1. Show that the inward normal component n a of the acceleration of a particle is given by 2 n v a ρ = where v is the particle speed and is the radius of curvature of the particle path. 2. A belt is moving through a series of pulleys as shown with a speed v such that dv a dt = . Express the accelerations of points 12 3 , a n d PP P in terms of unit vectors ˆˆ , ij ± ± along the x - and y -axes, respectively.
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MAE-102 Quiz #1: Solutions Winter ‘09 1.1 Normal Component of the Acceleration of a Particle. Consider: a Particle P moving along its path By definition, ˆˆ vv ts t = ± ² ³³³ dv av t s t dt =+ ± ±± ² ³ ³³ ³ Hence, 2 nt v a, a v == ± ρ ( ) t ϕ C P v ˆn ³ ˆ t ³ s(t) fixed arc(CP) = s(t) where: dv ˆ ˆ tn s n n ds ⎛⎞ = ⎜⎟ ⎝⎠ ± ± ± ³ ³ by definition, ds d =
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MAE-102 Quiz #1: Solutions Winter ‘09 1.2 Accelerations of Points on the Belt in terms of Cartesian Coordinates.
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Quiz#1-W09-Solutions - MECHANICAL & AEROSPACE...

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