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Unformatted text preview: Exam 1, TAM212, Fall, 2003 Friday, 26 September 2003 3:00-4:00 p.m. Name: Section: You must show all work to receive full credit. All problems carry equal weight 1. At t = 0, point mass P starts from rest at A and starts to move around the track with a tangential acceleration of k a t = , where k is a known constant. If the track is straight from A to B (a distance of L) and has a constant radius of curvature R from B to D (180 ° around the curve), find the normal and tangential components of the acceleration of point mass P at C. Express your answer in terms of k, L, and R. Answer: k a t = (1) ρ = 2 s a n & ; Integrate (1) twice to get + = kt s & and ( ) 2 2 / 1 kt s = ∆ . At C, 2 / R L s π + = ∆ , the time passed for P to reach this point is ( ) k R L t / 2 / 2 π + = , and , therefore, at C ( ) k R L k kt s / 2 / 2 π + = = & . This gives, again, for P at C ( ) ( ) ( ) π + = ⇒ π + = R L k a R k R L k a n n / 2 / 2 / 2 2 (2) k a t = C A B R L P D Exam 1, TAM212, Fall, 2003...
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This note was uploaded on 04/17/2008 for the course TAM 212 taught by Professor Keane during the Spring '08 term at University of Illinois at Urbana–Champaign.
- Spring '08