_lec16_ppt_ - Lecture 16 Feb 26, 2007 P112 Announcements...

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Unformatted text preview: Lecture 16 Feb 26, 2007 P112 Announcements Prelim Review session TBA Prelim on Thursday 7.30pm Bring: Your own Formula sheet (8.5x5.5) Non-graphing calculator Pen, protractor, ruler In past semesters students have regretted forgetting their protractor/ruler Agenda for today Continuing with Circular Motion Last lecture on forces! Rotating frame: nonintertial Loop the loop A R B Loop the loop Why does the ball stay in contact with the track at the top? Which factors determine if the ball stays in contact with the track? Loop the Loop What is the minimum speed such that the ball stays in contact with the track? solution A: N W a y Fy = N + W = m a Loop the Loop What is the minimum speed such that the ball still stays in contact with the track? Ball falls if N = 0 The corresponding minimum speed is: A: v2 a= R N =0 v = gR Fy = N + W = ma Car going over bump How fast must the car go to become airborne? Rounding a curve A 1500 kg car is traveling on a flat road that passes through a curve with 35m radius. Assuming the coefficient of static friction is 0.5, what is the maximum speed the car can have to stay on the road without sliding? solution Only centripetal force available is friction force, so the maximal speed is given by: N arad fs Fx = f s = marad v2 arad = R f s = s N Fy = N N = mg v max = sgR v max = 0.5 9.81m /s2 35m = 13m /s W mg = 0 Banked curve Avoid relying on friction to round a curve: build curve banked at angle : Banked curve Avoid relying on friction to round a curve. Build curve banked at angle : FBD: W Calculate the angle you need to round the curve at 25m/s! solution Fx = N sin = marad v2 arad = R Fy = N cos N = mg /cos v2 tan = gR (25m /s) 2 = 60deg = arctan 2 9.81m /s 35m mg = 0 Summary Dynamics with curved motion aT=v2/R ap=d|v|/dt Bumps and loops Leave surface: N=0 ...
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