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Unformatted text preview: 1 Dr. Saiful I. Khondaker Chapter 6: Circular Motion and Other Applications of Newtons Laws Uniform Circular Motion A force, F r is directed toward the center of the circle Applying Newtons Second Law along the radial direction gives 2 c v F ma m r = = If the force vanishes, the object would move in a straight-line path tangent to the circle s The force causing the centripetal acceleration is sometimes called the centripetal force Dr. Saiful I. Khondaker 2 C v a r = 2 Ex 6.2. The Conical Pendulum The object is in equilibrium in the vertical direction and undergoes uniform circular motion in the horizontal direction. Calculate the constant speed v sin tan v Lg = ...(1) .......... cos cos mg T mg T F y = = = ) ........(2 sin 2 r mv T F x = = Dividing (2) by (1) tan / tan 2 2 rg v rg v mg r mv = = = From the geometry: sin sin L r L r = = Dr. Saiful I. Khondaker Speed is independent of mass m Example 6.4: Banked Curve A civil engineer wishes to design a curved exit ramp for a highway in such a way that a car will not have to rely on friction (think icy road) to round the curve without speeding. Such a ramp is usually tilted toward the inside of the curve(banked). If the speed for the ramp is 13.4 m/s, and radius of the curve is 50 m, at what angle the curve should be banked? ......(1) cos mg n F y = = ) ........(2 sin 2 r mv n F r = = Dividing (2) by (1) rg v mg r mv 2 2 / tan = = = rg v 2 1 tan Dr. Saiful I. Khondaker 2 1 1 . 20 80 . 9 )( 50 ( ) 4 . 13...
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