This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 Dr. Saiful I. Khondaker Chapter 6: Circular Motion and Other Applications of Newton’s Laws Uniform Circular Motion • A force, F r is directed toward the center of the circle • Applying Newton’s Second Law along the radial direction gives 2 c v F ma m r = = ∑ • If the force vanishes, the object would move in a straightline 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 θ θ = ...(1) .......... cos cos mg T mg T F y = ⇒ = − = ∑ θ θ ) ........(2 sin 2 r mv T F x = = ∑ θ Dividing (2) by (1) θ θ tan / tan 2 2 rg v rg v mg r mv = ⇒ = = From the geometry: θ θ 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 = = ∑ θ ) ........(2 sin 2 r mv n F r = = ∑ θ Dividing (2) by (1) rg v mg r mv 2 2 / tan = = θ = ⇒ − rg v 2 1 tan θ Dr. Saiful I. Khondaker 2 1 1 . 20 80 . 9 )( 50 ( ) 4 . 13...
View
Full
Document
This note was uploaded on 07/30/2011 for the course PHY 2048 taught by Professor Bose during the Spring '08 term at University of Central Florida.
 Spring '08
 bose
 Physics, Circular Motion, Force

Click to edit the document details