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Unformatted text preview: Solution for Longanswer Homework 20 Motion in a Circle problems Solution to Longanswer Homework Problem 20.1() Problem: Consider a pendulum swinging back and forth as shown in the figures. P Q (a)In the figures below, point P is the end of the swing, and point Q is the bottom of the swing. Draw the acceleration vector of the pendulum bob at locations P and Q . Explain briefly. P Q (b)Draw freebody diagrams for the pendulum bob at locations P and Q . Below each diagram indicate the direction of the vector sum of the forces (if the vector sum is zero, state so explicitly). Explain briefly. 1 P Q Solution to Part (a) To determine acceleration, determine v over a small time interval about the position shown. The velocity of the bob is tangential to the trajectory. At P the bob reverses direction, so a must point as shown in the figure. At Q the speed of the bob is constant; the only acceleration is centripetal (since the direction of the velocity is changing). P Q a a Grading Key: Part (a) 2 Points Solution to Part (b) 2 The force of gravity parallel to the string will be balanced by the contact force provided by the string, which must be along the length of the string (strings can only pull). The component of gravity perpendicular to the string provides the acceleration needed to change the direction of the bob. In the second picture, gravity is straight down, exactly opposite the string, so there is no component of force perpendicular to the string, so the size of the velocity cannot change. However, to get it to continue to move in a circular path, there must be a net upward acceleration, so the string force must be bigger than the force due to gravity. This would be the position in the motion where the string is most likely to break. P Q F g eb F g eb,perp F g eb,parallel F c rb F g eb F c rb Grading Key: Part (b) 3 Points Total Points for Problem: 5 Points Solution to Longanswer Homework Problem 20.2() Problem: You have been hired to help troubleshoot a new airport baggage handling system. While inspecting the system, the manager shows you a downward inclined portion of the conveyor belt where frequent pileups occur. As you observe the belt, a small suitcase arrives at the top of the 20 downward incline and the manager yells: Its those types of slick suitcases that give us a hard time! Indeed, the suitcase begins to slide, creating a major spill. You immediately roll up your sleeves and, using a stationary piece of conveyor belt, you determine that the coefficient of static friction between the small suitcase and the rubber conveyor belt is . 3 . The manager, looking over your shoulder, tells you that most suitcases are much heavier than the one you are holding, and that the conveyor belt moves at a steady speed of 1 m s . You think for a moment about what you learned in UPI, and then recommend an adjustment in the angle of incline. Since this will cost money, you must justify your recommendation....
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 Spring '08
 Stewart
 Physics, Work

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