ME 274 Basic Mechanics II Spring 2012 February 8 2012 Problem 1 20 points Given Particle P is able to slide along a rigid guide whose shape is given in terms of its Cartesian components as y x 2x2 8 where x and y are given in meters The y component of the velocity of P is a constant 8 m s Find When particle P is at the position of x 2 m a Determine the Cartesian components for the velocity and acceleration of P b Determine the rate of change of speed and the radius of curvature for the path of P Exam 1 Page 2 of 7 ME 274 Basic Mechanics II Spring 2012 February 8 2012 Problem 2 20 points Given The mechanism shown below is made up of links AB BD and DE Link AB is rotating in the clockwise sense with constant angular speed of AB 6 rad s At the instant shown links AB and DE are vertical and link BD is horizontal Find At the instant shown a The angular velocity of links BD and DE b The angular acceleration of links BD and DE Exam 1 Page 4 of 7 ME 274 Basic Mechanics II Spring 2012 February 8 2012 Problem 3 20 points Part A 8 points The inner surface of a stepped drum rolls without slipping on an inclined surface The top of the inner surface moves with a constant speed v up the slope as shown Points A and B lie on the outer surface of the drum For this position a Draw the velocity vectors for points A and B on the figure b Draw the acceleration vectors for points A and B on the figure No Slip Part B 2 points A scale drawing of a rigid disk AB is shown below along with the paths for points A and B on the disk Also shown is the velocity of A where the speed of A is nonzero vA 0 Circle the response below that most accurately describes the speeds vA and vB a b c d e vB 0 0 vB vA vB vA 0 v B vA 0 More information is needed to compare the speeds vA and vB Exam 1 Page 6 of 7 ME 274 Basic Mechanics II Spring 2012 February 8 2012 Part C 10 points The car shown below moves to the right lifting the crate At the instant shown the car is moving forward with a speed x 2 m s and an acceleration of x 3 m s2 For this instant where x 4 m a Find the speed of the crate y b Find the acceleration of the crate y ACME Exam 1 Page 7 of 7 vB vB aB C IC aA 01 vA Since BC AC v B v A L length of cable 2 y x 2 32 const xx dL 0 2 y dt x 3 d2L x 2 x x 2 y 2 dt 2 0 2 y 0 2 y 2 2 x 3 4 2 2 2 2 4 3 y 1 34 m s UP 4 2 0 8 m s 4 2 9 1 xx 2xx 2 2 2 3 2 x 3 22 4 3 2 1 2 42 32 3 2 2 y 2 688 UP