Exam 1 January 31, 2012

Transcription

1 Exam 1 Instructions: You have 60 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a calculator during the exam. Usage of mobile phones and other electronic communication devices is NOT permitted during the exam. Problem 1 (20 pts) 2 (20 pts) 3 (20 pts) Total Score Name: Instructor: Exam 1 Page 1 of 9

2 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) = 1 2 x2 + 8, where x and y are given in meters. The x-component of the velocity of P is a constant 3 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 of P. (c) Determine the the radius of curvature for the path of P. y P x Exam 1 Page 2 of 9

3 This page is for extra work related to Problem 1. Exam 1 Page 3 of 9

4 Problem 2 (20 points): Given: The mechanism shown below is made up of links OA and AB. Point O is pinned to ground and Point B is constrained to move along a straight-line path. At the instant shown, link OA is vertical, link AB is horizontal, and v B is travelling at a constant speed of 5 m/s in the direction shown. Find: At this instant: (a) The angular velocity of links OA and AB. (b) The angular acceleration of links OA and AB. A 0.5 m B v B 0.5 m O Exam 1 Page 4 of 9

5 This page is for extra work related to Problem 2. Exam 1 Page 5 of 9

6 Problem 3 (20 points): Part A (6 points): v B no slip O no slip v A A disk is constrained to roll without slip between two moving surfaces. If each surface is moving to the right and v B > v A, determine the following (circle the correct answer): Point O moves: Left Right Not enough information to determine The angular velocity of the disk is: Clockwise Counter-Clockwise Not enough information to determine The speed of point O is best described by: v O < v A v A < v O < v B v O > v B Not enough information to determine Exam 1 Page 6 of 9

7 Part B (6 points):! A O no slip C B The stepped wheel shown above rolls without slip, in the direction indicated, along an inclined plane. Assuming ω is constant, on the drawing above: (a) Sketch the velocity and acceleration vectors associated with Point O. (b) Sketch the velocity and acceleration vectors associated with Point A. (c) Sketch the velocity and acceleration vectors associated with Point B. Exam 1 Page 7 of 9

8 Part C (4 points): x B h x A B A The motion of the two particle system shown above is constrained by an inextensible rope. Circle the correct answer for each of the following questions, assuming x B = 1 m at the instant shown. The rope-length constraint associated with this problem is best described by: 3x A + x b = L x A + x B = L x A + h 2 + x 2 B = L 3x A + h 2 + x 2 B = L The relationship between the speeds of particles A and B is best described by: v A < v B v A = v B v A > v B Not enough information to determine Exam 1 Page 8 of 9

9 Part D (4 points): ^j ^i v A R A B v B Particle A moves along a circular path (of radius R) with constant speed v A. Particle B moves along a straight-line path with constant speed v B. Circle the appropriate answer below relative to the position shown. The velocity of Particle A with respect to Particle B is: v A ĵ v B ĵ (v B v A )ĵ (v A + v B )ĵ 0 The acceleration of Particle A with respect to Particle B is: v 2 A R î v2 A R î 0 vb 2 v2 A R î (v B v A ) 2 î R Exam 1 Page 9 of 9