MIT16_07F09_hw03

MIT16_07F09_hw03 - NAME : . . . . . . . . . . . . . . . . ....

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NAME : . . . . . . . . . . . . . . . . . . . . . Massachusetts Institute of Technology 16.07 Dynamics Problem Set 3 Out date: Sept 17, 2007 Due date: Sept 26, 2007 Time Spent [minutes] Problem 1 Problem 2 Problem 3 Problem 4 Study Time Turn in each problem on separate sheets so that grading can be done in parallel
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Problem 1 (10 points) The large wheel of the quick-return mechanism rotates in the counterclockwise direction at a constant speed of 60 rpm (revolutions per minute). There is a “collar” at radius R on the wheel which positions the lever of length L which is free to slide through the collar. a) How many degrees of freedom does this system have? b) What is the relationship between the angle θ of the rotating wheel and the angle β between the lever and the horizontal? c) Determine the s , s ˙ and s ¨ as well as the velocity and acceleration of point P as a function of θ . d) Determine numerical values when θ = 45 o . Use R = 1 m, h = 1 . 5 m and L = 3 m. e) Calculate also the time it takes for the long bar to do i) the advance movement (rightmost position to the leftmost position) and ii) the return movement (left- most position to rightmost position). (Hint: at what angle θ does it reverse direction?)
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Problem 2 (10 points) Part A A vehicle moves at constant altitude y 0 . At time t = 0 it is located at x = 0, at which time it begins to accelerate in the x direction at a constant rate a x from an initial velocity v 0 at x = 0. Describe the motion in polar coordinates, r,θ as shown. We are going to express the acceleration in polar coordinates. Work out the various terms: 1) Show that ˙ r = v ( t ) x ( t ) /r ( t ) 2) Show that θ
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This note was uploaded on 11/06/2011 for the course AERO 112 taught by Professor Widnall during the Fall '09 term at MIT.

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MIT16_07F09_hw03 - NAME : . . . . . . . . . . . . . . . . ....

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