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DYNAMICS - CASE STUDY


Problem Graphic

  Introduction

 

As the utility truck pulls away, the worker at the top of the arm rotates the arm down and 180° toward the front of the truck. If the acceleration is too great, he may fall off the truck.

What is known:

  • All values are given at the instant the arm is perpendicular to the path of the truck.
  • The truck is traveling in a straight line at a constant rate of 35 ft/s.
  • The arm is 40 ft long, and is 30° up from horizontal.
  • The arm is rotating about a vertical axis toward the front of the truck at a rate of 0.2 rad/s, increasing at 0.8 rad/s2.
  • The arm is rotating about a horizontal axis parallel to the path of the truck at a constant rate of 0.1 rad/s.
     
    Question


Problem Diagram
 

When the arm is perpendicular to the path of the truck, what are the velocity and acceleration of the worker with respect to the ground?

   
  Approach

 
  • Consider a translating coordinate system located at the base of the arm.
  • Use the equations of general motion in three dimensions to determine the motion of the end of the arm with respect to a fixed (non-translating) coordinate system.
  • Only consider the instant in time when the arm is perpendicular to the path of the truck.
     
   
 
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