Search
 
 

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.
     
   
 
Practice Homework and Test problems now available in the 'Eng Dynamics' mobile app
Includes over 400 free problems with complete detailed solutions.
Available at the Google Play Store and Apple App Store.