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DYNAMICS - CASE STUDY

    Introduction


Problem Diagram

 

A new dock lift is being used to move delicate computer equipment off shipping trucks. You need to know what the acceleration of the boxes is when the boxes are at dock level.

What is known:

  • The bottom loading pistons accelerate horizontally at a constant 0.3 ft/s2.
  • The horizontal velocity of the pistons is 0.6 ft/s when the lift is 4 ft high.
  • The lifting arms (AC) is 6 ft long.
  • Point A and A' are constrained to move
    horizontally.
  • Point B is constrained to move vertically.
     

  Question

 

What is the vertical acceleration of the lift's platform when it reaches the top of the dock?

   
  Approach

 
  • Use the relative velocity equation

    vB = vA + vB/A

    (see piston problem) to determine the angular velocity of the lifting bar AC. This is needed to solve for the accelerations.
  • Use the relative acceleration equation to find the acceleration of point A.

    aB = aA + aB/A
     
   
 
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