The operation of this garage door is assisted using two springs AB and side members BCD

Chapter 18, Problem C18-3

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QUESTION:

The operation of this garage door is assisted using two springs AB and side members BCD, which are pinned at C. Assuming the springs are unstretched when the door is in the horizontal (open) position and ABCD is vertical, determine each spring stiffness k so that when the door falls to the vertical (closed) position, it will slowly come to a stop. Use appropriate numerical values to explain your result.

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QUESTION:

The operation of this garage door is assisted using two springs AB and side members BCD, which are pinned at C. Assuming the springs are unstretched when the door is in the horizontal (open) position and ABCD is vertical, determine each spring stiffness k so that when the door falls to the vertical (closed) position, it will slowly come to a stop. Use appropriate numerical values to explain your result.

ANSWER:

Problem C18-3

The operation of this garage door is assisted using two springs AB and side members BCD, which are pinned at C. Assuming the springs are unstretched when the door is in the horizontal (open) position and ABCD is vertical, determine each spring stiffness k so that when the door falls to the vertical (closed) position, it will slowly come to a stop. Use appropriate numerical values to explain your result.

                                                           Step by Step Solution

Step 1 of 6

First, it is convenient to draw a representation of the system in its initial and final states.

Note that we have considered that the length of the bars BCD is equal to 65 percent of the length of the garage door . Similarly, the distance BC is equal to 15 percent of the length of the door. Also it is important to remark that we have included the displacements of the center of mass of the door and the bars( and , respectively).

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