The mechanism shown is one of two identical mechanisms attached to the two sides of a 185-lb uniform rectangular door. Edge \(ABC\) of the door is guided by wheels of negligible mass that roll in horizontal and vertical tracks. A spring of constant \(k\) is attached to wheel \(B\) in such a way that its tension is zero when \(\theta = 30^\circ\). Knowing that the door is released from rest in the position \(\theta = 45^\circ\) and reaches the vertical position with an angular velocity of 0.6 rad/s, determine the spring constant \(k\).**Diagram Explanation:**- The diagram shows a rectangle labeled \(ABC\), with a pivot point at \(A\).- A spring attached to point \(B\) is shown, exerting force along the line perpendicular to the wall.- The rectangle is tilted at angle \(\theta\), which is variable as described in the problem.- The lengths \(AB\) and \(BC\) are each 5 ft.The spring constant is \(\boxed{58.72}\) lb/ft.

Given data :w = 185 lbSpring constant = kT1= 0 g= 32.2 ft/s2θ= 30°θ2 =…

The mechanism shown is one of two identical mechanisms attached to the two sides of a 185-lb uniform rectangular door. Edge ABC of the door is guided by wheels of negligible mass that roll in horizontal and vertical tracks. A spring of constant k is attached to wheel B in such a way that its tension is zero when e = 30°. Knowing that the door is released from rest in the position e = 45° and reaches the vertical position with an angular velocity of 0.6 rad/s, determine the spring constant k. k B 5 ft 5 ft

The mechanism shown is one of two identical mechanisms attached to the two sides of a 185-lb uniform rectangular door. Edge ABC of the door is guided by wheels of negligible mass that roll in horizontal and vertical tracks. A spring of constant k is attached to wheel B in such a way that its tension is zero when e = 30°. Knowing that the door is released from rest in the position e = 45° and reaches the vertical position with an angular velocity of 0.6 rad/s, determine the spring constant k. k B 5 ft 5 ft

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The mechanism shown is one of two identical mechanisms attached to the two sides of a 185-lb uniform rectangular door. Edge \(ABC\) of the door is guided by wheels of negligible mass that roll in horizontal and vertical tracks. A spring of constant \(k\) is attached to wheel \(B\) in such a way that its tension is zero when \(\theta = 30^\circ\). Knowing that the door is released from rest in the position \(\theta = 45^\circ\) and reaches the vertical position with an angular velocity of 0.6 rad/s, determine the spring constant \(k\).

**Diagram Explanation:**

- The diagram shows a rectangle labeled \(ABC\), with a pivot point at \(A\).
- A spring attached to point \(B\) is shown, exerting force along the line perpendicular to the wall.
- The rectangle is tilted at angle \(\theta\), which is variable as described in the problem.
- The lengths \(AB\) and \(BC\) are each 5 ft.

The spring constant is \(\boxed{58.72}\) lb/ft.

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