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At the instant 0 = 40 ° , the slotted guide is moving upward with an acceleration of 3 m/s and a veloc m/s. (Figure 1)

At the instant 0 = 40 ° , the slotted guide is moving upward with an acceleration of 3 m/s and a veloc m/s. (Figure 1)

Elements Of Electromagnetics
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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**Problem 16.41** At the instant \(\theta = 40^\circ\), the slotted guide is moving upward with an acceleration of \(3 \, \text{m/s}^2\) and a velocity of \(3 \, \text{m/s}\) (Figure 1). **Figure Explanation** The diagram shows a slotted guide mechanism. A rod \(AB\) is moving within the slot. The slotted path is a horizontal bar with a vertical guide that moves upward. The key components are labeled as follows: - Point \(A\) - Point \(B\) which is attached to the guide and moving within the slot - The distance between points \(A\) and \(B\) is given as \(300 \, \text{mm}\) - θ is the angle formed by the rod and horizontal line - The positive \(y\)-direction is indicated as downward **Part B** Determine the angular acceleration of link \(AB\) at this instant. Note: The upward motion of the guide is in the negative \(y\)-direction. Express your answer to three significant figures and include the appropriate units. Correct answer is shown as: \[ \omega = 15.55 \, \text{rad/s} \] Your input: \[ \alpha = -56.1 \, \text{rad/s}^2 \] *Note*: Your answer of \(15.55 \, \text{rad/s}\) may be rounded differently or use a different number of significant figures than required for this part. **Additional Information** This problem involves rotational motion and the dynamics of rigid bodies. The calculation requires understanding how changes in angular position, velocity, and acceleration correlate with linear motion, particularly given constraints like slot guides.
Transcribed Image Text:**Problem 16.41** At the instant \(\theta = 40^\circ\), the slotted guide is moving upward with an acceleration of \(3 \, \text{m/s}^2\) and a velocity of \(3 \, \text{m/s}\) (Figure 1). **Figure Explanation** The diagram shows a slotted guide mechanism. A rod \(AB\) is moving within the slot. The slotted path is a horizontal bar with a vertical guide that moves upward. The key components are labeled as follows: - Point \(A\) - Point \(B\) which is attached to the guide and moving within the slot - The distance between points \(A\) and \(B\) is given as \(300 \, \text{mm}\) - θ is the angle formed by the rod and horizontal line - The positive \(y\)-direction is indicated as downward **Part B** Determine the angular acceleration of link \(AB\) at this instant. Note: The upward motion of the guide is in the negative \(y\)-direction. Express your answer to three significant figures and include the appropriate units. Correct answer is shown as: \[ \omega = 15.55 \, \text{rad/s} \] Your input: \[ \alpha = -56.1 \, \text{rad/s}^2 \] *Note*: Your answer of \(15.55 \, \text{rad/s}\) may be rounded differently or use a different number of significant figures than required for this part. **Additional Information** This problem involves rotational motion and the dynamics of rigid bodies. The calculation requires understanding how changes in angular position, velocity, and acceleration correlate with linear motion, particularly given constraints like slot guides.
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