Q1. The slender 15 kg bar is initially at rest and standing in the vertical position when the bottom end A is displaced slightly to the right. If the track in which it moves is smooth, determine the speed at which end A strikes the corner D. The bar is constrained to move in the vertical plane. Neglect the mass of the cord BC.**Diagram Explanation:**The diagram depicts a vertical setup of a bar and a cord:- The bar is positioned vertically from point A at the bottom to point B, which is 4 meters above A.- A cord extends from point B to point C, which is 5 meters from B, and is shown at an angle.- Point A is positioned 4 meters horizontally to point D, which is marked on the ground.- This setup suggests that the bar and the cord form part of a right triangle with the ground. In this problem, you are asked to calculate the speed of point A as it strikes point D after its initial displacement.

The data given is,Initial velocity, v1 = 0mass of slender, m = 15 kgTo determine:The speed at which end A strikes the corner D.The instantaneous center would be at point C and the final position when the end A strikes D will be as follows,This problem can be solved by applying the principle of conservation of energy at initial and final positions. The conservation of energy principle reads,The initial kinetic and potential energies,Use geometry to determine the final position of the slender,The angle ? is given as,Now calculate the distance between the center of mass of slender and instantaneous center at the final position,The moment of inertia of the rod is given by,Now the kinetic energy at final position is given by,The potential energy at the final position is given by,Now apply the energy principle discussed in step-2 to obtain the angular velocity,Finally, the velocity of point A at the time of striking(final position) is given by,The speed at which end A strikes the corner D=

Engineering

Mechanical Engineering

Q1. The slender 15 kg bar is initially at rest and standing in the vertical position when the bottom end A is displaced slightly to the right. If the track in which it moves is smooth, determine the speed at which end A strikes the corner D. The bar is constrained to move in the vertical plane. Neglect the mass of the cord BC. B 4 m 5 m 4m D

Q1. The slender 15 kg bar is initially at rest and standing in the vertical position when the bottom end A is displaced slightly to the right. If the track in which it moves is smooth, determine the speed at which end A strikes the corner D. The bar is constrained to move in the vertical plane. Neglect the mass of the cord BC. B 4 m 5 m 4m D

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

Q1. The slender 15 kg bar is initially at rest and standing in the vertical position when the bottom end A is displaced slightly to the right. If the track in which it moves is smooth, determine the speed at which end A strikes the corner D. The bar is constrained to move in the vertical plane. Neglect the mass of the cord BC.

**Diagram Explanation:**

The diagram depicts a vertical setup of a bar and a cord:

- The bar is positioned vertically from point A at the bottom to point B, which is 4 meters above A.
- A cord extends from point B to point C, which is 5 meters from B, and is shown at an angle.
- Point A is positioned 4 meters horizontally to point D, which is marked on the ground.
- This setup suggests that the bar and the cord form part of a right triangle with the ground.

In this problem, you are asked to calculate the speed of point A as it strikes point D after its initial displacement.

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Step 1: Determine the given data

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Step 2: Write the equation of conservation of energy

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Step 3: Calculate the initial energies

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Step 4: Calculate the final position of slender

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Step 5: Calculate the moment of inertia

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Step 6: Calculate the kinetic energy at final position

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Step 7: Calculate the potential energy at final position

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Step 8: Calculate the angular velocity

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Step 9: Calculate the velocity

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