The 2 kg C cuff can slide freely along the straight AB shaft. Determine the acceleration of the C cuff, a) If the shaft is fixed, (b) If the A cuff fixed to the AB shaft is moving downwards at a constant speed along the vertical rod, and (c) In the case of the A cuff being subjected to a downward acceleration of 2 m/s^2. In each case, assume that the cuff performs planar motion. B

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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The 2 kg C cuff can slide freely along the straight AB shaft. Determine the acceleration of the C cuff:

a) If the shaft is fixed,
b) If the A cuff fixed to the AB shaft is moving downwards at a constant speed along the vertical rod, and
c) In the case of the A cuff being subjected to a downward acceleration of 2 m/s^2.

In each case, assume that the cuff performs planar motion.

**Diagram Explanation:**

1. **Diagram Description**:
   - The diagram shows an AB shaft oriented at a 45-degree angle to the vertical.
   - Point A is at the lower end of the vertical rod, and point B is at the upper end, inclined at a 45-degree angle.
   - The 2 kg C cuff is positioned on the AB shaft and can slide along its length.

2. **Provided Information**:
   - The AB shaft is inclined at a 45-degree angle.
   - The motion and acceleration of the C cuff need to be determined under three different scenarios.

3. **Scenarios Breakdown**:
   - **Fixed Shaft (a)**: If the AB shaft is stationary, the analysis will consider only the forces acting along the AB shaft due to the weight of the cuff.
   - **Constant Downward Speed (b)**: The AB shaft is moving downwards along the vertical rod at a constant speed, implying no acceleration in the vertical direction.
   - **Downward Acceleration (c)**: The AB shaft is accelerating downwards at 2 m/s², which will affect the relative acceleration of the C cuff along the shaft.

This exercise requires applying principles of physics, specifically kinematics and dynamics, to resolve the accelerations in each scenario involving planar motion.
Transcribed Image Text:The 2 kg C cuff can slide freely along the straight AB shaft. Determine the acceleration of the C cuff: a) If the shaft is fixed, b) If the A cuff fixed to the AB shaft is moving downwards at a constant speed along the vertical rod, and c) In the case of the A cuff being subjected to a downward acceleration of 2 m/s^2. In each case, assume that the cuff performs planar motion. **Diagram Explanation:** 1. **Diagram Description**: - The diagram shows an AB shaft oriented at a 45-degree angle to the vertical. - Point A is at the lower end of the vertical rod, and point B is at the upper end, inclined at a 45-degree angle. - The 2 kg C cuff is positioned on the AB shaft and can slide along its length. 2. **Provided Information**: - The AB shaft is inclined at a 45-degree angle. - The motion and acceleration of the C cuff need to be determined under three different scenarios. 3. **Scenarios Breakdown**: - **Fixed Shaft (a)**: If the AB shaft is stationary, the analysis will consider only the forces acting along the AB shaft due to the weight of the cuff. - **Constant Downward Speed (b)**: The AB shaft is moving downwards along the vertical rod at a constant speed, implying no acceleration in the vertical direction. - **Downward Acceleration (c)**: The AB shaft is accelerating downwards at 2 m/s², which will affect the relative acceleration of the C cuff along the shaft. This exercise requires applying principles of physics, specifically kinematics and dynamics, to resolve the accelerations in each scenario involving planar motion.
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