The frame is made from uniform rod which has a mass p per unit length. A smooth recessed slot constrains the small rollers at A an to travel horizontally. Force P is applied to the frame through a cable attached to an adjustable collar C. Determine the magnitudes directions of the normal forces which act on the rollers if (a) h = 0.25L, (b) h = 0.50L, and (c) h = 0.83L. The forces will be positive if u negative if down. Evaluate your results for p = 1.1 kg/m, L = 370 mm, and P = 45 N. What is the acceleration of the frame in each ca L L P

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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**Problem Statement:**

The frame is constructed from a uniform rod with mass \(\rho\) per unit length. It is designed to travel horizontally, constrained by small rollers at points \(A\) and \(B\) in a smooth recessed slot. A force \(P\) is applied to the frame through a cable connected to an adjustable collar \(C\). The task is to determine the magnitudes and directions of the normal forces acting on the rollers for different values of \(h\) (the vertical distance from \(C\) to the upper part of the frame):

- \((a) \, h = 0.25L\)
- \((b) \, h = 0.50L\)
- \((c) \, h = 0.83L\)

Positive forces are directed upwards, and negative forces are directed downwards. Evaluate the results using these parameters: \(\rho = 1.1 \, \text{kg/m}, \, L = 370 \, \text{mm}, \, \text{and} \, P = 45 \, \text{N}\). Determine the acceleration of the frame in each case.

**Diagram Explanation:**

The diagram illustrates a square frame with side length \(L\) mounted horizontally. The force \(P\) is applied to the right. The adjustable collar \(C\) is shown on the top horizontal member of the frame, indicating the distance \(h\) from \(C\) to the frame. Rollers at \(A\) and \(B\) keep the frame in position, allowing horizontal movement.

**Answers:**

- For each scenario \((a)\), \((b)\), and \((c)\), calculate:

  - The normal force at roller \(A\) \((N_A)\).
  - The normal force at roller \(B\) \((N_B)\).
  - The acceleration of the frame \((a)\) in \(\text{m/s}^2\).

The table is structured with sections for each scenario, allowing input of calculated values for \(N_A\), \(N_B\), and \(a\) for each given \(h\).
Transcribed Image Text:**Problem Statement:** The frame is constructed from a uniform rod with mass \(\rho\) per unit length. It is designed to travel horizontally, constrained by small rollers at points \(A\) and \(B\) in a smooth recessed slot. A force \(P\) is applied to the frame through a cable connected to an adjustable collar \(C\). The task is to determine the magnitudes and directions of the normal forces acting on the rollers for different values of \(h\) (the vertical distance from \(C\) to the upper part of the frame): - \((a) \, h = 0.25L\) - \((b) \, h = 0.50L\) - \((c) \, h = 0.83L\) Positive forces are directed upwards, and negative forces are directed downwards. Evaluate the results using these parameters: \(\rho = 1.1 \, \text{kg/m}, \, L = 370 \, \text{mm}, \, \text{and} \, P = 45 \, \text{N}\). Determine the acceleration of the frame in each case. **Diagram Explanation:** The diagram illustrates a square frame with side length \(L\) mounted horizontally. The force \(P\) is applied to the right. The adjustable collar \(C\) is shown on the top horizontal member of the frame, indicating the distance \(h\) from \(C\) to the frame. Rollers at \(A\) and \(B\) keep the frame in position, allowing horizontal movement. **Answers:** - For each scenario \((a)\), \((b)\), and \((c)\), calculate: - The normal force at roller \(A\) \((N_A)\). - The normal force at roller \(B\) \((N_B)\). - The acceleration of the frame \((a)\) in \(\text{m/s}^2\). The table is structured with sections for each scenario, allowing input of calculated values for \(N_A\), \(N_B\), and \(a\) for each given \(h\).
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