**Problem Description:**A puck weighing 9 lb rests in equilibrium on the frictionless surface of a ramp, held there by ropes AC and BC. The task is to determine:- The normal force the ramp exerts on the puck.- The tension in each of the two ropes.**Diagram Explanation:**The diagram shows a ramp inclined in relation to the x, y, and z coordinate axes. A puck (C) is positioned at the center of the ramp, with ropes extending from points A and B to C. The layout includes:- **Rope AC:** Extends from point A to point C on the ramp.- **Rope BC:** Extends from point B to point C.The triangle involving points A, B, and C forms the spatial setup of the ropes and ramp.**Variables and Dimensions:**The dimensions relevant to the problem are listed below. The variables correspond to different length dimensions in the setup. Note that the diagram may not be drawn to scale:- \(a = 44.0 \, \text{in}\)- \(b = 48.4 \, \text{in}\)- \(c = 24.2 \, \text{in}\)- \(d = 50.8 \, \text{in}\)- \(e = 50.6 \, \text{in}\)- \(f = 12.1 \, \text{in}\)- \(g = 71.3 \, \text{in}\)**Objective:**By analyzing these dimensions and the equilibrium conditions, calculations can be performed to find the required forces and tensions.

Given:To Find:(a) Normal force the ramp exerts on the puck.(b) Tension in each of the two ropes.

A puck weighs 9 lb and rests on the center of the frictionless surface of the ramp supported in equilibrium by ropes AC and BC. Determine the normal force the ramp exerts on the puck as well as the tension in each of the two ropes.

A puck weighs 9 lb and rests on the center of the frictionless surface of the ramp supported in equilibrium by ropes AC and BC. Determine the normal force the ramp exerts on the puck as well as the tension in each of the two ropes.

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

**Problem Description:**

A puck weighing 9 lb rests in equilibrium on the frictionless surface of a ramp, held there by ropes AC and BC. The task is to determine:
- The normal force the ramp exerts on the puck.
- The tension in each of the two ropes.

**Diagram Explanation:**

The diagram shows a ramp inclined in relation to the x, y, and z coordinate axes. A puck (C) is positioned at the center of the ramp, with ropes extending from points A and B to C. The layout includes:

- **Rope AC:** Extends from point A to point C on the ramp.
- **Rope BC:** Extends from point B to point C.

The triangle involving points A, B, and C forms the spatial setup of the ropes and ramp.

**Variables and Dimensions:**

The dimensions relevant to the problem are listed below. The variables correspond to different length dimensions in the setup. Note that the diagram may not be drawn to scale:

- \(a = 44.0 \, \text{in}\)
- \(b = 48.4 \, \text{in}\)
- \(c = 24.2 \, \text{in}\)
- \(d = 50.8 \, \text{in}\)
- \(e = 50.6 \, \text{in}\)
- \(f = 12.1 \, \text{in}\)
- \(g = 71.3 \, \text{in}\)

**Objective:**

By analyzing these dimensions and the equilibrium conditions, calculations can be performed to find the required forces and tensions.

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Step 1: Write the given data and what is to find

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Step 2: Determine the coordinates of the different points and inclination angle of the ramp:

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Step 3: Write the position vector of CA and force vector CA:

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Step 4: Write the position vector of CB and force vector CB:

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Step 5: Write the normal vector to the ramp:

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