Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Question
**Q11.** A 2.6-kg collar travels down a smooth slope as shown. The spring has an unstretched length of 8 m and spring constant \( k = 31 \, \text{N/m} \), and it is always horizontal. Determine the work done by the **weight** to the collar during the process when it moves from \( s_1 = 13 \, \text{m} \) to \( s_2 = 7 \, \text{m} \). Please pay attention: the numbers may change since they are randomized. A negative sign must be included if the work done is negative. Your answer must include 1 place after the decimal point, and use the proper SI unit. Take \( g = 9.81 \, \text{m/s}^2 \). --- **Diagram Explanation:** The diagram illustrates a spring and collar mechanism. The collar is positioned on a smooth curve defined by the equation \[ y = \frac{1}{4} x^{\frac{3}{2}} \] This curve is part of a coordinate system where the horizontal axis is marked as \( x \) and the vertical as \( y \). The spring is attached horizontally from a fixed point on the vertical axis to the collar. As you follow the path, the slope of the curve decreases as you move from top to bottom. An origin, labeled \( O \), marks the starting point of the \( x \)-axis, and the length measurements are taken along this axis. Distances \( s_1 \) and \( s_2 \) are indicated, marking the initial and final positions of the collar along the curve. The diagram helps convey the physical setup required for calculating the work done by the weight of the collar as it moves along the defined path. **Your Answer:** \[ \_\_\_\_\_\_ \text{ Answer} \quad \_\_\_\_\_\_ \text{ units} \] Fill in your calculated answer with one decimal point precision.
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Transcribed Image Text:**Q11.** A 2.6-kg collar travels down a smooth slope as shown. The spring has an unstretched length of 8 m and spring constant \( k = 31 \, \text{N/m} \), and it is always horizontal. Determine the work done by the **weight** to the collar during the process when it moves from \( s_1 = 13 \, \text{m} \) to \( s_2 = 7 \, \text{m} \). Please pay attention: the numbers may change since they are randomized. A negative sign must be included if the work done is negative. Your answer must include 1 place after the decimal point, and use the proper SI unit. Take \( g = 9.81 \, \text{m/s}^2 \). --- **Diagram Explanation:** The diagram illustrates a spring and collar mechanism. The collar is positioned on a smooth curve defined by the equation \[ y = \frac{1}{4} x^{\frac{3}{2}} \] This curve is part of a coordinate system where the horizontal axis is marked as \( x \) and the vertical as \( y \). The spring is attached horizontally from a fixed point on the vertical axis to the collar. As you follow the path, the slope of the curve decreases as you move from top to bottom. An origin, labeled \( O \), marks the starting point of the \( x \)-axis, and the length measurements are taken along this axis. Distances \( s_1 \) and \( s_2 \) are indicated, marking the initial and final positions of the collar along the curve. The diagram helps convey the physical setup required for calculating the work done by the weight of the collar as it moves along the defined path. **Your Answer:** \[ \_\_\_\_\_\_ \text{ Answer} \quad \_\_\_\_\_\_ \text{ units} \] Fill in your calculated answer with one decimal point precision.
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