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3. Examine your data in Data Table 2 and in Data Table 3. For the data with the smallest percentage difference, compare the total energy at each point. Calculate the sum U₁+U₂ at x₁ as ½kx-mgx₁. Calculate that sum at x₂ as ½kx2-mgx₂. Do you expect them to agree reasonably well? Explain why they should or should not be the same. 4. Consider the same data as used in Question 3. Calculate the value of x halfway between x₁ and x₂. Calculate U₁+Ug = ½kx² - mgx for that point. Do you expect them to agree with the energy calculated in Question 3? If they agree reasonably well, explain why they do. If they do not agree, explain why they do not agree.

3. Examine your data in Data Table 2 and in Data Table 3. For the data with the smallest percentage difference, compare the total energy at each point. Calculate the sum U₁+U₂ at x₁ as ½kx-mgx₁. Calculate that sum at x₂ as ½kx2-mgx₂. Do you expect them to agree reasonably well? Explain why they should or should not be the same. 4. Consider the same data as used in Question 3. Calculate the value of x halfway between x₁ and x₂. Calculate U₁+Ug = ½kx² - mgx for that point. Do you expect them to agree with the energy calculated in Question 3? If they agree reasonably well, explain why they do. If they do not agree, explain why they do not agree.

Elements Of Electromagnetics
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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Certainly! Here is the transcription of the image for an educational website: --- 3. Examine your data in Data Table 2 and in Data Table 3. For the data with the smallest percentage difference, compare the total energy at each point. Calculate the sum \( U_k + U_g \) at \( x_1 \) as \( \frac{1}{2}kx_1^2 - mgx_1 \). Calculate that sum at \( x_2 \) as \( \frac{1}{2}kx_2^2 - mgx_2 \). Do you expect them to agree reasonably well? Explain why they should or should not be the same. 4. Consider the same data as used in Question 3. Calculate the value of \( x \) halfway between \( x_1 \) and \( x_2 \). Calculate \( U_k + U_g = \frac{1}{2}kx^2 - mgx \) for that point. Do you expect them to agree with the energy calculated in Question 3? If they agree reasonably well, explain why they do. If they do not agree, explain why they do not agree. --- No graphs or diagrams are present in the image.
Transcribed Image Text:Certainly! Here is the transcription of the image for an educational website: --- 3. Examine your data in Data Table 2 and in Data Table 3. For the data with the smallest percentage difference, compare the total energy at each point. Calculate the sum \( U_k + U_g \) at \( x_1 \) as \( \frac{1}{2}kx_1^2 - mgx_1 \). Calculate that sum at \( x_2 \) as \( \frac{1}{2}kx_2^2 - mgx_2 \). Do you expect them to agree reasonably well? Explain why they should or should not be the same. 4. Consider the same data as used in Question 3. Calculate the value of \( x \) halfway between \( x_1 \) and \( x_2 \). Calculate \( U_k + U_g = \frac{1}{2}kx^2 - mgx \) for that point. Do you expect them to agree with the energy calculated in Question 3? If they agree reasonably well, explain why they do. If they do not agree, explain why they do not agree. --- No graphs or diagrams are present in the image.
### Data Table 2 This table presents initial and final positions of an object, along with its mass. | \( x_1 \) (m) | \( x_2 \) (m) | \( m \) (kg) | |---------------|---------------|--------------| | 0.2500 | 0.745 | 0.5000 | | 0.3000 | 0.700 | 0.5000 | | 0.3500 | 0.655 | 0.5000 | | 0.4000 | 0.602 | 0.5000 | ### Calculations Table 2 This table shows calculations of work done by gravity and elastic potential energy, along with their percentage difference. | \( mg (x_2 - x_1) \) (J) | \( \frac{1}{2}k (x_2^2 - x_1^2) \) (J) | % Diff | |---------------------------|---------------------------------------|---------| | 2.43 | 2.40 | 1.24% | | 1.96 | 1.94 | 1.03% | | 1.49 | 1.48 | 0.67% | | 0.99 | 0.98 | 1.02% | ### Data Table 3 This table documents a second set of initial and final positions, with the same mass as in Data Table 2. | \( x_1 \) (m) | \( x_2 \) (m) | \( m \) (kg) | |---------------|---------------|--------------| | 0.282 | 0.750 | 0.5000 | | 0.326 | 0.700 | 0.5000 | | 0.374 | 0.650 | 0.5000 | | 0.403 | 0.600 | 0.5000 | ### Calculations Table 3 This table provides another set of work and energy calculations along with their percentage differences. | \( mg (x_2 - x_1) \) (J) | \( \frac{1}{
Transcribed Image Text:### Data Table 2 This table presents initial and final positions of an object, along with its mass. | \( x_1 \) (m) | \( x_2 \) (m) | \( m \) (kg) | |---------------|---------------|--------------| | 0.2500 | 0.745 | 0.5000 | | 0.3000 | 0.700 | 0.5000 | | 0.3500 | 0.655 | 0.5000 | | 0.4000 | 0.602 | 0.5000 | ### Calculations Table 2 This table shows calculations of work done by gravity and elastic potential energy, along with their percentage difference. | \( mg (x_2 - x_1) \) (J) | \( \frac{1}{2}k (x_2^2 - x_1^2) \) (J) | % Diff | |---------------------------|---------------------------------------|---------| | 2.43 | 2.40 | 1.24% | | 1.96 | 1.94 | 1.03% | | 1.49 | 1.48 | 0.67% | | 0.99 | 0.98 | 1.02% | ### Data Table 3 This table documents a second set of initial and final positions, with the same mass as in Data Table 2. | \( x_1 \) (m) | \( x_2 \) (m) | \( m \) (kg) | |---------------|---------------|--------------| | 0.282 | 0.750 | 0.5000 | | 0.326 | 0.700 | 0.5000 | | 0.374 | 0.650 | 0.5000 | | 0.403 | 0.600 | 0.5000 | ### Calculations Table 3 This table provides another set of work and energy calculations along with their percentage differences. | \( mg (x_2 - x_1) \) (J) | \( \frac{1}{
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