Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
Describe the extent to which your data indicate that mechanical energy is conserved. Consider the percentage differences in the energy changes in Data Table 2 and Data Table 3 in your answer.

Describe the extent to which your data indicate that mechanical energy is conserved. Consider the percentage differences in the energy changes in Data Table 2 and Data Table 3 in your answer.

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
See similar textbooks
icon
Related questions
Question

Describe the extent to which your data indicate that mechanical energy is conserved. Consider the percentage differences in the energy changes in Data Table 2 and Data Table 3 in your
answer.

**Data Table 3** | \( x_1 \) (m) | \( x_2 \) (m) | \( m \) (kg) | |---------------|---------------|--------------| | 0.282 | 0.750 | 0.500 | | 0.326 | 0.700 | 0.500 | | 0.374 | 0.650 | 0.500 | | 0.403 | 0.600 | 0.500 | **Calculations Table 3** | \( mg(x_2 - x_1) \) (J) | \( \frac{1}{2}k(x_2^2 - x_1^2) \) (J) | % Diff | |------------------------|--------------------------------------|--------| | 2.29 | 2.34 | 2.16% | | 1.83 | 1.86 | 1.63% | | 1.35 | 1.37 | 1.47% | | 0.97 | 0.96 | 1.04% | These tables present data and calculations related to a physics experiment involving displacement and energy. The first table, "Data Table 3," lists initial and final positions \( x_1 \) and \( x_2 \) in meters alongside a consistent mass \( m \) of 0.5 kg. The second table, "Calculations Table 3," shows the computed energy using potential energy and kinetic energy equations, along with the percentage difference between the two energy calculations. This analysis helps understand the energy dynamics in a physical system.
Transcribed Image Text:**Data Table 3** | \( x_1 \) (m) | \( x_2 \) (m) | \( m \) (kg) | |---------------|---------------|--------------| | 0.282 | 0.750 | 0.500 | | 0.326 | 0.700 | 0.500 | | 0.374 | 0.650 | 0.500 | | 0.403 | 0.600 | 0.500 | **Calculations Table 3** | \( mg(x_2 - x_1) \) (J) | \( \frac{1}{2}k(x_2^2 - x_1^2) \) (J) | % Diff | |------------------------|--------------------------------------|--------| | 2.29 | 2.34 | 2.16% | | 1.83 | 1.86 | 1.63% | | 1.35 | 1.37 | 1.47% | | 0.97 | 0.96 | 1.04% | These tables present data and calculations related to a physics experiment involving displacement and energy. The first table, "Data Table 3," lists initial and final positions \( x_1 \) and \( x_2 \) in meters alongside a consistent mass \( m \) of 0.5 kg. The second table, "Calculations Table 3," shows the computed energy using potential energy and kinetic energy equations, along with the percentage difference between the two energy calculations. This analysis helps understand the energy dynamics in a physical system.
### Data Table 2 | \( x_1 \) (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 | \( mg \, (x_2 - x_1) \) (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% | ### Explanation - **Data Table 2:** - Contains measurements of initial and final positions (\( x_1 \) and \( x_2 \)) in meters, and mass (\( m \)) in kilograms for a series of experiments. - **Calculations Table 2:** - Shows calculations of gravitational potential energy differences (\( mg \, (x_2 - x_1) \)) and elastic potential energy differences (\( \frac{1}{2}k \, (x_2^2 - x_1^2) \)), both in joules. - "% Diff" indicates the percentage difference between the two energy calculations, providing insight into the consistency or experimental error.
Transcribed Image Text:### Data Table 2 | \( x_1 \) (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 | \( mg \, (x_2 - x_1) \) (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% | ### Explanation - **Data Table 2:** - Contains measurements of initial and final positions (\( x_1 \) and \( x_2 \)) in meters, and mass (\( m \)) in kilograms for a series of experiments. - **Calculations Table 2:** - Shows calculations of gravitational potential energy differences (\( mg \, (x_2 - x_1) \)) and elastic potential energy differences (\( \frac{1}{2}k \, (x_2^2 - x_1^2) \)), both in joules. - "% Diff" indicates the percentage difference between the two energy calculations, providing insight into the consistency or experimental error.
Expert Solution
steps

Step by step

Solved in 4 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Engineering Drawing
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS