ENGR 216 Course Notes
ENGR 216 Engineering Mechanics: The Introduction
Course Overview
- The purpose of this course is to understand the fundamental principles of Engineering Mechanics.
- Structure of the course will cover a variety of topics relevant to engineering disciplines.
The Why of the Course
Importance of Engineering Mechanics in various engineering fields.
Past student feedback indicated disconnection between mechanics and practical applications in PHYS 218.
Efforts will be made to incorporate engineering content throughout the mechanics curriculum.
Course material is designed to be applicable across the students' entire engineering education program.
The Who of the Course
Course facilitation consists of:
- 1 Engineering instructor (the lecturer).
- A team of PTs (Peer Tutors)/GATs (Graduate Assistant Tutors).Instructor will conduct lectures while PTs/GATs will lead the labs.
Assessment and grading will be handled by the instructor in conjunction with the PTs/GATs.
Final grades will be determined at the instructor’s discretion.
The What of the Course
The course consists of:
- 6 labs that explore various aspects of engineering mechanics.
- 14 lectures covering topics that prepare students for the labs and additional engineering and analysis concepts.
The Where and When of the Course
Lectures take place in rooms ZACH 353 or ZACH 340, dependent on the course section.
Labs are conducted in ZACH 398, which contains five sub-rooms (B, D, E, F, G).
It is essential for students to attend the correct sub-room as per their registration on the Howdy portal.
The How of the Course
Assignments include:
- In-Class Work (ICW) and Homework (HW), deadlines detailed in the syllabus.
- Lab reports need to be submitted via the Morris Canvas section.Labs are conducted face-to-face in groups comprising three to four students; group assignments will change with each lab.
Important reminders include:
- Final assessment on lecture material will occur during the finals period (timing and location depend on section).
How for Labs
Significant emphasis on conducting labs with assigned groups.
- Lab reports submitted with outside group members might be subject to non-credit.Group allocations for each lab can be found on Canvas (multisection).
Labs are scheduled based on enrollment sections:
- Each lab has a bi-weekly schedule, with students attending labs every other week.
- Specific dates and rooms are available in the Canvas multisection; consistent room location will be maintained throughout the semester.Importance of distinguishing between sections ENGR 216-206 and PHYS 216-206.
Syllabus Overview
Required Equipment
Students must have either a RJ45 port or an adapter for their laptops.
Lecture 1: Descriptive Statistics
Experimental Errors
Concept of error in measurements:
- All measurements inherently contain errors, leading to uncertainty.
- Recognizing uncertainty is crucial for engineering applications, as it confines the limits of designs.
- Note: Gravity is considered constant, but enhancement in measurement techniques is always ongoing.
Definition of Error
Error is defined as the difference between a measured/calculated value and the true value.
Engineers must:
- Identify types of errors.
- Numerically express the error magnitudes.
- Establish the confidence level in printed numbers.
Precision and Accuracy
Role of precision and accuracy on experimental error:
- Being both precise and accurate reduces error, making results more representative of reality.
Causes of Experimental Errors
Reasons for errors:
1. Instruments possess inherent accuracy which may limit measurement precision.
2. Environmental factors can affect measurements (e.g., how a ball is dropped can influence speed).
Estimating Experimental Uncertainty
Regarding single measurements:
- Limited by the precision and accuracy of the instrument.
- Example: If a ruler's smallest tick is 1/8”, no measurements can be more accurate than this value.Such precision and accuracy are often specified by manufacturers or estimated by experimenters.
- Note: This course will focus on techniques beyond single measurements.
Uncertainty with Repeated Measurements
To estimate uncertainty based on multiple independent measurements, statistical methods are required.
Multiple Measurements Example
Measurement data (as units of m/s²) from 100 experiments:
- Data points include values such as:
- 9.12, 10.29, 10, 10.15, 9.64, 9.79, 10.26…
Data Processing Steps
Initial step is to plot the data visually to identify trends and distributions.
Histograms
A histogram is the preferred graphical representation for such data.
- Histograms show how values are distributed across a range defined by minimum and maximum values.
- Steps for creating a histogram:
1. Subdivide the range into equally spaced intervals (bins).
2. Count how many data points fall within each bin.
3. Graph the result with bins on the x-axis and frequency on the y-axis.
Histogram Guidelines
General rules for creating histograms:
- Use between 6 to 15 classes.
- Square root of n (where n is the number of data points) gives a rough estimate of classes.
- Ensure all data points fit into one class and ideally, intervals should be equal.
Creating Histograms with Python
Example process assumes data is in a CSV file (gVals.csv).
Code illustrates how to:
- Read data from CSV.
- Count bin frequencies.
- Generate visual plots of the histogram.
Python Code Example for Histogram Generation
Example code provided to:
1. Import necessary libraries.
2. Read in the data and process it into bins.
3. Print histogram counts and edges.
Displaying the Histogram
Further Python code details how to:
- Specify bin ranges and assign labels for output visuals.
- Show the plotted histogram with appropriate titles and labels.
Measures of Central Tendency
There are three main measures to describe the center of data sets:
1. Mean (average).
2. Median.
3. Mode.
Estimating Uncertainty with Repeated Measurements
Formula for estimating the best estimate (mean) from multiple measurements:
ar{x} = rac{x_1 + x_2 + ext{…} + x_n}{n}
- As the number of measurements (n) increases, the average becomes a more precise estimate of the true value.
Median Calculation
For an odd number of entries:
- Arrange values in order and select the middle one.Example:
- Given set: [3, 4, 9, 5, 7, 7, 5, 2, 8, 5, 5, 3, 1, 9, 2], ordered as [1, 2, 2, 3, 3, 4, 5, 5, 5, 5, 7, 7, 8, 9, 9].
Median Calculation for Even Number
For an even number of entries, the median is taken as the average of the two middle numbers in an ordered list.
Mode Definition
The mode is the value that appears most frequently in a dataset.
Measures of Variation
Variation measures describe the spread of a dataset:
- Maximum and Minimum values indicate the range.
- Variance measures the degree of spread.
- Standard Deviation quantifies variation around the mean.
Variation around the Center - Summary
Minimum and Maximum values define the spread boundary.
- Minimum: Smallest value; Maximum: Largest value in the dataset.
Population Measures of Variation
Mean and the population variance help quantify spread across a complete dataset:
- Population Variance: Derived from the squared differences from the mean:Population Standard Deviation: Indicates how data values disperse around the mean.
Sample Measures of Variation
Sample variance measures degree of spread among a subset of a population.
- Different calculations apply for small versus larger samples.
Python Statistics Module
Functions in Python to compute key statistical measures:
-mean(data),median(data),mode(data), variance calculations, min and max functions.
Python Descriptive Statistics Examples
Input example demonstrates calculations of mean, median, mode, variance, population variance, standard deviation, and identifying minimum and maximum.
Standard Error of the Mean
The mean and standard deviation help estimate the experimental error with the formula:
- This value represents the standard error of the mean.
- Detailed explanations on this topic will follow later in the course.