MECE 102: Engineering Mechanics Lab
A First Year Course in
Newtonian Mechanics, Experimentation,
and Computer Tools
Created by the Faculty of the Mechanical Engineering
Department in the Kate Gleason College of Engineering at RIT
Week 2 Lecture
Newton’s Law of Gravity
• We will study the motion of a single body of mass m in
free-fall due to gravity.
• The Ultrasonic Transducer calibration data from week 1
will be used to convert “voltage” to “distance”.
Q1. Sir Isaac Newton’s “Principa” developed a strong
theoretical foundation governing the motion of
bodies in which year?
• Select your Answer:
A. 1687
B. 1768
C. 1812
D. 1876
E. 1971
Q1. Sir Isaac Newton’s “Principa” developed a strong
theoretical foundation governing the motion of
bodies in which year?
• Select your Answer:
A. 1687
B. 1768
C. 1812
D. 1876
E. 1971
Q2. Which one of the following is the normally
reported value for the acceleration due to gravity
near the Earth’s surface?
• Select your Answer:
A. 32.2 m/s2
B. 9.81 ft/s2
C. 1.6 m/s2
D. 3.8 m/s2
E. 9.81 m/s2
Q2. Which one of the following is the normally
reported value for the acceleration due to gravity
near the Earth’s surface?
• Select your Answer:
A. 32.2 m/s2
B. 9.81 ft/s2
C. 1.6 m/s2  acceleration due to gravity on Moon
D. 3.8 m/s2  acceleration due to gravity on Mars
E. 9.81 m/s2
Q3. What is the acronym for the Problem Solving
Approach we will be using in this class, and future
ME classes?
• Select your Answer:
A. S.O.L.U.T.I.O.N.
B. A.N.S.W.E.R.
C. F.A.C.E.T.
D. R.E.S.U.L.T.
E. E.D.G.E.
FACET Problem Solving Method
Recall from Recitation and ch. 1.4.2 the problem
solving method we will be using in class:
• Formulate
• Assume
• Chart
• Execute
• Test
Formulate  State the Problem
The following information is provided:
m =  [kg]
Mass of Dead Weight (Constant)
g = 9.81 [m/s2]
Standard value of gravitational acceleration
W = mg [N]
Gravitational Force Upon mass m (Constant)
We use the symbol  to indicate that the quantity is known prior to the start of
the problem solving method.
State the Desired Information
Upon conclusion of the experiment and analysis, we shall be required to report:
𝑔 ≈ 𝑎𝑧 𝑡 = ?⊘ [m/s2] Vertical acceleration of m vs time
We use the symbol ⊘ to indicate that this quantity is unknown, and it's value
must be determined as a result of the problem solving method.
NOTE:
We will report the estimate of the local acceleration of gravity, 𝒈, as being equal
to time average of the object's vertical acceleration during free-fall.
Assume  Identify Assumptions
The following assumptions may be employed during the analysis.
m = Constant [kg] ⊕
z = 0 Origin measured from initial position of mass [m] ⊕
|V (t = 0) | = 0 Mass initially at rest [m/s] ⊕
We use the symbol ⊕ to indicate that this fact is assumed to be true.
NOTE:
We need top justify each assumption used in our analysis.
Chart Schematic Diagram
• Conveys information, identifies all bodies in the System, establishes
sign conventions, and sets up nomenclature for a problem.
• We are interested in figuring out what happens next.
Figure 2.1: Schematic Diagram of a Ball in the proximity of the Earth.
Chart Free Body Diagram
Every time we draw a Free Body Diagram (FBD) in this course, we must
insure that every force appears in two separate FBDs.
Figure 2.2: Free Body Diagrams for a Ball and the Earth.
Q4. If we do not show each force in two, and only two,
FBDs then we have violated which law?
Select your Answer:
A. Conservation of Energy
B. Newton’s 1st Law
C. Newton’s 2nd Law
D. Newton’s 3rd Law
Q4. If we do not show each force in two, and only two,
FBDs then we have violated which law?
Select your Answer:
A. Conservation of Energy
B. Newton’s 1st Law
C. Newton’s 2nd Law
D. Newton’s 3rd Law
Chart  Free-Body Diagram
Your Free-Body Diagrams (FBD’s) should address these key elements:
1. Clearly identify and label all FORCES acting on the system
2. Clearly identify all relevant DIMENSIONS
(ie. lengths, angles, etc) with appropriate SYMBOLS, and a consistent set of UNITS
when solving for unknowns.
3.
Clearly identify the COORDINATE SYSTEM used in your analysis
Q4. From the time the ball is released to the instant
before impacting the floor, which of the following
relationships is correct between Kinetic Energy (KE)
and Potential Energy (PE) of the ball?
• Select your Answer:
A. KE will increase and PE will increase
B. KE will decrease and PE will increase
C. KE will increase and PE will decrease
D. KE will decrease and PE will decrease
Q4. From the time the ball is released to the instant
before impacting the floor, which of the following
relationships is correct between Kinetic Energy (KE)
and Potential Energy (PE) of the ball?
• Select your Answer:
A. KE will increase and PE will increase
B. KE will decrease and PE will increase
C. KE will increase and PE will decrease
D. KE will decrease and PE will decrease
Execute Equations for Position,
Velocity, and Acceleration
We hypothesize that the vertical Position, z (t), of the object may be
approximated as a third order polynomial function of time:
𝑧 𝑡 ≈ 𝑐0 + 𝑐1 𝑡 + 𝑐2 𝑡 2 + 𝑐3 𝑡 3
The vertical velocity, vz (t), of the object is defined as the change in the
vertical position during a small interval of time
(1st derivative of Position):
Execute Equations for Position,
Velocity, and Acceleration
By substituting our polynomial Position approximation into the
Velocity limit equation it can be shown that:
Recall that the definition of vertical acceleration, az (t), of the object is
defined as the change in the vertical velocity during a small interval of
time (2nd derivative of Position):
Execute Equations for Position,
Velocity, and Acceleration
By substituting our Velocity approximation into the Acceleration limit
equation it can be shown that:
6
The coefficient c2 [m/s2] is equal to ½ the initial acceleration of the
object.
The coefficient c3 [m/s3] is related to the initial “jerk” of the object.
Iterate Conduct Multiple Trials
Trial #1
Trial #2
Trial #3
Trial #4
• We will be using Experimental Modeling that focuses
on understanding physical phenomena, in this case the
acceleration due to gravity.
• We will be acquiring data (Measurements) which will
be analyzed to determine the numerical value of the
acceleration due to gravity.
Week 2 Ball Drop Experimental Equipment
Week 2 Ball Drop Experimental Apparatus
Week 2 Ball Drop LABView Screenshot
Homework
• Prior to LAB tomorrow
• Read section 2.2 of the textbook
• Watch LAB Videos
• Complete the on-line LAB quiz in myCourses
• Attempt to solve all assigned chapter problems in your
logbook before RECITATION.
• WEEK 2 Problem Set:
• From Section 2.5: Problems 1, 3, 13, 16, 17, 20, 21
• Lab Report #1 is due Monday by 6pm!
• The Scribe must upload the LAB REPORT to the myCourses
Lab Report #1 Dropbox by 6pm tonight!
Questions?