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 12 Lecture
Circular Motion
• This week we will:
• Study the response of a system subjected to
uniform circular motion
Problem A: Theoretical analysis of motion of a body in uniform circular motion
Problem B: Experimental analysis of uniform circular motion
• Use a video capture system to acquire data and Matlab to
simulate system
iCLICKER:
Which assumption is incorrect when analyzing this
week’s system?
• Select your Answer:
A.
B.
C.
D.
Mass of rod = 0
Mass of bob = constant
Acceleration = 0
Friction force = 0
iCLICKER:
Which assumption is incorrect when analyzing this
week’s system?
• Select your Answer:
A.
B.
C.
D.
Mass of rod = 0
Mass of bob = constant
Acceleration = 0
Friction force = 0
FORMULATE: Problem A: State the Known and Desired Information
FORMULATE: Identify Assumptions
iCLICKER:
Which of the following statements is CORRECT with
respect to the Bob mass?
• Select your Answer:
A.
B.
C.
D.
The velocity is directed radially inward
The velocity is directed radially outward
The acceleration is directed radially inward
The acceleration is directed radially outward
iCLICKER:
Which of the following statements is CORRECT with
respect to the Bob mass?
• Select your Answer:
A.
B.
C.
D.
The velocity is directed radially inward
The velocity is directed radially outward
The acceleration is directed radially inward
The acceleration is directed radially outward
CHART: Schematic Diagram
CHART: Schematic Diagram
CHART: Velocity Vector Diagram
CHART: Acceleration Vector Diagram
EXECUTE: Calculate the Acceleration Components
By taking the first derivative of the Velocity components with
respect to time we determine the acceleration components.
iCLICKER:
Which of the following statements is CORRECT with
respect to the centripetal acceleration?
• Select your Answer:
A.
B.
C.
D.
It is directly related to the distance R
It is inversely related to the distance R
It is directly related to the velocity v
It is inversely related to the velocity v
iCLICKER:
Which of the following statements is CORRECT with
respect to the centripetal acceleration?
• Select your Answer:
A.
B.
C.
D.
It is directly related to the distance R
It is inversely related to the distance R
It is directly related to the velocity v
It is inversely related to the velocity v
EXECUTE: Calculate the “Centripetal” Acceleration
Note that the acceleration is constant with respect to time
since x2(t) + y2(t) = R2 !
This acceleration is a result of the changing direction of
motion, and is referenced as the “Centripetal Acceleration”.
FORMULATE: Problem B: State the Known and Desired Information
FORMULATE: Identify Assumptions
B.
Also neglect all Frictional effects associated with the bearing
in the armature and pendulum.
CHART: Picture of Test Set-Up – Side View
CHART: Picture of Test Set-Up – Top View
CHART: Schematic Diagram – Side View with Parameters Identified
CHART: Schematic Diagram – Side View with Displacement Angle
CHART: Schematic Diagram – Top View with Displacement Angle
We need to make sure we account for “perceived” side view
distances of the Armature length and the pendulum rod length!
CHART: Lab Set-Up with Parameters Identified
iCLICKER:
When analyzing the FBD of the Bob mass, how many
forces are acting on it?
• Select your Answer:
A.
B.
C.
D.
1
2
3
4
iCLICKER:
When analyzing the FBD of the Bob mass, how many
forces are acting on it?
• Select your Answer:
A.
B.
C.
D.
1
2
3
4
CHART: Free Body Diagram of the Bob
The Bob mass has 2 Forces acting on it - The Weight and the
Tension force in the pendulum rod.
The system achieves a form of Equilibrium when subjected to a
uniform circular motion.
Execute: Derive Equations
Using Newton’s 2nd Law we sum forces in both the “radial” and “z”
directions:
We observe that the angular displacement q is a constant when the
armature is revolved at a constant angular speed. This implies that there
is no acceleration in the z direction.
Execute: Derive Equations
Substituting the relationship for “T” from our analysis in the z-direction
gives:
Equation 12.45 provides us with a convenient experimental means to
measure the centripetal acceleration of our system.
Test: Comparing Theoretical to Experimental Acceleration Values
Equations 12.24 and 12.45 provide us with relationships to determine the
theoretical and experimental centripetal acceleration values.
Recall that the distance from the orign to the center of the mass of the
Bob is given by:
Test: Comparing Theoretical to Experimental Acceleration Values
In-Class problem ……
• A 3 [kg] rock is attached to a massless rope and swings in
a circle of diameter 10 [m]. The rope can withstand a
tensile force up to 40 [N] before breaking.
If the rock has a constant speed of 8 m/s, calculate the
A) Centripetal acceleration [m/s2]
B) Corresponding centripetal force [N] in the rope
C) Will the rope break?
In-Class problem ……
• A 3 [kg] rock is attached to a massless rope and swings in
a circle of diameter 10 [m]. The rope can withstand a
tensile force up to 40 [N] before breaking.
If the rock has a constant speed of 8 m/s, calculate the
A) Centripetal acceleration = 12.8 [m/s2]
B) Corresponding centripetal force = 38.4 [N] in the rope
C) Will the rope break? No since Fcent < Fmax
Homework
• Pendulum Lab Report due tonight!
• Prior to LAB tomorrow
• Read section 12.2 of the textbook
• Watch LAB Videos
• Complete the on-line LAB quiz in myCourses
• Attempt to solve all assigned Homework problems in your
logbook before RECITATION.
• WEEK 12 Problem Set:
• From Section 12.5: Problems 1, 2, 4