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
MECE-102 Course Grades
Exam #1 Performance:
Average Grade = 70%
Max Grade = 100%
Week 7 Lecture
Impulse and Momentum
• We will study:
• the impact of two carts moving along a horizontal path
• the tradeoff between Impulse and Momentum that occurs during
the impact of the carts
• We will be using the Ultrasonic Transducer to determine
distances travelled, velocities and momentums of the
moving carts.
iCLICKER:
The week 7 Lab Experiment studies the relationship
between Impulse and Momentum of a system. Which
one of the following is the definition of Impulse?
• Select your Answer:
A.
B.
C.
D.
E.
The distance integral of force.
The time integral of force.
The time derivative of acceleration.
The time derivative of velocity.
None of the above.
iCLICKER:
The week 7 Lab Experiment studies the relationship
between Impulse and Momentum of a system. Which
one of the following is the definition of Impulse?
• Select your Answer:
A.
B.
C.
D.
E.
The distance integral of force.
The time integral of force.
The time derivative of acceleration.
The time derivative of velocity.
None of the above.
iCLICKER:
Which of the following are units of Impulse?
• Select your Answer:
A.
B.
C.
D.
E.
[kg m/s]
[kg m/s2]
[N s]
[N m]
None of the above
iCLICKER:
Which of the following are units of Impulse?
• Select your Answer:
A.
B.
C.
D.
E.
[kg m/s]
[kg m/s2]
[N s]
[N m]
None of the above
FORMULATE: State the Known Information
• Determine the speed of a vehicle with mass m1 after its
collision and attachment to a vehicle of mass m2.
• Estimate the work done during the collision process by
comparing the theoretical speed versus the observed
speed of the combined vehicles, m1 + m2 .
FORMULATE: Identify the Desired Information
iCLICKER:
For our Week 7 experiment, which one of the
following assumptions is FALSE?
• Select your Answer:
A.
B.
C.
D.
E.
Air resistance is negligible.
Friction force is negligible.
Mass of the system being analyzed is constant.
Heat Transfer between the vehicles and track is negligible.
Elastic Spring Energy is negligible.
iCLICKER:
For our Week 7 experiment, which one of the
following assumptions is FALSE?
• Select your Answer:
A.
B.
C.
D.
E.
Air resistance is negligible.
Friction force is negligible.
Mass of the system being analyzed is constant.
Heat Transfer between the vehicles and track is negligible.
Elastic Spring Energy is negligible.
FORMULATE: Identify Assumptions
CHART: Schematic
Diagram
Figure 7.1: Schematic Diagram of a first car colliding with
and attaching to a second cart.
CHART: Free Body Diagrams
CHART: Data Tables
• Each row in the STATE TABLE corresponds to one unique position as
the cart moves along the track.
• This Lab Experiment will analyze the impact of the two carts along a
horizontal surface where we define our elevation datum, z = 0.
CHART: Data Tables
• The PROCESS Table describes the exchange of energy, work, heat,
Impulse and Momentum as the system moves between states.
• For this experiment we are interested in the Impact “Process” which
takes place starting at an initial state, i , and ending at a final state, f .
EXECUTE: Recall the Governing Equations
EXECUTE: Recall the Governing Equations
Newton’s 2nd Law states the “The net external force acting upon a body is
equal to the time rate of change of the linear momentum of the body.”
Separating the differential and integrating between an initial time, ti , and
a final time, tf gives:
EXECUTE: Recall the Governing Equations
Recall that Impulse is defined as “The integral of force over
time.”
This generalized version of Newton’s 2nd Law allows us to
predict the motion of a system of interacting bodies.
iCLICKER:
Based on the concepts of Impulse and Momentum
from Week 7, we should expect that the velocity of
cart 1 just prior to impact will be greater than the
velocity of the combined carts after impact.
• Select your Answer:
A. True
B. False
iCLICKER:
Based on the concepts of Impulse and Momentum
from Week 7, we should expect that the velocity of
cart 1 just prior to impact will be greater than the
velocity of the combined carts after impact.
• Select your Answer:
A. True
B. False
EXECUTE: Recall the Governing Equations
Analysis of the cart FBD’s confirms that action and reaction
forces between the 2 carts are equal and opposite
(Newton’s 3rd Law). Applying the previous Assumptions to the
analysis generates the following equations:
EXECUTE: Recall the Governing Equations
Analysis of the Momentum equations associated with the
initial mass m1 and the final combined mass (m1+ m2) gives:
Solving for the final velocity of the combined mass (m1+ m2)
gives:
Consider the following Problem ………
Consider the following Problem ………
Given a cart with initial mass, m1 , determine the mass, m2 , of a
second cart that generates a final velocity, Vf , of the combined
𝟏
masses (m1+ m2) equal to of the initial velocity, Vi .
𝟖
Consider the following Problem ………
Given a cart with initial mass, m1 , determine the mass, m2 , of a
second cart that generates a final velocity, Vf , of the combined
𝟏
masses (m1+ m2) equal to of the initial velocity, Vi .
𝟖
Answer: m2 = 7m1
Lab Experiment Set-up
Figure 7.3: Apparatus and two body impact within the field of view
of an ultrasonic transducer
Now let’s talk about Asteroids …
http://news.cnet.com/8301-11386_3-57564621-76/europes-space-agency-kicks-offasteroid-collision-mission/
Homework
• Prior to LAB tomorrow
• Read section 7.2 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 7 Problem Set:
• From Section 7.5: Problems 1, 10, 17, 18, 19
• Lab Report is due Monday by 6pm!
• The Scribe must upload the LAB REPORT to the myCourses Dropbox.
Questions?
Consider the following Problem ………
Given a cart with initial mass, m1 , determine the mass, m2 , of a
second cart that generates a final velocity, Vf , of the combined
𝟏
masses (m1+ m2) equal to of the initial velocity, Vi .
𝟒
Consider the following Problem ………
Given a cart with initial mass, m1 , determine the mass, m2 , of a
second cart that generates a final velocity, Vf , of the combined
𝟏
masses (m1+ m2) equal to of the initial velocity, Vi .
𝟒
Answer: m2 = 3m1