Download Week 3

EGR 105
Foundations of Engineering I
Fall 2007 – Week 3
EGR105 – Week 3 Topics
• Project Description
• Graphing with Excel
• Assignment # 3
Bungee Jumping Project
Project goal is to demonstrate that a
proper combination of physics, math,
and engineering can successfully yield a
predictable and safe jump design.
Specifically, your team is to combine
theory with experimental measurements
to design, build, and test a small-scale
model of a bungee jump.
Initially When Jumper is at Top
• Potential energy
only is present
W = mg
center of gravity
of the jumper
Ep  mgh
h
During Free Fall
• Fall distance d,
0≤d≤L
d
• Some potential energy
is converted to kinetic,
so
E  mg h  d   2 mv
1
v = velocity
2
During Cord Stretching
• Now the cord starts to
store energy since d > L
• Energy stored in cord
equals the integral of
the cord force F
E  m g h  d   12 m v 2
d L

 F (s)ds
0
original cord length
L (without stretch)
d
stretch = d – L
At the Bottom, distance d0
• Velocity v is now zero, so
mgh  m g h  d 0  
d0  L
 F (s)ds
L
0
 mgd0 
d0  L
 F (s)ds
d0
0
• We could solve for d0 if we
knew F. So we need to
characterize bungee cord!
(next week)
v=0
Typical Models for Cords
• Linear Model (Hooke’s Law): F ( s )  ks
• More Realistic Nonlinear Model
Cubic Model: F ( s)  k1s  k 2 s 2  k3 s 3
Linear
Force F(s)
Cubic
Stretch s
Excel Plotting Techniques
• Enter or Calculate Data – Typically In Columns
• Then Employ Chart Wizard
• Plotting and Excel’s terminology:
– “Chart” (use XY scatter, not line!!)
– “Category” is the independent variable, horizontal
axis, abscissa
– “Value” is the dependent variable, vertical axis,
ordinate
• Live demo in a few minutes
Assignment # 3
•
•
•
•
•
Excel plotting assignment
Separate worksheet for each problem
Keep graphs on same sheet with data
Save as lastname_3.xls
E-mail to me as an attachment (Office
2003 file format – Please)