projectile motion with air drag
DESCRIPTION
Projectile Motion with air drag. A Computer Lab for Calculus Based Physics Dr. Richard Taylor Department of Physics & Engineering Muskingum University. www.muskingum.edu/~richardt. Overview. Developing an Algorithm Kinematics Dynamics Algorithm Implementing the Algorithm MATLAB Excel - PowerPoint PPT PresentationTRANSCRIPT
PROJECTILE MOTION WITH AIR DRAGA Computer Lab for Calculus Based Physics
Dr. Richard Taylor
Department of Physics & Engineering
Muskingum University
www.muskingum.edu/~richardt
Overview• Developing an Algorithm
• Kinematics• Dynamics• Algorithm
• Implementing the Algorithm• MATLAB• Excel
• Calibrating the Program• Digitizing Real Data• Applying the Program
• Determine the Initial Velocity• Turn Air Drag Off for Comparison
Developing an Algorithm:Kinematics
21 , ,
, 1 , ,
21 , ,
, 1 , ,
1
2
1
2
i i x i x i
x i x i x i
i i y i y i
y i y i y i
x x v t a t
v v a t
y y v t a t
v v a t
1 ,
, 1 , ,
1 ,
, 1 , ,
i i x i
x i x i x i
i i y i
y i y i y i
x x v t
v v a t
y y v t
v v a t
Air drag is a variable force.Therefore, acceleration is not constant!But…If the time interval is small, thenacceleration can be treated as a constant.
Developing an Algorithm:Dynamics
2dragF Bv
1
2B C A
2 2,
2 2,
cos
sin
xdrag x x
ydrag y y
vF Bv Bv Bvv
vv
F Bv Bv Bvvv
0x
y
g
g
F
F mg
,
,
x x
y y
net drag x g xx
net drag y g yy
F F F Bvva
m m mF F F Bvv mg
am m m
Developing an Algorithm:Algorithm
1 ,
,, 1 ,
1 ,
,, 1 ,
2 2, ,
i i x i
x ix i x i
i i y i
y iy i y i
x i y i
x x v t
Bvvv v t
my y v t
Bvv mgv v t
m
v v v
Constants & Initial Values
Implementing the Algorithm:MATLAB
Implementing the Algorithm:Excel
Calibrating the Program
Find the range for the no air drag problem by hand.Find the range using the program.Reduce the time interval in the program until the ranges agree.
0 2 4 6 8 10 12-0.5
0
0.5
1
1.5
2
2.5
3
x (m)
y (m
)
Trajectory
Digitizing Real Data
Applying the Program:Determine the Launch Speed
0 0.5 1 1.5 2 2.5-0.2
0
0.2
0.4
0.6
0.8
1
1.2
x (m)
y (m
)
Trajectory
0 0.2 0.4 0.6 0.8 1 1.2 1.4-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
x (m)
y (m
)
Trajectory
Adjust the launch speed in the program until the two curves overlap.
Applying the Program:Turn Air Drag Off for Comparison
0 0.5 1 1.5 2 2.5 3-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x (m)
y (m
)Trajectory
Materials can be downloaded fromwww.muskingum.edu/~richardt/aapt2013