The College at Brockport: State University of New York
Digital Commons @Brockport
Lesson Plans
CMST Institute
3-1-2005
Using a Ballistic Pendulum to Determine Muzzle
Velocity of a Marble Launcher
Steve Whitman
The College at Brockport, [email protected]
Follow this and additional works at: http://digitalcommons.brockport.edu/cmst_lessonplans
Part of the Physical Sciences and Mathematics Commons
Recommended Citation
Whitman, Steve, "Using a Ballistic Pendulum to Determine Muzzle Velocity of a Marble Launcher" (2005). Lesson Plans. Paper 311.
http://digitalcommons.brockport.edu/cmst_lessonplans/311
This Lesson Plan is brought to you for free and open access by the CMST Institute at Digital Commons @Brockport. It has been accepted for inclusion
in Lesson Plans by an authorized administrator of Digital Commons @Brockport. For more information, please contact [email protected].
BHS Physics
LAB #12
•BALLISTIC
PENDULUM
BHS Physics
GOALS
• TO USE A BALLISTIC PENDULUM TO
DETERMINE MUZZLE VELOCITY OF A
MARBLE LAUNCHER
• TO DETERMINE THE KE LOST IN THE
COLLISION
• TO SIMULATE A BALLISTIC PENDULUM
AND COMPARE RESULTS.
BHS Physics
PROCEDURE
• SHOOT THE PROJECTILE INTO THE BALLISTIC
PENDULUM WITH PHOTOGATE TIMER IN
PLACE
• MEASURE THE MAXIMUM ANGLE OF
DEFLECTION OF THE PENDULUM
• RECORD PHOTOGATE TIME TO DETERMINE V
PHOTO
• REPEAT FOR ALL FIVE NOTCHES OF THE
LAUNCHER
• BUILD AN I.P. BALLISTIC PENDULUM
• REPEAT THE EXPERIMENT WITH THE VIRTUAL
PENDULUM
• COMPARE RESULTS FOR EACH
BHS Physics
Ballistic Pendulum
At Impact
Before Impact
At Highest Swing
Θ
Vo = ?
m
M
V
Vo
Po = Pf
mvo = (M+m) V
∆h
KE lost = PE gain
½(M+m)V2 = (M+m) g∆h
BHS Physics
Ballistic Pendulum Equation
2
mvo = (M+m) V ½(M+m)V = (M+m) g∆h
vo = (M+m) V
m
vo = (M+m)
m
V2
V=
= 2g∆h
2g∆h
2g∆h
BHS Physics
Determine ∆h from Θ
At Highest Swing
L = length of pend
(pivot to center of bob)
L Θ Y
∆h = L - Y
Y = L cos Θ
∆h
∆h = L - L cos Θ
BHS Physics
DATA TABLE 1
I
I
!SAMPLE DATA TABLE: (REAL BALLISTIC PENDULUM)
I
I
!CONSTANTS:
NOTCH
1
2
3
4
5
ti.~
M (kg) = 0.077
V Photo
®MAX
-
m (kg) = 0.028
COS®
L COS®
I
r--
Ah (m)
I
I
L (m) = 0.65
Vf lm/sl
I
I
I
I
I
I
I
I
I
I
I
dia (m) = 0.019
Pf= Po
Vo lm/sl
Vo dev
BHS Physics
DATA TABLE 2
I
I
!SAMPLE DATA TABLE: (I.P. BALLISTIC PENDULUM)
I
I
I
!CONSTANTS:
TRIAL
1
2
,1-
3
4
5
I.P.Vo
I
m (kg)=
M (kg)=
®MAX
COS®
L COS®
I
J
L (m) =
Ah (m)
Vf
I
1
Pf= Po
Vo fm/sl
I
Vo dev
.
-
BHS Physics
K.E. ANALYSIS
I
I
I
!SAMPLE DATA TABLE: (REAl BAlliSTIC PENDULUM)
I
I
I
-
!CONSTANTS:
M (kg)=
TRIAl
KE MARBLE (J} KE CATCHER (J}
1
~
-
m (kg)=
I
KE lOST (Jl
%KE lOST
2
-
~
3
4
5
I
-
_j_
I
SAMPLE DATA TABLE: (I.P. BAlliSTIC PENDULUM)
CONSTANTS:
TRIAl
1
2
3
4
5
M (kg)=
KE MARBLE (J) KE CATCHER (J)
I
m (kg)=
KE lOST {J)
%KE lOST
BHS Physics
Marble Vo
GRAPH #1: REAL PENDULUM
V=
2g∆h
BHS Physics
Marble Vo
GRAPH #2: I.P. PENDULUM
V=
2g∆h
BHS Physics
WRITE-UP
• SCREEN DUMP OF IP PEND
– SHOW BALLISTIC PEND EQ PROOF
• DATA TABLES
• GRAPHS
– TRENDLINES
– GRAPH ANALYSIS
• CONCLUSION
BHS Physics
LAB #12
DATA
ANALYSIS
BHS Physics
Marble Vo
GRAPH #1: REAL PENDULUM
vo = (M+m)
m
2g∆h
y=mx+b
(M+m)
Slope = m
V=
2g∆h