The College at Brockport: State University of New York
Digital Commons @Brockport
Lesson Plans
CMST Institute
11-1-2004
Using an Atwood Machine to Determine the
Acceleration Due to Gravity
Steve Whitman
The College at Brockport, stevewhitman27@gmail.com
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 an Atwood Machine to Determine the Acceleration Due to Gravity" (2004). Lesson Plans. Paper 312.
http://digitalcommons.brockport.edu/cmst_lessonplans/312
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 kmyers@brockport.edu.
BHS Physics
LAB #7
•ATWOOD
MACHINE
BHS Physics
GOALS
• TO USE AN ATWOOD
MACHINE TO DETERMINE
THE ACCELERATION DUE TO
GRAVITY:
– OF EARTH (REAL ATWOOD)
– OF THE MOON (IP ATWOOD)
BHS Physics
PROCEDURE
• Set up Atwood machine with 2 equal masses (500g)
• Add a 10 g mass to one side
• Clamp 5 paper clips to each side
– Each clamp is ~4g
• Release system and clock the time required for
heavier mass to reach the table top
• Measure Y, record time
• Transfer one clamp from one side to the other and
repeat
• Continue trials until all clamps are on one side of
system
BHS Physics
ATWOOD MACHINE
LAB #.7:
00 MACH INE
0
I
I
- r - - - - - - -,- - - - - - -
I
I
---- -- -n=-1 ~610 mts ~2 ---q
-------.------,-------
I
0
1 - - - - - - - T - - - - - - - .- - - - - - -
0
( Gravity... )
I
I
I
I
0
I
0
I
I
(MOqN)
I
... L .................... I .................... J ..................... .1. .................... '- ............... ...
I
I
I
I
- r - - - - - - -,- - - - - - -
I
I
I
I
I
I
I
I
0
0
.................... L .................. .. 1.. ................. J .................... L ......... ...
-------.-------.------0
1 - - - - - - - T - - - - - - - .- - - - - - -
0
I
I
I
I
I
- - - - - - - r - - - - - - -,- - - - - - -
I
I
I
1 - - - - - - -
r- - - 0
0
0
0
.. L ..........
0
0
0
0
...............
0
0
0
0
0
0
0
- - - - - - -~ - - - - - - +-------<~-----1- - - - - - --:- - -- -
.............. L .............. '- .......... ..
0
M2 :2 Mass
---- ---
-------·-- - ----~------
L ........
0
............
0
0
Ml
-------~------
------ -.------- +-- - ---1t-- - - -+------ -.----- -1------ ~ ~---0
0
0
0
0
-------,----0
-------~------~------
0
:
~
4 _90
-~-----
0
:
0
:
------~-------~------
- - - - - - - r - - - - - - -,- - - - - - I
0
I
I
I
I
I
I
- i------ -,------- i------- i------ -,--- - ----,---- - --
I
T -- -- -
-
-
r - - - - - - -,-- -- -- - ,
I
I
I
I
I
I
I
I
-~ ~ ~-?- t---I
I
0
______ i 0 _______ i0 ___ _
BHS Physics
ATWOOD MACHINE PROOF
M1 g > M 2 g
Fnet =
Fnet =
ma
M1g – M2g
= (M + M ) a
– M ) g = (M + M ) a
M1g – M2g
a
a
M1g
M2g
(M1
1
2
1
a= g
2
2
( )
M1 – M2
M 1 + M2
BHS Physics
ATWOOD MACHINE: OBSERVED ACCEL
Theoretical a:
a= g
( )
Vo = 0
Observed a: (from data)
Vo
a=?
a
M1g
M2g
Y
M1 – M2
M 1 + M2
Vf
a
t
d
Vf = Vo + at
d = Vot + ½ (at2)
Vf 2 = Vo2 + 2ad
BHS Physics
DATA TABLE PART 1: Earth’s g
I
I
I
r-- y
I
I
I
SAFM1PLE DATA TABLE: PART 1: SOLVE FOR EARTH·s (I
(rM1
-
-
I
l'll12)
-
=
CO NSTANT=
rM
11 (kg)
rM
12 (kg)
0.530
0.520
0.534
0.516
0.538
0.512
0.542
0.508
0.546
0.504
0.550
0.500
I
I
I
kg
I
I
I
I
FM1 TOTAL
(kg)
(rAA11+ rM
12) (rM
11- rM
12)
UM11- rM
12l
(FM
11+ rM
12)
I
9.8
g=
Y (1n)
I
a (1nl~)
t (s)
I
I
I
BHS Physics
DATA TABLE PART 2: Moon’s
I
I
I
I
I
I
I
g
I
J SAfM1PL~ DAJA T~BLE: PART 2: SO LVE FOR fM
10_o N·s u (INT_ERA\ fiVE PHYSICS)
r--
(rll'l1l+
g=
kg
I
fAA11 (kg)
rM12 (kg)
0.530
0.520
0.534
0.516
0.538
0.512
0.542
0.508
0.546
0.504
0.550
I
r~121 = c~NSTANT I
rM1 TOTAL
(kg)
(M1 + fM
12)
1.67
I
n~1- r~21
(fw
11- rM12)
(fM
11+ fM12)
Y (n1)
a (tn/~)
t (s)
-
0.500
I
I
I
I
I
I
I
-
Acceleration (m/s2)
BHS Physics
GRAPH #1: Earth
Mass ratio
( )
M 1 – M2
M 1 + M2
Acceleration (m/s2)
BHS Physics
GRAPH #2: Moon
Mass ratio
( )
M 1 – M2
M 1 + M2
BHS Physics
WRITE-UP
• ABSTRACT:
– BACKGROUND
– METHOD
• SKETCH: ENHANCED I.P. SCREEN DUMP
– INCLUDE PROOF OF ATWOOD EQUATION
• DATA TABLES
• GRAPHS
– TRENDLINES
– GRAPH ANALYSIS
a= g
( )
M1 – M2
M 1 + M2
• TEXT BOX TO TELL STORY OF EACH GRAPH
• INCLUDE THE SIGNIFICANCE OF SLOPE OF LINEAR TRENDLINES
• CONCLUSION
BHS Physics
LAB #7
DATA
ANALYSIS
Acceleration (m/s2)
BHS Physics
GRAPH #1: Earth
a α Mass Ratio
Slope = g
?
b=0
Mass ratio
( )
a=g
M1 - M2
M 1 + M2
Y = (m) x + b
( )
M1 - M2
M 1 + M2
Acceleration (m/s2)
BHS Physics
GRAPH #2: Moon
a α Mass Ratio
Slope = g
?
b=0
Mass ratio
( )
a=g
M1 - M2
M 1 + M2
Y = (m) x + b
( )
M1 - M2
M 1 + M2
BHS Physics
ATWOOD MACHINE: g OF EARTH
0.500
_/
0.450
0.400
<
.
~
-
0.350
/
E
z 0.300
0
~
L.LJ
....J
L.LJ
0.250
0.200
u
u 0.150
<
0.100
/
/
/
/
/
/
SLOPE= g
y = 9.8x
+ a (m/s2)
-
~
0.050
0.000
0.000
I
I
I
I
0.010
0.020
0.030
0.040
MASS RATIO ((M1-M2)/(M1 +M2))
0.050
Linear (a (m/s2))
BHS Physics
ATWOOD MACHINE: g OF MOON
0.090
.,
0.080
-
0.070
.
;/
-
<
~
-z
E
;,
0
0.050
LU
0.040
~
r£
0.060
SLOPE= g
y = 1.67x- 1E-16
.-
/
+ a (m/s2)
Linear (a (m/s 2))
;/
...J
LU
u
u 0.030
; _,
ex
/
,.
0.020
(.-
0.010
0.000
0.000
0 .010
0 .020
0.030
MASS RATIO ((M1-M2)/(M1 +M2))
0 .040
0 .050