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LAB #7

LAB #7. ATWOOD MACHINE. ATWOOD MACHINE. George Atwood 1745 - 1807. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Atwood.html. George Atwood. http://batgirl.atspace.com/Atwood.html. ATWOOD MACHINE. PULLEY. a. M2. M 1. a. ATWOOD MACHINE. M 1 > M 2. M 1 g > M 2 g.

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LAB #7

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  1. LAB #7 ATWOOD MACHINE

  2. ATWOOD MACHINE George Atwood 1745 - 1807 http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Atwood.html

  3. George Atwood http://batgirl.atspace.com/Atwood.html

  4. ATWOOD MACHINE

  5. PULLEY a M2 M1 a ATWOOD MACHINE M1 > M2 M1g > M2g M1g > T T netF1 = M1g – T = (M1)a T M2g M2g < T M1g netF2 = T–M2g = (M2)a

  6. M1g – T = (M1)a = (M2)a T–M2g SUB M1g – (M2a+M2g) = M1a M1a + M2 a = M1g – M2g a (M1 + M2) = g (M1 - M2) ATWOOD PROOF Solve for T T = (M2a+M2g) FACTOR

  7. ATWOOD PROOF (cont.) a (M1 + M2) = g (M1 - M2) (M1 - M2) = a g (M1 + M2) SOLVE FOR g (M1 + M2) = g a (M1 - M2)

  8. PULLEY M1g T T M2g a a a T M2 M2 T M2g M1g M1 M1 M1 a a M2 M1g M2g ATWOOD PROOF (alternate) Eliminate the pulley, rotate masses with vectors T1= -T2 Eliminates T Eliminates Rope Bond masses together & treat as one.

  9. a M1g M1 ( ) M2 a= g M1 – M2 M2g M1 + M2 ATWOOD PROOF (alternate) M1+M2 = MT M1g > M2g Fnet = M1g – M2g = MT a (M1 – M2) g = (M1 + M2) a

  10. GOALS TO USE AN ATWOOD MACHINE TO DETERMINE THE ACCELERATION DUE TO GRAVITY (g): OF EARTH OF THE MOON (REAL ATWOOD) (IP ATWOOD)

  11. PROCEDURE: Part A • Set up Atwood machine with 2 equal masses (500g) • Add a 10 g mass to one side • Clamp 5 paper clamps to each side • Each clamp is ~4g • Measure the distance the heavier mass has to travel to the tabletop. • Release system and measure the time required for heavier mass to reach the table top and record • Transfer one clamp from the less massive side to the other and repeat • Continue trials until all clamps are transferred.

  12. PROCEDURE: Part B • Create your I.P. simulated Atwood • Change g to the moon’s • Set masses equal to Earth machine • Run simulation stopping mass before it hits table • Record time and distance of travel • Reset masses to next trial • Repeat

  13. ATWOOD MACHINE

  14. ( ) a= g M1 – M2 M1 + M2 Vf = Vo + at d = Vot + ½ (at2) Vf 2 = Vo2 + 2ad Vo Vf M1g a t M2g d ATWOOD MACHINE: OBSERVED ACCEL Theoretical a: M1>M2 Observed a: (from data) Vo = 0 a=? a Y

  15. DATA TABLE PART 1: Earth’s g

  16. DATA TABLE PART 2: Moon’s g

  17. ( ) M1 – M2 M1 + M2 GRAPH #1: Earth Plot atheory and aobserved Acceleration (m/s2) Mass ratio

  18. ( ) M1 – M2 M1 + M2 GRAPH #2: Moon Plot atheory and aobserved Acceleration (m/s2) Mass ratio

  19. ( ) a= g M1 – M2 M1 + M2 WRITE-UP • ABSTRACT: • BACKGROUND • METHOD • SKETCH: ENHANCED I.P. SCREEN DUMP • INCLUDE PROOF OF ATWOOD EQUATION • DATA TABLES • GRAPHS • TRENDLINES • GRAPH ANALYSIS • TEXT BOX TO TELL STORY OF EACH GRAPH • INCLUDE THE SIGNIFICANCE OF SLOPE OF LINEAR TRENDLINES • CONCLUSION

  20. LAB #7 DATA ANALYSIS

  21. ( ) a = gM1 - M2 M1 + M2 ( ) M1 - M2 M1 + M2 GRAPH #1: Earth a a Mass Ratio g Slope = ? Acceleration (m/s2) b = 0 Y = (m)x + b Mass ratio

  22. ( ) a = gM1 - M2 M1 + M2 ( ) M1 - M2 M1 + M2 GRAPH #2: Moon a a Mass Ratio g Slope = ? Acceleration (m/s2) b = 0 Y = (m)x + b Mass ratio

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