8i4-COL-Worksheet (1)

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Case Western Reserve University *

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121

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Mechanical Engineering

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Dec 6, 2023

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COL Worksheet Your N ame: ________________________ Signature: ____________________________ Lab partner(s): _____________________________________________________________ Course & Section: ______________ Station # ______________ Date: ______________ Section D. Procedure 1. What are the masses of your two carts, gratings, and mass bars? m cart1 = ______ ± _____ ______ (units) m cart2 = ______ ± _____ ______ (units) m grating1 = ______ ± _____ ______ (units) m grating2 = ______ ± _____ ______ (units) m bar1 = ______ ± _____ ______ (units) m bar2 = ______ ± _____ ______ (units) 2. What is the average velocity for each photogate? Remember that if the two don’t agree, you will have to find their ratios and adjust the velocities of all subsequent velocity measurements. v photogate1 = ______ ± _____ ______ (units) v photogate2 = ______ ± _____ ______ (units) Section E Analysis 3. Record your data in the tables below. Do not forget to include the directions for the vector quantities. Collision 1 Cart 1 before collision Cart 1 after collision Cart 2 before collision Cart 2 after collision Mass (kg) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Velocity (m/s) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Momentum (kg m/s ) Kinetic energy (J) ε p =________ ε k = _______ 1 COL Worksheet Aiden Le Escanord Le 495.6 0.1 grams 490.9 0.1 grams 13.1 0.1 grams 13.3 0.1 grams 49 6.7 0.1 grams 49 5.2 0.1 grams 0.349 0.025 m/s 0.352 0.021 m/s PHYS 121 - 5B 5 Oct 12th, 2023 1.005 1x10^-4 0.976 0.005 0 0 1.005 1x10^-4 0.999 1x10^-4 0.999 1x10^-4 0 0 0.839 0.006 0 0 0 0 0.838 0.352 0.981 0.479 -0.146 -0.265

Collision 2 Cart 1 before collision Cart 1 after collision Cart 2 before collision Cart 2 after collision Mass (kg) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Velocity (m/s) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Momentum (kg m/s ) Kinetic energy (J) ε p =________ ε k = _______ Collision 3* Cart 1 before collision Cart 1 after collision Cart 2 before collision Cart 2 after collision Mass (kg) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Velocity (m/s) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Momentum (kg m/s ) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Kinetic energy (J) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± ε p =________ ε k = _______ Collision 4 Cart 1 before collision Cart 1 after collision Cart 2 before collision Cart 2 after collision Mass (kg) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Velocity (m/s) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Momentum (kg m/s ) Kinetic energy (J) ε p =________ ε k = _______ Collision 5 Cart 1 before collision Cart 1 after collision Cart 2 before collision Cart 2 after collision Mass (kg) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Velocity (m/s) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Momentum (kg m/s ) Kinetic energy (J) ∆ p = ______ Kg.m/s ∆ K = _______ J COL Worksheet 2 1.005 1x10^-4 1.005 1x10^-4 0.504 1x10^-4 0.504 1x10^-4 0.851 0.005 0 0 0 0 1.008 0.011 0.856 0 0 0.508 0.364 0 0 0.256 -0.407 -0.297 0.509 1x10^-4 0.509 1x10^-4 0.999 1x10^-4 0.999 1x10^-4 0.789 0.013 -0.198 0.011 0 0 0.428 0.007 0.401 0.007 -0.101 0.006 0 0 0.428 0.007 0.158 0.005 -0,010 0.001 0 0 0.214 0.003 1.005 1x10^-4 1.005 1x10^-4 0.999 1x10^-4 0.999 1x10^-4 0.999 1x10^-4 0.999 1x10^-4 -0.185 +- 0.010 0.291 +- 0.006 1.242 0.004 0.561 0.008 0 0 0.561 0.008 1.249 0.564 0 0 0.558 0.775 0.158 0.156 -0.102 -0.595 0.509 1x10^-4 0.509 1x10^-4 0 0 -1.339 0.003 0 0 0.589 0.008 0 0 -0.681 0.456 0 0 0.589 0.173 -0.0982 -0.283

Collision 6 Cart 1 before collision Cart 1 after collision Cart 2 before collision Cart 2 after collision Mass (kg) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Velocity (m/s) _____ _____ ± _____ _____ ± _____ _____ ± _____ _____ ± Momentum (kg m/s ) Kinetic energy (J) ∆ p = ______ Kg.m/s. ∆ K = _______ J. 4*. Write out the error analysis for collision 3 to find the uncertainties in momentum and kinetic energy, and the uncertainties in ε p and ε k . 3 COL Worksheet 0 0 0 0 0 0 0 0 0.509 1x10^-4 0.509 1x10^-4 0.504 1x10^-4 0.504 1x10^-4 -1.309 0.002 1.264 0.004 -0.666 0.436 0.637 0.403 -0.029 -0.033 Sp , , m , = 1p4m , , vi) -p(m , + 8 m 1, vi)1 = 8 x 10 - 5 kym/s Sp ,, Vi = (pem ,, v) -p(m , + m ,, Svi)1 = 0 . 007kym/s 8 , = 8p,m , Sp ? , V , = 0 . 007kymls Sp ! , m , =(Pem ,, vi) -p(m , + 8 m , vi)l = 2 x 10-5 Rym/s I I I I 3 S Sp , , vi=(pem , ~) -p(m , + m ,, Svi)l = 0 . 000kymIs Spi = Sim , Op ? v ! = 0 . 006kgmls Sp , m = 1P4m , v) - p(m2 + 8 m -, v2)1 = 4 x 105kgmIs 22 22 Sp' = (am , r') -p(m + m , Si2)1 = 0 . 007kymls Sp ! = Sim , Sin= 0 . 007kymls W 22 E 2 : , im , =(kem ,, vi) -k(m , + 8 m 1, vi)1 = 3x10-55 k 8 ,, V 1 = (kem ,, v) -k(m , + m , Svi)l = 0 . 005 [ S S , = Am , m , +83r , = 0 .. 805kgmls k I 8 , , m = Mem , vi) -k(m , +8m , vi)l= 2x10-5 Gr ! = Si , mitSE= 0 . 88lkgrls R Sa ,, v ! = Ikem , r') -k(m , + m , Svi)l = 0 . 001 I I I I jaz , m = (kem , v) -k(m2+8m , v2)1 = 9 x 1085 Ski - Samitfair = 8 . 003kym's 22 2 : W I I n , = (Remz , 2) - k(m+ m , Sv2)1 = 0 . 003 E 2 Sap = 18 + 8 + B = 0 . 010 82k = 8 + 8 +8 = 0 . 006

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5. For the elastic collisions, did your data fit the conservation of energy and momentum model? Explain. 6. For the inelastic collisions, did your data fit the conservation of momentum model? Explain. What was the relative energy loss? Where did the energy go? 7. For the “explosion,” did your data fit the conservation of momentum model? Explain. What was the energy gained? GRADE:_______ GRADED BY ________ (out of 30 points) (TA’s initials) COL Worksheet 4 According to the collected data , energy and Momentum is conserved because the difference between Exand Ep in the clastic collisions and zero d very small . - Momentum is conserved in the inelastic collisions , since the Ep is very small and close to zero - Relative energy is still quite small , but not negligible . This can be because of the verenc Between Zcarts are quite old and easy te falloff - the collected data fit the conservation of momentur model , since ED is quite small - The energ gacred was the word dene by the spring