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# UB PHY 158 - Lab 3

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VI-1h(cm)D (cm)h/ D (cm)-2.10 25.0 -0.084-1.70 25.0 -0.068-1.70 25.0 -0.068-1.80 25.0 -0.072-1.20 25.0 -0.0480.20 30.0 0.00666670.80 30.0 0.02666670.70 30.0 0.02333330.80 30.0 0.02666670.90 30.0 0.033.70 35.0 0.10571434.60 35.0 0.13142864.80 35.0 0.13714295.50 35.0 0.15714292.00 35.0 0.05714299.60 40.0 0.249.60 40.0 0.249.80 40.0 0.24511.20 40.0 0.2810.30 40.0 0.257515.40 45.0 0.342222216.20 45.0 0.3616.50 45.0 0.366666716.90 45.0 0.375555617.00 45.0 0.377777822.20 50.0 0.44422.60 50.0 0.45222.60 50.0 0.45222.70 50.0 0.45423.00 50.0 0.4628.50 55.0 0.518181829.60 55.0 0.538181829.70 55.0 0.5430.20 55.0 0.549090930.60 55.0 0.556363640.40 60.0 0.673333341.30 60.0 0.688333342.20 60.0 0.703333343.80 60.0 0.7339.80 60.0 0.6633333VI-220.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0-0.2-0.100.10.20.30.40.50.60.70.8f(x) = 0.02x − 0.62ℎ vs /� ��, cmℎ/�The line of best fit is a straight line which is what we predicted for this plot.VI-3slope 0.0214813 -0.616237 intunc slope 0.0003283 0.0144493 unc intFrom Excel, s=¿0.0214813, σs=¿ 0.0003283b=−¿0.616237, σb= ¿0.01444931. Calculating θe:b=−tan ⁡(θe) θe=−arctan(b)=−arctan(−0.616237)=31.6429 degσθe=σb1+b2=0.01444931+(−0.616237)2=0.01047242 deg2. Measuring θm:θm=θ1+θ2+θ3n=33+32+323=32.333degσθm=0.5(33−32)=0.5 degThe values for θ agrees with each other and their common range falls within 31.5 deg to 31.6 deg. The value for θ taken experimentally is more reliable since the value for θ takenwith the protractor is based on just 3 readings which could have parallax error and it also has a much greater uncertainty.VI-4To find v02: we know,s=g2 v02cos2(θ) and g=980 cm/s21. Using the experimental value of θ:θ ± σθ=31.6 ± 0.01 degdeθ ± σθ=32 ±0.5 degdev0=√g2 s cos2(θ)=√9802∗0.02148∗cos2(31.6429)=177.4110793 cm/s2σv0=v0❑√(b σb❑1+b2)2+(σs2 s)2 σv0=177.411√(−0.616237∗0.01444931+(−0.616237)2)2+(0.00032832∗0.0214813)2=0.010002027 cm/s22. Using the measured value of θ:v0=√9802∗0.02148∗cos2(32.333)=178.7507498 cm/s2σv0=178.751√(−0.616237∗0.01444931+(−0.616237)2)2+(0.00032832∗0.0214813)2=0.01007757 cm/s2VI-5S = 34.5 cmExpected value of v0=√10 gS9=√10∗980∗34.59=193.8212235 cm/s2VI-6The value of v0 from VI-4 does not agree with the predicted value of v0 in VI-5. This couldbe caused if the ball was not released in the correct way, thereby giving it an initial velocity, which would alter calculations. The other reason could be due to parallax error while measuringfrom the reference line to the center of the dot at distance h.v0❑± σv0=177 ± 0.01 cm/s2v0❑± σv0=179 ± 0.01 cm/s2v0=193.82

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