Use the first equation attached below. To calculate the initial ball velocity vi with error found by propagating uncertainty in θ. For error propgating use the following the equation to calculate the uncertainty in cos (θ), necessary for calculation using the derived expression. Note that the uncertainty comes from the 2/3 method. δcos (θ) = | cos (θ + δθ) -2cos (θ - δθ) |Mass of ball66.0 g0.1 gMass of pendulum245.0 g0.1 g Theoretical velocity4.19 +/- 0.02 m/s TrialFinal angle 128.00 degrees 228.00 degrees 328.10 degrees 428.00 degrees 528.10 degrees 627.90 degrees 2(m + M) gR(cose,- cose)m2 cos(0)cos(0 -(6.10)O cos(0)2Note, the uncertainty in 0 comes from the 2/3 method as discussed in 3.2.1.2

Find the average value angle for the given trial values,Substitute the values,

Answered: 2(m + M) gR(cose,- cose) m2…

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter16: The Solar System

Section: Chapter Questions

Problem 4FIB

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Use the first equation attached below. To calculate the initial ball velocity v_iwith error found by propagating uncertainty in θ. For error propgating use the following the equation to calculate the uncertainty in cos (θ), necessary for calculation using the derived expression. Note that the uncertainty comes from the 2/3 method.

δ_{cos (}_θ)= | ^{cos (}^{θ + δθ) -}₂^{cos (}^{θ - δθ)} |

Mass of ball	66.0 g	0.1 g
Mass of pendulum	245.0 g	0.1 g

Theoretical velocity	4.19 +/- 0.02 m/s

Trial	Final angle
1	28.00 degrees
2	28.00 degrees
3	28.10 degrees
4	28.00 degrees
5	28.10 degrees
6	27.90 degrees

cos(0)cos(0 -
(6.10)
O cos(0)
2
Note, the uncertainty in 0 comes from the 2/3 method as discussed in 3.2.1.2

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