Analysis and Calculations

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At any point of the plane's journey, a right triangle can be made (shown below) that will give the radius of rotation simply using the Pythagorean theorem. 

 

                       | \
                 |  \
                 |   \
                 |    \
 94.8 cm    |      \   99 cm
                 |       \
                 |        \
                 | _____\
                     r     * 

     

And the angle at the top can be found via

\cos^{-1}\left(\frac{94.8}{99}\right)=\theta\:=\:16.75^o

 

Then, once a free body diagram is drawn (also shown below) it is easy to see that the vertical component of the force of tension is equal to the force of gravity because the system is at equilibrium in the y direction

 

 

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From there an "Fnet" equation can be made and solved with our measured information. 

 

F_{net\:y}=F_T\cos\left(\theta\right)-F_G

We know it is not accelerating the y direction, so the net force must be 0, therefore,

F_T\cos\left(\theta\right)=F_G

F_T=\frac{mg}{\cos\left(\theta\right)}

 

F_T=2.37\:N

 

 

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