The angle the string makes with the vertical is : 34.6°
Given data :
mass of rubber stopper ( m ) = 45 g
Radius ( r ) = 2.9 m
Time to complete one revolution ( T ) = 4.1 secs
Calculate the angle the string makes with the vertical
applying the formula below
Tan ∅ = [tex]\frac{mw^2r}{mg}[/tex] --- ( 1 )
cancel out m from equation ( 1 )
Tan ∅ = [tex]\frac{w^2r}{g}[/tex] ----- ( 2 )
where ; w = [tex]\frac{2\pi }{T}[/tex]
Therefore equation ( 2 ) becomes
Tan ∅ = [tex]\frac{4\pi ^2r}{T^2g}[/tex] --- ( 3 )
where ; r = 2.9 m, T = 4.1 secs , g = 9.8
Insert values into equation ( 3 )
Tan ∅ = 0.69
∅ = Tan ( 0.69 )
= 34.6°
Hence we can conclude that The angle the string makes with the vertical is : 34.6°.
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