A ball is tied to an elastic string of length 8.0 m and swung in a horizontal circle with a velocity of 0.8 m/s. When a metallic object is tied to a rope of length 2.75 m and swung in a horizontal circle, it makes one revolution in 2.9 s. The ratio of the centripetal force in the string to the centripetal force in the rope is 1/3.0. Find the mass of the metallic object attached to the rope, if the centripetal force in the string is 0.20 N.

Question

A ball is tied to an elastic string of length 8.0 m and swung in a horizontal circle with a velocity of 0.8 m/s.  When a metallic object is tied to a rope of length 2.75 m and swung in a horizontal circle, it makes one revolution in 2.9 s.  The ratio of the centripetal force in the string to the centripetal force in the rope is 1/3.0.  Find the mass of the metallic object attached to the rope, if the centripetal force in the string is 0.20 N.

MathMate · Answer

Centripetal force on string, F1
= m1v²/r1
F1=0.2 N

Centripetal force on rope, F2
= m2r2ω²
Since 3F1=F2, therefore F2=0.6N

Equate F2=m2r2ω²
Since all variables are known except m2,
you can readily solve for m2.

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