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A 56.6 kg carpenter at a construction site plans to swing in a circular arc from one roof top to an adjacent roof at the end of a 12.8 meter rope suspended from a crane boom. If her wiry arms, toughened by years of driving spikes with a No. 22 framing hammer, are capable of exerting 1018 N of force on the rope, what is the maximum speed that she can tolerate at the low point of her swing? 15.2 m/s (T/F)

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Answer

given,

mass of the carpenter = 56.6 Kg

length of the rope = 12.8 m

Force on the cable = 1018 N

maximum speed = ?

centripetal force = [tex]\dfrac{mv^2}{r}[/tex]

                            =  [tex]\dfrac{56.6v^2}{12.8}[/tex]

                            =  [tex]4.42 v^2[/tex]

gravitation force = m g = 56.6 x 9.8 = 554.68 N

 4.42 v² + 554.68  = 1018

  4.42 v² = 463.32

        v² = 104.82

        v = 10. 24 m/s

hence, maximum speed is equal to  v = 10. 24 m/s

 15.2 m/s speed is false.

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