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A 62.5 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 13.4 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 1034 N of force on the rope, what is the maximum speed that she can tolerate at the low point of her swing?

Respuesta :

Answer:

    v = 9.45 m/s

Explanation:

given,

mass of the carpenter = 62.5 Kg

length of rope = 13.4 m

Capable of exerting force = 1034 N

centripetal force acting on the body

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

                   [tex]F = \dfrac{62.5\times v^2}{13.4}[/tex]

                  F =4.664 v²  N

Gravitational force on her =

                  F = m g

                  F = 62.5 x 9.81

                  F = 613.125 N

now,

4.664 v² + 613.125 = 1034

4.664 v² = 420.875

   v²  = 90.24

    v = 9.45 m/s

Maximum speed which she can tolerate = v = 9.45 m/s

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