Question

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?

Answer 1

v = 9.45 m/s

Step-by-step 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

`F = (mv^2)/(r)`

`F = (62.5* v^2)/(13.4)`

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