Answer to Question #77496 in Physics for JoseGomez

Question

A girl sits in a tire that is attached to an overhanging tree limb by a rope 1.5 m in length. The girl’s father pusher her with a tangential speed of 4.0 m/s. If the magnitude of the force that maintains her circular motion is 110.0 N, what is the girl’s mass?

Answer 1

We can find the girl’s mass from the definition of the centripetal force:
F_c=ma_c=m v^2/r,
here, F_c is the centripetal force that maintains the circular motion of the girl, m is the girl’s mass, a_c is the centripetal acceleration, v is the girl’s tangential speed and r is radius of the curved path (or the length of the rope).
Then, from this formula we can find the girl’s mass:
m=(F_c r)/v^2 =(110.0 N∙1.5 m)/(4.0 m/s)^2 =10.3 kg.