Rotational Motion

Question

A 55.7 kg ice skater is moving at 3.92 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.798 m around the pole.
(a) Determine the force exerted by the horizontal rope on her arms.

N
(b) What is the ratio of this force to her weight?

(force from part a / her weight)

Answer 1

Hi Dominic!

 

Presuming the speed of the skater does not change as she grabs the rope and moves in the circle, and she still moves at a constant 3.92 m/s, then she is in uniform circular motion, and the net force on her (due to the horizontal rope, pointing toward the center of the circle) must be the centripetal force.  This is the force the rope must exert on her to keep her moving in a circle (if she let go and didn't move, she would glide off in a straight line along her last trajectory, as Newton's first law says, because no net force is acting on her anymore).

 

The centripetal force required to move a mass m (considered as a point mass) in a circle of radius r at speed v is:

 

F_c = mv²/r

 

Then you can calculate her weight:  F_g = mg, and compute the ratio of the two, as requested.

 

I hope this helps!  Let me know if you would like to check an answer, or if you have other questions about this.