On an ice rink, two skaters of equal mass grab hands and spin in a mutual circle once every 2.3 s . if we assume their arms are each 0.85 m long and their individual masses are 65.0 kg , how hard are they pulling on one another

We have to
 m = 65 kg
 r = 0.85 m
 t = 2.3 s
 The perimeter of the circle is given by:
 P = 2 * pi * r
 P = 2 * pi * (0.85 m)
 P = 5.34 m
 Then, by definition, the distance equals the speed by time:
 d = v * t
 v = d / t
 v = (5.34 m) / (2.3 s)
 v = 2.32 m / s
 Then, to find the radial acceleration, we must use the speed found and the radius of the circle:
 a = v ^ 2 / r
 a = (2.32 m / s) ^ 2 / (0.85 m)
 a = (5.38 m ^ 2 / s ^ 2) / (0.85 m)
 a = 6.32 m / s ^ 2
 Finally, we have that by definition the force is equal to the mass by acceleration:
 F = m * a
 F = (65 kg) * (6.32 m / s ^ 2)
 F = 410.8 N
 answer
 F = 410.8 N

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