A speed skater goes around a turn that has a radius of 31 m. The skater has a speed of 13 m/s and experiences a centripetal force of 460 N. What is the mass of the skater?

F=mv²/R

m=FR/ v²

To find the mass of the skater, we can use the following formula:

F = (m * v^2) / r

Where:
F is the centripetal force
m is the mass of the skater
v is the velocity of the skater
r is the radius of the turn

In this case, we know the following values:
F = 460 N
v = 13 m/s
r = 31 m

Rearranging the formula, we can solve for m:

m = (F * r) / v^2

Substituting the given values, we get:

m = (460 N * 31 m) / (13 m/s)^2

m = (460 N * 31 m) / 169 m^2/s^2

m = 14260 Nm / 169 m^2/s^2

m ≈ 84.38 kg

Therefore, the mass of the skater is approximately 84.38 kg.