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.