A hockey skater turns in a circular path with radius of 31.0 m while going 10.5 m/s. If he experiences a centripetal force of 565 N, what is the mass of the skater?
To find the mass of the skater, we need to use the relationship between centripetal force, mass, and acceleration.
The centripetal force (F_c) acting on an object moving in a circular path is given by the formula:
F_c = (m * v^2) / r
Where:
F_c is the centripetal force
m is the mass of the object
v is the velocity of the object
r is the radius of the circular path
We are given:
F_c = 565 N
v = 10.5 m/s
r = 31.0 m
Rearranging the formula, we can solve for the mass (m):
m = (F_c * r) / v^2
Substituting the given values:
m = (565 N * 31.0 m) / (10.5 m/s)^2
Now we can calculate the mass:
m = (565 N * 31.0 m) / (110.25 m^2/s^2)
m = 17315 N m / 110.25 m^2/s^2
m ≈ 157 kg
Therefore, the mass of the skater is approximately 157 kg.