A speed skater goes around a turn that has a radius of 33 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=ma=mv²/R
m=FR/ v²=…..
To find the mass of the skater, we can use the formula for centripetal force:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the skater
v is the speed of the skater
r is the radius of the turn
In this case, we know F = 460 N, v = 13 m/s, and r = 33 m.
Substituting these values into the formula, we have:
460 = (m * 13^2) / 33
Let's solve for m:
460 * 33 = m * 13^2
15180 = m * 169
Divide both sides of the equation by 169:
m = 15180 / 169
m = 90
Therefore, the mass of the skater is 90 kg.
To find the mass of the skater, we can use the centripetal force formula:
F = (m * v^2) / r
Where:
F = Centripetal force (460 N)
m = Mass of the skater (unknown)
v = Velocity of the skater (13 m/s)
r = Radius of the turn (33 m)
Rearranging the formula to solve for mass:
m = (F * r) / v^2
Plugging in the values:
m = (460 N * 33 m) / (13 m/s)^2
m = (15180 N * m) / (169 m^2/s^2)
m = 15180 N·m / 169 m^2/s^2
m ≈ 89.88 kg
Therefore, the mass of the skater is approximately 89.88 kg.