Question

A speed skater goes around a turn that has a radius of 27 m. The skater has a speed of 12 m/s and experiences a centripetal force of 450 N. What is the mass of the skater?

Answer 1

m = 84.375 kg

Step-by-step explanation

Given:

• The radius of the circular path, r = 27m

,

• The tangential speed of the skater, v = 12m/s

,

• The centripetal force the skater experiences, Fc = 450N

Unknown:

• The mass of the skater, m

The centripetal force an object of mass m experiences while moving through a circular path of radius r, with a tangential speed v is,

`F_c=m\cdot(v^2)/(r)`

To solve for m, divide both sides by v² and multiply both sides by r,

`m=F_c\cdot(r)/(v^2)`

Replace with the given values,

Hence, the mass of the skater is 84.375 kilograms.