ANSWER
m = 84.375 kg
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,
[tex]F_c=m\cdot\frac{v^2}{r}[/tex]To solve for m, divide both sides by v² and multiply both sides by r,
[tex]m=F_c\cdot\frac{r}{v^2}[/tex]Replace with the given values,
[tex]m=450N\cdot\frac{27m}{12^2m^2/s^2}=450\operatorname{kg}\cdot m/s^2\cdot\frac{3}{16}s^2/m=84.375\operatorname{kg}[/tex]Hence, the mass of the skater is 84.375 kilograms.
