Question

If the horizontal circular path the riders follow has a 7.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration whose magnitude is 2.25 times that due to gravity?

Answer 1

Revolutions per minute of rider is 212.4

Explanation:

Radius , r = 7 m

Centripetal acceleration, a = 2.25 g = 22.07 m/s²

We have equation for centripetal acceleration

              $a=\frac{v^2}{r}$

Substituting

              $a=\frac{v^2}{r}\\\\22.07=\frac{v^2}{7}\\\\v=12.43m/s$

We have equation for frequency

             $f=\frac{2\pi }{\omega }\\\\f=\frac{2\pi r}{v}\\\\f=\frac{2\pi \times 7}{12.43}=3.54Hz$

Revolutions per minute = 3.54 x 60 = 212.4

Revolutions per minute of rider is 212.4