circular motion - You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘death- well’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m ?

Grigori (last edited 7 days ago) (Student, UG2 Grade)

Given that

Radius of the chamber r = 25 m

Acceleration due to gravity g = 10 m/s^2

When the biker reaches the top of the death well, the centrifugal force acting on the motorcycle rider balances his weight as well as the normal reaction of the chamber's ceiling.

Centrifugal force F_c = \frac{mv^2}{r}

F_c=mg+N

Step 1: Calculating the minimum possible speed at the uppermost point

minimum possible speed at the uppermost point when normal force is zero

F_c = mg

\frac{mv^2}{r} = mg

v = \sqrt{rg}

v = \sqrt{25 * 10} = \sqrt{250}

v = 15.8 m/s^2

Hence, minimum possible speed at the uppermost point v = 15.8 m/s^2