Question

A handful of professional skaters have taken a skateboard through an inverted loop in a full pipe. For a typical pipe with a diameter of 14 feet (4.27 meters), what is the minimum speed the skater must have at the very top of the loop?

Answer 1

Answer

given,

diameter of the pipe is  =  (14 ft)4.27 m

minimum speed of the skater must have at very top = ?

At the topmost point of the pipe the  normal force will be equal to zero.

F = mg

centripetal force acting on the skateboard

$F = \dfrac{mv^2}{r}$

equating both the force equation

$mg = \dfrac{mv^2}{r}$

$v = \sqrt{gr}$

r = d/2 = 14/ 2 = 7 ft

or

r = 4.27/2 = 2.135 m

g = 32 ft/s²   or g = 9.8 m/s²

$v = \sqrt{32 \times 7}$

v = 14.96 ft/s

or

$v = \sqrt{9.8 \times 2.135}$

v = 4.57 m/s