In a circus performance, a large 3.8 kg hoop with a radius of 1.3 m rolls without slipping. if the hoop is given an angular speed of 6.7 rad/s while rolling on the horizontal and is allowed to roll up a ramp inclined at 15◦ with the horizontal, how far (measured along the incline) does the hoop roll? the acceleration of gravity is 9.81 m/s 2 . answer in units of m

L = 30 m

Explanation:

As per mechanical energy conservation law we can say that total kinetic energy of the hoop is equal to the total gravitational potential energy at the top

So here we can say for initial total kinetic energy as

for pure rolling we will have

also for large hoop we will have

now we have

now for gravitational potential energy we can say

now by energy conservation we have