Exciting Physics Problem: Rolling Hoop on an Incline

How far does a large hoop roll up a ramp inclined at 24° with the horizontal?

Given data: Mass = 3.0 kg, Radius = 1.3 m, Angular speed = 6.8 rad/s, Acceleration of gravity = 9.81 m/s².

Answer:

The distance is 19.58 m.

In a fascinating physics scenario, we have a large hoop with certain properties rolling without slipping and then rolling up a ramp inclined at 24° with the horizontal. We are tasked with determining the distance the hoop travels along the incline during this process.

Given the mass of the hoop as 3.0 kg, radius as 1.3 m, angular speed as 6.8 rad/s, and acceleration of gravity as 9.81 m/s², we can apply the principles of kinetic and potential energy to solve for the distance traveled.

By equating the initial kinetic energy of the rolling hoop with its potential energy on the inclined ramp, we can use the relevant formulas to arrive at the solution. Calculations involving the mass, radius, angular speed, angle of inclination, and acceleration of gravity lead us to the final result of 19.58 meters.

Therefore, the large hoop rolls a distance of 19.58 meters along the inclined ramp, showcasing the application of physics concepts in a dynamic scenario.