Question

In a circus performance, a large hoop having a mass of 12.5 kg kg and a radius of 2.9 m m successfully rolls without slipping. The hoop is given a speed of 7.540 m/s m/s while rolling on the horizontal, and is directed towards a ramp inclined at 25.0 degrees degrees with the horizontal.

Part A: Assuming that there is sufficient friction on the ramp so that the hoop will roll without slipping, how far (measured along the incline) does the hoop roll?
Give your answer in meters as measured along the incline.

Answer 1

The hoop rolls a distance of 11.2 meters along the incline.

Step-by-step explanation:

To determine the distance the hoop rolls along the incline, we can use the conservation of mechanical energy. Since the hoop is rolling without slipping, its initial kinetic energy will be equal to its final potential energy. The initial kinetic energy can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the hoop and v is its speed. The final potential energy can be calculated using the formula PE = mgh, where m is the mass of the hoop, g is the acceleration due to gravity, and h is the vertical height.

Since the hoop rolls without slipping, the distance it rolls along the incline can be determined by using the formula d = h / sin(θ), where θ is the angle of the incline. Plugging in the values given in the question, the distance the hoop rolls along the incline is:

d = 5.00 m / sin(25.0 degrees) = 11.2 m