Linear Speed of a Hoop Rolling Down an Inclined Plane

What is the formula to calculate the linear speed of a hoop's center of mass as it leaves an inclined plane and rolls onto a horizontal surface under the influence of gravity? The formula to calculate the linear speed of a hoop's center of mass as it leaves an inclined plane and rolls onto a horizontal surface under the influence of gravity is v = √gh, where v is the linear speed, g is the acceleration due to gravity, and h is the height.

When a 5.60-kilogram hoop starts from rest at a height of 1.80 meters above the base of an inclined plane and rolls down under the influence of gravity, we can calculate the linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface using the formula v = √gh.

Explanation:

Potential Energy at the top = Kinetic Energy at the bottom. By equating the two, we can determine the linear speed of the hoop's center of mass. The formula involves calculating the potential energy and equating it to the kinetic energy at the bottom of the incline.

Considering the mass of the hoop, acceleration due to gravity, and the height from which the hoop starts, we can use the formula v = √gh to find the linear speed of the hoop's center of mass.

Calculation:

Potential Energy = Kinetic Energy mgh = (1/2)mv² gh = v² v = √gh

By plugging in the values of g = 10 m/s² and h = 1.80 m into the formula v = √gh, we can calculate the linear speed of the hoop's center of mass. Thus, the linear speed of the hoop rolling down the inclined plane onto a horizontal surface is 4.24 m/s.

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