A Creative Approach to Solving Physics Problems

How can we use the law of conservation of energy to solve a physics problem involving a rolling hoop?

In what scenario does the total mechanical energy of an object remain constant?

Answer:

The linear velocity is v = 4.08 m/s

The total mechanical energy of an object remains constant in a frictionless environment where the object is rolling without slipping.

When dealing with a physics problem involving a rolling hoop, the law of conservation of energy can be a powerful tool to determine unknown quantities. In this particular scenario, a 4.40-kilogram hoop starts from rest at a height of 1.70 meters above the base of an inclined plane and rolls down under the influence of gravity.

By applying the law of conservation of energy, we can equate the potential energy at the initial position of the hoop to the kinetic energy at the final position. This allows us to calculate the linear speed of the hoop's center of mass as it leaves the incline and rolls onto a horizontal surface.

Assuming a frictionless environment and that the hoop is rolling without slipping, the total mechanical energy of the hoop remains constant throughout its motion. This conservation of energy principle enables us to determine the linear velocity of the hoop's center of mass, which is found to be 4.08 m/s.