Reflecting on the Conservation of Energy in Physics

What principle is applied in determining the linear speed of an object rolling down an inclined plane?

A. Conservation of Momentum

B. Newton's Laws of Motion

C. Conservation of Energy

Answer:

The principle applied in determining the linear speed of an object rolling down an inclined plane is Conservation of Energy.

When analyzing the motion of objects in physics, the Conservation of Energy principle plays a crucial role in predicting and understanding various phenomena. In the scenario where a 4.20-kilogram hoop rolls down an inclined plane under the influence of gravity, the principle of Conservation of Energy helps calculate the linear speed of the hoop's center of mass.

By carefully considering the initial potential energy of the hoop at a certain height above the base of the inclined plane and then equating it to the kinetic energy of the hoop as it reaches the bottom of the incline, we can determine the linear speed of the hoop. This calculation involves converting potential energy into kinetic energy and applying the appropriate formulas.

The Conservation of Energy principle states that the total energy of a closed system remains constant over time, with energy being converted from one form to another. In the case of the hoop rolling down the inclined plane, the potential energy stored in the hoop due to its initial height is converted into kinetic energy as it gains speed during its descent.

Therefore, by accurately applying the equations derived from the Conservation of Energy principle and considering factors like mass, height, and gravitational acceleration, we can calculate the linear speed of the hoop as it leaves the incline and transitions onto a horizontal surface. This process enables us to understand the relationship between potential and kinetic energy in the context of motion and gravity.