Which Object Will Travel Furthest Up an Incline Plane?

Explanation:

Reasoning behind the Answer

The solid sphere will travel farther up the plane in this scenario. This is due to the differences in their moments of inertia.

Moment of Inertia

Definition: Moment of inertia is the measure of an object's resistance to changes in its rotational motion.

Calculation: For any mass given and any radius, the hoop requires more energy than the sphere to overcome its rotational inertia. The moment of inertia of the hoop is greater than that of the solid sphere (Moment of Inertia of hoop > Moment of Inertia of the sphere).

Kinetic Energy Distribution

Formula Comparison: When comparing the formulas, for the hoop (mr²) > for the sphere (2/5mr²).

Energy Usage: The initial kinetic energy given to the shapes is used more times for rotation by the hoop than for translation by the solid sphere (moving in a straight line up the incline).