Question

A uniform, solid sphere of radius 2.75 cm and mass 2.25 kg starts with a purely translational speed of 1.50 m/s at the top of an inclined plane. the surface of the incline is 2.50 m long, and is tilted at an angle of 26.0∘ with respect to the horizontal.

Answer 1

The problem involves using the conservation of mechanical energy to calculate the final translational speed of a solid sphere rolling down an inclined plane, given its initial translational speed, radius, mass, and the incline's dimensions.

Step-by-step explanation:

The student's question is about calculating the final speed of a uniform, solid sphere that rolls down an inclined plane with an initial translational speed. To solve this, one may use principles of both translational and rotational dynamics, considering the conservation of mechanical energy. Given the sphere's initial conditions, one would factor in the translational kinetic energy, the rotational kinetic energy (since it's rolling), and the potential energy at the top of the incline. Without friction, the total mechanical energy remains constant. You would set up an equation with initial mechanical energy (potential + translational + rotational kinetic) equal to the final mechanical energy (translational + rotational kinetic) at the bottom of the incline to find the final translational speed of the sphere. Details like mass, radius, and the angle of the incline are pertinent to this calculation.