AP PHYSICS PROBLEM PLANE AND BALL
AN INCLINED PLANE MAKES AN ANGLE OF q WITH THE HORIZONTAL, AS SHOWN ABOVE. A SOLID SPHERE OF RADIUS R AND MASS M IS INITIALLY AT REST IN THE POSITION SHOWN, SUCH THAT THE LOWEST POINT OF THE SPHERE IS A VERTICAL HEIGHT H ABOVE THE BASE OF THE PLANE. THE SPHERE IS RELEASED AND ROLLS DOWN THE PLANE WITHOUT SLIPPING. THE MOMENTUM OF INERTIA OF THE SPHERE ABOUT AN AXIS THROUGH ITS CENTER IS 2/5 (M R2).
EXPRESS YOUR ANSWERS IN TERMS OF M, R, H, g, AND q.
A) DETERMINE THE FOLLOWING FOR THE SPHERE WHEN IT IS AT THE BOTTOM OF THE PLANE.
I) ITS TRANSLATIONAL KINETIC ENERGY
II) IT ROTATIONAL KINETIC ENERGY
B) DETERMINE THE FOLLOWING FOR THE SPHERE WHEN IT IS ON THE PLANE.
I) ITS LINEAR ACCELERATION
II) THE MAGNITUDE OF THE FRICTIONAL FORCE ACTING ON IT.
THE SOLID SPHERE IS REPLACED BY A HOLLOW SPHERE OF IDENTICAL RADIUS R AND MASS M. THE HOLLOW SPHERE, WHICH IS RELEASED FOR THE SAME LOCATION AS THE SOLID SPHERE, ROLLS DOWN THE INCLINE WITHOUT SLIPPING.
C) WHAT IS THE TOTAL KINETIC ENERGY OF THE HOLLOW SPHERE AT THE BOTTOM OF THE PLANE?
D) STATE WHERE THE THE ROTATIONAL KINETIC ENERGY OF THE HOLLOW SPHERE IS GREATER THAN, LESS THAN, OR EQUAL TO THAT OF THE SOLID SPHERE AT THE BOTTOM OF THE PLANE. JUSTIFY YOUR ANSWER.