As shown in the figure, a small spherical ball of mass m rolls down a loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circular part shown has a radius R . Determine the kinetic energy of the ball when it is at a point A , where the radius makes an angle with the horizontal.

Step-by-step solution

Let the lowest point of the loop track be the reference level for zero gravitational potential energy ( U = 0 ). The ball is released from rest at a vertical height H . Therefore, its initial kinetic energy is zero, and its initial mechanical energy is entirely potential: E_i = mgH At point A, the radius of the circular track makes an angle heta with the horizontal. The center of the circular loop is at a height R from the lowest point. The vertical height of point A from the center of the loop is R . Thus, the tot