Figure (10-E15) shows a small spherical ball of mass m rolling down the 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. (a) Find the kinetic energy of the ball when it is at a point A where the radius makes an angle θ with the horizontal. (b) Find the radial and the tangential accelerations of the center when the ball is at A. (c) Find the normal force and the frictional force acting on the ball if H = 60 cm, R = 10 cm, θ = 0 and m = 70 g.

Figure (10-E15) shows a small spherical ball of mass m rolling down the 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.
(a) Find the kinetic energy of the ball when it is at a point A where the radius makes an angle θ with the horizontal.

(b) Find the radial and the tangential accelerations of the center when the ball is at A.

(c) Find the normal force and the frictional force acting on the ball if H = 60 cm, R = 10 cm, θ = 0 and m = 70 g.

Given:

Mass of the ball = m, radius of the circular path= R

Kinetic energy=

According to the question

c) at θ= 0 degree, the normal force is given as

Frictional force f is

f= mg - ma

= 0.07(10) – 0.70 (5/7) (10) = 0.2N

1