Abowler releases a bowling ball with no spin, sending it sliding straight down the alley toward the pins. the ball continues to slide for some distance before its motion becomes rolling without slipping; what is the magnitude of this distance? assume the ball maintains an essentially constant speed of 5.90 m/s and that the coefficient of kinetic friction for the polished alley is 0.105.

Time, t = 0.197 s

Solution:

As per the question:

Constant speed of the ball, v = 5.90 m/s

Coefficient of Kinetic friction,

Now,

the ball will initially rotate with some angular velocity and then slide without rolling.

Friction force, f =

where

N = mg = normal reaction

Thus

f =   (1)

Now, consider the ball to be a solid sphere,

Moment of inertia of the ball, I =       (2)

where

R = radius of the ball

Torque is given by:

         (3)

where

Thus from eqn (1), (2) and (3):

Now, the time taken is given by kinematic eqn:

t =

massxgravity x heght=weightxheight= pe

4900=490xh

h=10

neither accurate nor precise.