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 =

kinetic

i'm so sorry if this is wrong i'm only in 6th grade xd

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards