I need help with the following problem. It states that a ball is rolling on the

Question

I need help with the following problem. It states that a ball is rolling on the ground (the ground has friction). The mass of the ball is 6g (radius is 2cm). The problem only includes the translational velocity, which is 2 m/s (angular velocity is unknown). How far would it have to travel in order to not experience reverse or forward rolling? Also, static coefficient = 0.5; kinetic coefficient = 0.3

I don't know where to start. I just know that Newton's law (F=ma) and torque would have to be considered. Thanks!

Explanation / Answer

    The ball has energy in two forms, translational k.e. and rotational k.e.    KT   =   (1/2) * m * v2             =   0.5 * 6 * 10-3 * 22             =   1.20 * 10-2    J    KR   =   (1/2) * I * 2    I   =  (2/5) * m * r2          =   0.40 * 6 * 10-3 * 0.022          =   9.60 * 10-7   kg-m2       =   v / r          =   2 / 0.02          =   100   rad/s    KR   =   0.5 * 9.60 * 10-7 * 1002             =   4.80 * 10-3   J    Total k.e.   K   =   KT +   KR                            =   1.20 * 10-2   +   4.80 * 10-3                            =   1.68 * 10-2     J    When the ball comes to complete halt, its k.e. must be lost against friction.    K   =   W          =   Force of friction * distance          =   kinetic * m * g * d    1.68 * 10-2   =   0.3 * 6 * 10-3 * 9.8 * d    distance covered   d   =   1.68 * 10-2 / 1.764 * 10-2                                       =   0.952   m                                        =   95.2   cm

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