1. The problem statement, all variables and given/known data A solid spherical ball of mass 0.75 kg and radius 5.0 cm is thrown onto a horizontal surface with coefficient of kinetic friction μ . It’s initial velocity at time t = 0 is horizontal and its initial angular velocity is zero. After rolling with slipping for a time t1 = 0.76 seconds, the ball begins to roll without slipping with angular speed ω1 = 120 rad/s. It continues to roll without slipping up a short ramp of height h = 16 cm What is the value of μ? 2. Relevant equations KE = .5mv^2 = 5Iω^2 f= μN T=Fr=Iα vf=vi +at 3. The attempt at a solution I was thinking about solving this problem with conservation of energy. .5mv^2 + .5Iω^2 - μmgd = .5mv^2 + .5Iω^2 However, we don't know the initial velocity, or the distance that the ball traveled with slipping. In order to solve for initial velocity I thought about using one of the four kinematic equations. However, for each of the equations where are at least 2 unknowns. So I also tried using forces to solve this problem as well. Acceleration due to friction f= μN ma= μN a=μg Rotational acceleration T=Fr=Iα α= 5μg / 2r Then I'd use the equation vf=vi +at and it's rotational equivalent. But this is where I'm stuck again, because there are also 2 unknown variables.