Question

The figure on the right illustrates a ball which is a uniform solid sphere having mass M and radius R. The ball is initially traveling in the positive direction with pure translational motion along a friction-less region of a horizontal surface (i.e. it slips with angular speed ω0-0). The initial translational speed of the ball is Vo. The friction-less region extends to a region having coefficient of kinetic friction Figure for WAH #10 V. Friction Friction-less No longer slipping ' While in the friction region, the ball travels a distance D for a time interval At while experiencing frictional torque, Tr and angular acceleration, α, such that it rolls while slipping, while also undergoing an angular displacement Δθ and translational acceleration acm After traveling the distance D, the angular and translational speeds become synchronized and the friction force becomes zero. Thus, ignoring the effects of rolling resistance, the ball continues to roll without slipping with constant translational speed Vf and constant angular speed of. While the friction force is applied, rotational work, Wrot, is done which results in a change in the rotational kinetic energy, дКЕд, and translational work. Wtran, is done which results in a change in the translational kinetic energy, AKEtran. The net loss of kinetic energy of the ball results in a corresponding increase of thermal energy ΔΕ.herm 2) Determine expressions for the following: a) D {ν, μ, g); c) Wrot, and ΔΚΕ,ot M, Vo) and show that they are equal; d) Wtran, and AKEtran M, Vo} and show that they d e) ΔΕtherm M, Vo) and the % of the initial kinetic energy lost to heat. b) Δθ { R, Vo, μ, g); are equal: an

Answer 1

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c) nitia nesgy 2 つ, MU 19 98 frnel chesg heat 25 93 MU MU Cs Scanned with CamScanner