QuestionDetails: Imagine Spaceman Spiff spits his gum, mass 15 g, withspeed 8.0

Question

QuestionDetails: Imagine Spaceman Spiff spits his gum, mass 15 g, withspeed 8.0 m/s. The gum hits and sticks to the small stem of hisfloating Jack-o-Lantern (mass 1.5 kg, radius 20 cm, assume an emptyspherical shell, and ignore the very minor contribution of the stemto the pumpkin's moment of inertia). Describe the motion ofthe Jack-o-Lantern and gum, in terms of transitional center of massspeed, vf cm, and the angularspeed, , in revolutions per second. (Take the referencepoint, O (the pumpkin's nose), to be the initial position of thecenter of the Jack-o-Lantern.

Explanation / Answer

kinetic energy of the gum completely transfers to the jackafter hitting the jack , the jack will pocesses both transilational and rotationalkinetic energy                   mv^2 /2 = I^2 / 2 + MV^2 / 2                   mv^2 /2 = I(V/r)^2 / 2 + MV^2 / 2          M = mass ofthe jack          V = linearvelocity of the jack         m= mass of thegum         v = velocity of thegum before hitting the jacj         r = radius of thejack         I = moment ofinerta of the jack = Mr^2 / 2 . plugging in the known values we can solve for thelinear velocity ' V ' of the jack ans hence angularveloctiy of the jack = V/r                           from the above equation we can solve for the velocity ofthe jack     

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