Question

a bowling ball of mass 7.3 kg and radius 9.6 cm rolls without slipping down a lane at 3.1 m/s . part a calculate its total kinetic energy. express your answer using two significant figures.

Answer 1

49 J   is the total kinetic energy. If a bowling ball of mass 7.3 kg and radius 9.6 cm rolls without slipping down a lane at 3.1 m/s. Kinetic energy is the energy an bowling ball has because of its motion.

Given:    m = 7.3 Kg ;  r = 9.4 cm = 0.094 m   ;   v = 3.1 m

Now total kinetic energy in this case is given by KE = Kinetic energy due to rotation  + Kinetic energy due to translation

i,e     KE = 1/2*m*v2   +   1/2*I*ω2      where   I is the moment of inertia of the bowling ball about it's center and ω is the angular velocity

Now for pure rotation (without slipping)    v = rω  

also for the ball (solid sphere)  I = 2/5*m*r2

Hence our kinetic energy becomes  

 KE = 1/2*m*v2 +  1/5*m*v2 = 7/10*m*v2

so   KE = 0.7*7.3*(3.1)2 = 49.10 J = 49 J

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