Question

A 14 lb bowling ball is thrown onto a lane with a backspin angular speed of 10 rad/s and forward velocity of 25 ft/s. After a few seconds, the ball starts rolling without slip and forward velocity of 17.2 ft/s and angular velocity of 48.6 rad/s. The ball has a mass moment of inertia of 0.0204 slugs-ft2. Determine the work done by friction on the ball from the initial time until when it starts rolling without slip.

Answer 1

`W_(loss) = 47.368\,J`

Step-by-step explanation:

The situation is modelled after the Principle of Energy Conservation and Work-Energy Theorem:

`K_(t.1) - K_(t,2) + K_(r,1) - K_(r,2) = W_(loss)`

`W_(loss)=(1)/(2)\cdot (0.428\,slug)\cdot \left[\left(25\,(ft)/(s) \right)^(2)-\left(17.2\,(ft)/(s) \right)^(2)\right] + (1)/(2)\cdot \left(0.0204\,slug\cdot ft^(2)\right)\cdot \left[\left(10\,(rad)/(s) \right)^(2)-\left(48.6\,(ft)/(s) \right)^(2)\right]`

`W_(loss) = 47.368\,J`