posted by alba .
A bowling ball of mass 7.45 kg is rolling at 2.56 m/s along a level surface.
(a) Calculate the ball's translational kinetic energy.
(b) Calculate the ball's rotational kinetic energy.
(c) Calculate the ball's total kinetic energy.
(d) How much work would have to be done on the ball to bring it to rest?
A- Translational KE, or Kt, = (1/2)mv^2. Plug in the mass and velocity.
B- Rotational KE, or Kr, = (1/2)Iw^2. Taking the ball's point of contact with the ground as the reference point, the moment of inertia I is (2/5)mr^2+mr^2 (due to the parallel axis theorem and that a solid sphere has a moment of inertia of (5/2)mr^2). Also, v=rw, so w=v/r, so w^2 = v^2/r^2. Plug this into the Kr equation and simplify and you will get:
Kr=(7/10)mv^2. plug in mass and velocity to get Kr.
C- The total kinetic energy is the answer to A plus the answer to B.
D- Due to the work-KE theorem we have W=Kfinal - Kinitial. If the Kfinal is zero because we are trying to stop the ball and when it is stopped KE=0, then W=0-Ki, W=-Ki. Plug in the total kinetic energy (answer to C) and you find the work needed to be done.