physics
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.
J
(b) Calculate the ball's rotational kinetic energy.
J
(c) Calculate the ball's total kinetic energy.
J
(d) How much work would have to be done on the ball to bring it to rest?
J

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 workKE 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=0Ki, W=Ki. Plug in the total kinetic energy (answer to C) and you find the work needed to be done.
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