physics

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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

  • physics -

    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.

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