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
To answer these questions, we need to understand the concepts of translational kinetic energy, rotational kinetic energy, and total kinetic energy.
(a) Translational kinetic energy is the energy an object possesses due to its motion in a straight line. It is calculated using the formula:
Translational Kinetic Energy = (1/2) * mass * velocity^2
Plugging in the values given:
Translational Kinetic Energy = (1/2) * 7.45 kg * (2.56 m/s)^2
Translational Kinetic Energy = 24.352 J
Therefore, the ball's translational kinetic energy is 24.352 J.
(b) Rotational kinetic energy is the energy an object possesses due to its rotational motion. For a solid sphere like a bowling ball, the rotational kinetic energy is calculated using the formula:
Rotational Kinetic Energy = (1/2) * moment of inertia * angular velocity^2
The moment of inertia for a solid sphere is given by the formula: moment of inertia = (2/5) * mass * radius^2
Since the question doesn't provide the radius of the bowling ball, we cannot calculate the exact rotational kinetic energy.
(c) Total kinetic energy is the sum of translational kinetic energy and rotational kinetic energy:
Total Kinetic Energy = Translational Kinetic Energy + Rotational Kinetic Energy
Since we only have the translational kinetic energy, we cannot calculate the total kinetic energy without knowing the rotational kinetic energy as well.
(d) To bring the ball to rest, we need to remove all its kinetic energy. The work done to bring the ball to rest is equal to its initial kinetic energy. Therefore, the work done on the ball to bring it to rest is equal to its translational kinetic energy:
Work Done = Translational Kinetic Energy = 24.352 J
Therefore, the work done on the ball to bring it to rest is 24.352 J.