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) Well, the translational kinetic energy of a bowling ball can be calculated using the formula: KE = 1/2 * mass * velocity^2. Plugging in the values, we get KE = 1/2 * 7.45 kg * (2.56 m/s)^2 = 24.143 J. So the ball's translational kinetic energy is approximately 24.143 J.

(b) Now, let's calculate the rotational kinetic energy of the ball. The formula for rotational kinetic energy is: KE_rot = 1/2 * moment of inertia * angular velocity^2. Since there is no information given about the ball's angular velocity or moment of inertia, it's impossible to calculate the rotational kinetic energy. Sorry, this question is as tough to solve as trying to juggle bowling pins!

(c) To calculate the ball's total kinetic energy, you need to add up the translational and rotational kinetic energies. Unfortunately, since we couldn't figure out the rotational kinetic energy in the previous question, we'll have to just stick with the translational kinetic energy of 24.143 J as the ball's total kinetic energy. At least it's still a strikingly good amount of energy!

(d) When bringing the ball to rest, all its kinetic energy has to be dissipated in the form of work done against friction or any other opposing force. So the amount of work done on the ball would be equal to its initial kinetic energy. Therefore, the work done on the ball to bring it to rest would be approximately 24.143 J. It's like spending all your energy on the bowling alley, but hey, someone's gotta do the cleaning!

(a) To calculate the translational kinetic energy of the bowling ball, we can use the formula:

Translational kinetic energy = 1/2 * mass * velocity^2

Given that the mass of the ball is 7.45 kg and the velocity is 2.56 m/s, we can substitute these values into the formula:

Translational kinetic energy = 1/2 * 7.45 kg * (2.56 m/s)^2

Translational kinetic energy = 1/2 * 7.45 kg * 6.5536 m^2/s^2

Translational kinetic energy = 24.38168 J (rounded to five decimal places)

Therefore, the ball's translational kinetic energy is approximately 24.38168 J.

(b) To calculate the rotational kinetic energy of the bowling ball, we can use the formula:

Rotational kinetic energy = 1/2 * moment of inertia * angular velocity^2

Since the ball is rolling without slipping along a level surface, we can assume that the ball's rotational and translational motions are related by the equation:

Rotational kinetic energy = Translational kinetic energy / 2

Substituting the previously calculated translational kinetic energy into the formula:

Rotational kinetic energy = 24.38168 J / 2

Rotational kinetic energy = 12.19084 J (rounded to five decimal places)

Therefore, the ball's rotational kinetic energy is approximately 12.19084 J.

(c) The total kinetic energy of the ball is the sum of its translational and rotational kinetic energies:

Total kinetic energy = Translational kinetic energy + Rotational kinetic energy

Substituting the previously calculated values:

Total kinetic energy = 24.38168 J + 12.19084 J

Total kinetic energy = 36.57252 J (rounded to five decimal places)

Therefore, the ball's total kinetic energy is approximately 36.57252 J.

(d) To bring the ball to rest, all of its kinetic energy needs to be dissipated. Therefore, the amount of work done on the ball to bring it to rest is equal to its initial kinetic energy, which is the total kinetic energy calculated in part (c):

Work = Total kinetic energy

Work = 36.57252 J

Therefore, the amount of work that would have to be done on the ball to bring it to rest is 36.57252 J.

To calculate the answers to these questions, we need to use the formulas for translational kinetic energy, rotational kinetic energy, and work.

(a) Translational kinetic energy can be calculated using the formula:
Kinetic energy = (1/2) * mass * velocity^2

Given:
Mass of the ball (m) = 7.45 kg
Velocity of the ball (v) = 2.56 m/s

Applying the formula:
Translational kinetic energy = (1/2) * 7.45 kg * (2.56 m/s)^2
Translational kinetic energy ≈ 24.12 J

(b) Rotational kinetic energy can be calculated using the formula:
Rotational kinetic energy = (1/2) * moment of inertia * angular velocity^2

However, to calculate the moment of inertia, we need to know the ball's radius or a given value related to its shape.

(c) Total kinetic energy is the sum of translational and rotational kinetic energies. Since we don't have the value for rotational kinetic energy, we cannot calculate the total kinetic energy.

(d) Work done on an object is equal to its change in kinetic energy. In this case, the work done on the ball to bring it to rest would be equal to its initial kinetic energy.

Given:
Translational kinetic energy = 24.12 J

Therefore, to bring the ball to rest, the work done on it would be approximately 24.12 J.