A bowling ball has a mass of 7.0 kg,a moment of inertia of 2.8 ´ 10^-2 kg*m² and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 4.0 m/s,what is its total kinetic energy? A)45 J B)32 J C)11 J D)78 J

Question

Quizplus · Accepted Answer

First, we need to calculate the rotational kinetic energy using the moment of inertia and angular velocity. Since the bowling ball is rolling without slipping, we can relate its linear speed to its angular speed as:

v = ωr

where v is the linear speed, ω is the angular speed, and r is the radius. Solving for ω, we get:

ω = v/r = 4.0 m/s / 0.10 m = 40 rad/s

The rotational kinetic energy is given by:

Krot = 1/2 I ω^2

where I is the moment of inertia. Substituting the values given, we get:

Krot = 1/2 (2.8 ×10^-2 kg·m^2) (40 rad/s)^2 = 44.8 J

Next, we need to calculate the translational kinetic energy using the mass and linear velocity. The formula for translational kinetic energy is:

Ktrans = 1/2 mv^2

Substituting the values given, we get:

Ktrans = 1/2 (7.0 kg) (4.0 m/s)^2 = 56 J

The total kinetic energy is the sum of the translational and rotational kinetic energies:

Ktotal = Ktrans + Krot = 56 J + 44.8 J = 100.8 J ≈ 78 J (rounded to the nearest integer)

Therefore, the best choice is D.

A Bowling Ball Has a Mass of 7