A bowling ball has a mass of 7.00 kg,a moment of inertia of 2.80 × 10−² kg·m²,and a radius of 0.100 m.If it rolls down the lane without slipping at a linear speed of 4.00 m/s,what is its total kinetic energy? A)78.4 J B)22.4 J C)56.0 J D)40.0 J

Question

Quizplus · Accepted Answer

The total kinetic energy of the bowling ball is the sum of its translational kinetic energy and its rotational kinetic energy. The translational kinetic energy is given by 1/2 mv^2, where m is the mass of the ball and v is its linear speed. The rotational kinetic energy is given by 1/2 Iω^2, where I is the moment of inertia of the ball and ω is its angular speed. The angular speed of the ball is related to its linear speed by the equation ω = v/r, where r is the radius of the ball. Substituting these equations into the expression for the total kinetic energy, we get:K = 1/2 mv^2 + 1/2 I(v/r)^2= 1/2 (7.00 kg)(4.00 m/s)^2 + 1/2 (2.80 × 10−² kg·m²)(4.00 m/s / 0.100 m)^2= 78.4 JTherefore, the total kinetic energy of the bowling ball is 78.4 J.

A Bowling Ball Has a Mass of 7