Question

In: Physics

A disc and solid sphere are both rolling without slipping so that both have a kinetic...

A disc and solid sphere are both rolling without slipping so that both have a kinetic energy of 294. What is the translational kinetic energy of the disc ? What is the translational kinetic energy of the solid sphere ?

Expert Solution

Mass of the disc = M₁

Radius of the disc = R₁

Moment of inertia of the disc = I₁ = M₁R₁²/2

Speed of the disc = V₁

Angular speed of the disc = ₁ = V₁/R

Total kinetic energy of the disc = E₁ = 294 J

Translational kinetic energy of the disc = E_1t

Rotational kinetic energy of the disc = E_1r

E_1r = 0.5E_1t

E₁ = E_1t + E_1r

294 = E_1t + 0.5E_1t

E_1t = 196 J

Mass of the solid sphere = M₂

Radius of the solid sphere = R₂

Moment of inertia of the solid sphere = I₂ = 2M₂R₂²/5

Speed of the solid sphere = V₂

Angular speed of the solid sphere = ₂ = V₂/R

Total kinetic energy of the solid sphere = E₂ = 294 J

Translational kinetic energy of the solid sphere = E_2t

Rotational kinetic energy of the solid sphere = E_2r

E_2r = 0.4E_2t

E₂ = E_2t + E_2r

294 = E_2t + 0.4E_2t

E_2t = 210 J

A) Translational kinetic energy of the disc = 196 J

B) Translational kinetic energy of the solid sphere = 210 J

genius_generous answered 7 months ago

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