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A solid sphere is released from height h from the top of an incline making an angle θ with the horizontal. (a) Calculate the speed of the sphere when it reaches the bottom of the incline in the case that it rolls without slipping. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)

Respuesta :

The speed of the sphere when it reaches the bottom of the incline in the case that it rolls without slipping is; v = √(¹⁰/₇gh)

Conservation of Energy

Using the concept of conservation of energy, we will have the following equation;

Kinetic Energy + Rotational Kinetic energy = Potential Energy

⇒ ¹/₂mv² + ¹/₂Iω² = mgh

where I is moment of inertia and formula for moment of inertia of the solid sphere is; I = ²/₅mr²

Also, we know that ω = v/r

Thus;

¹/₂mv² + ¹/₂(²/₅mr²)(v²/r²) = mgh

This will reduce to;

¹/₂v² + ¹/₅v² = gh

⇒ ⁷/₁₀v² = gh

⇒ v² = 10gh/7

v = √(¹⁰/₇gh)

Read more on conservation of energy at; https://brainly.com/question/11549071

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