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Mashutka [201]
4 years ago
8

13. A solid sphere is rolling without slipping along a horizontal surface with a speed of 5.50

Physics
1 answer:
9966 [12]4 years ago
5 0

Answer:

E) 3.53 m/s

Explanation:

KE₁ + RE₁ = KE₂ + RE₂ + PE

½ mv₁² + ½ Iω₁² = ½ mv₂² + ½ Iω₂² + mgh

For a sphere, I = ⅖ mr²

½ mv₁² + ½ (⅖ mr²) ω₁² = ½ mv₂² + ½ (⅖ mr²) ω₂² + mgh

½ mv₁² + ⅕ mr² ω₁² = ½ mv₂² + ⅕ mr² ω₂² + mgh

Rolling without slipping means v = ωr.

½ mv₁² + ⅕ mv₁² = ½ mv₂² + ⅕ mv₂² + mgh

⁷/₁₀ mv₁² = ⁷/₁₀ mv₂² + mgh

⁷/₁₀ v₁² = ⁷/₁₀ v₂² + gh

Substitute:

⁷/₁₀ (5.50 m/s)² = ⁷/₁₀ v₂² + (9.8 m/s²) (3.00 m sin 25.0°)

v₂ = 3.53 m/s

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