Ask Question
3 August, 11:10

A regulation basketball has a 32 cm diameter

and may be approximated as a thin spherical

shell.

How long will it take a basketball starting

from rest to roll without slipping 4.8 m down

an incline that makes an angle of 39.4◦ with

the horizontal? The acceleration of gravity is

9.81 m/s^2

Answer in units of s

+1
Answers (1)
  1. 3 August, 11:12
    0
    1.8 s

    Explanation:

    Potential energy = kinetic energy + rotational energy

    mgh = ½ mv² + ½ Iω²

    For a thin spherical shell, I = ⅔ mr².

    mgh = ½ mv² + ½ (⅔ mr²) ω²

    mgh = ½ mv² + ⅓ mr²ω²

    For rolling without slipping, v = ωr.

    mgh = ½ mv² + ⅓ mv²

    mgh = ⅚ mv²

    gh = ⅚ v²

    v = √ (1.2gh)

    v = √ (1.2 * 9.81 m/s² * 4.8 m sin 39.4°)

    v = 5.47 m/s

    The acceleration down the incline is constant, so given:

    Δx = 4.8 m

    v₀ = 0 m/s

    v = 5.47 m/s

    Find: t

    Δx = ½ (v + v₀) t

    t = 2Δx / (v + v₀)

    t = 2 (4.8 m) / (5.47 m/s + 0 m/s)

    t = 1.76 s

    Rounding to two significant figures, it takes 1.8 seconds.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “A regulation basketball has a 32 cm diameter and may be approximated as a thin spherical shell. How long will it take a basketball starting ...” in 📗 Physics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers