Respuesta :
The distance travelled by the bowling ball is 18.6566 ft
Circumference = 2πr = 27
Weight of the ball = 14 lb
Radius of gyration = 3.28
Velocity = rω = 20 ft/s
Coefficient of friction = 0.20
Total force on y axis= 0, therefore N = W
= F = μN = μW
and, ∑M = Iα
Hence,
= Fr = Iα
Total force on x axis = 0,
= F = ma = μW
= a = μg
Combining all the equations,
= Fr = Iα
= μWr = mk²α
= α = (μgr) / k²
If initial velocity = 0 then, ω = αt
= ω = αt = [ (μgr) / k² ] t
= t = (vk²) / (μgr²)
Now, v = u + αt
= v - u = (μg) + (vk²) / (μgr²)
= u = v [ 1 +(k²/r²) ]
Distance travelled by the ball = s =
= v² = u² - 2αs
= ( u² ) / [ 1 +(k²/r²) ] ² = u² - 2μgs
= s = (u²/2μg) [1 - (1/(1 + (k²/r²))²)]
= s = 18.6566 ft
To know more about Friction:
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