In the figure, a solid cylinder of radius 15 cm and mass 14 kg starts from rest

Question

In the figure, a solid cylinder of radius 15 cm and mass 14 kg starts from rest and rolls without slipping a distance L = 6.0 m down a roof that is inclined at angle = 27°. (a) What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof's edge is at height H = 4.4 m. How far horizontally from the roof's edge does the cylinder hit the level ground?

In the figure, a solid cylinder of radius 15 cm and mass 14 kg starts from rest and rolls without slipping a distance L 6.0 m down a roof that is inclined at angle 6 270. (a) What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof's edge is at height H 4.4 m. How far horizontally from the roof's edge does the cylinder hit the level ground? (a) Number Units (b) Number Units click if you would like to show work for this question Open Show Work

Explanation / Answer

eight of cylinder above the roof = 6 sin 27 = 2.724 m apprx

using conservation of energy

mgh= 1/2mv^2 + 1/2 Iw^2

I for cylinder = 1/2 mr^2, w= v/r

mgh = 1/2 mv^2 + 1/2 ( 1/2 mr^2) ( v^2/r^2)

gh = 1/2 v^2 + 1/4 v^2

9.8 ( 2.724) = v^2 ( 0.75)

v= 5.966 m/s

a) angular speed= 5.966/ ( 0,15) = 39.77 rad/ sec apprx

b)time to cover a height of 4.4 m = sqroot ( 2 x 4.4/ 9.8) = 0.947 sec apprx

horizontal distance = 5.966 ( 0.947) =5.653 m apprx

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