In the figure, a solid cylinder of radius 21 cm and mass 24 kg starts from rest
ID: 1910953 • Letter: I
Question
In the figure, a solid cylinder of radius 21 cm and mass 24 kg starts from rest and rolls without slipping a distance L = 4.4 m down a roof that is inclined at angle ? = 20?. (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 = 3.5 m. How far horizontally from the roof's edge does the cylinder hit the level ground?
In the figure, a solid cylinder of radius 21 cm and mass 24 kg starts from rest and rolls without slipping a distance L = 4.4 m down a roof that is inclined at angle ? = 20?. (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 = 3.5 m. How far horizontally from the roof's edge does the cylinder hit the level ground?Explanation / Answer
a) conservation of energy Ei = m g L sin theta Ef = 1/2 mv^2 + 1/2 I w^2 = 1/2 m (w r)^2 + 1/2 (1/2 m r^2) w^2 =3/4 m r^2 w^2 Ei = Ef 9.81m/s^2*4.4m*sin(20) = 3/4 * (.21m)^2 w^2 w=21.13 rad/s b) when it leaves the roof it has a speed in y and x first do y direction y = y0 + v0y t -1/2 gt^2 0 = 3.5 m + (-21.131/s *.21m *sin(20) ) t - 0.5*9.81m/s^2*t^2 t=0.704 s now x direction x = v0x t = 21.13 1/s*.21m*cos(20)*0.704s=2.94 m
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