Asked by Joey
In the figure below, a solid cylinder of radius 12 cm and mass 11 kg starts from rest and rolls without slipping a distance L = 6.0 m down a roof that is inclined at angle è = 30°.
(a) What is the angular speed of the cylinder about its center as it leaves the roof?
1 rad/s
(b) The roof's edge is at height H = 5.0 m. How far horizontally from the roof's edge does the cylinder hit the level ground?
2 m
(a) What is the angular speed of the cylinder about its center as it leaves the roof?
1 rad/s
(b) The roof's edge is at height H = 5.0 m. How far horizontally from the roof's edge does the cylinder hit the level ground?
2 m
Answers
Answered by
drwls
Are 1 rad/s and 2 m your answers?
(a) I suggest you apply conservation of energy. The total kinetic energy is the sum of (1/2) M V^2 and (1/2) I w^2. where w = V/R.
w is the angular speed.
M g *L sin 30 = (1/2) M V^2 and (1/2) I w^2
= (1/2) M (Rw)^2 and (1/2)(1/2)MR^2) w^2
Solve for w. M cancels out
(b) Multiply the horizontal component of the velocity at the end of the roof by the time it takes to fall a distance H. Note that is leaves the roof with a downward velocity component.
(a) I suggest you apply conservation of energy. The total kinetic energy is the sum of (1/2) M V^2 and (1/2) I w^2. where w = V/R.
w is the angular speed.
M g *L sin 30 = (1/2) M V^2 and (1/2) I w^2
= (1/2) M (Rw)^2 and (1/2)(1/2)MR^2) w^2
Solve for w. M cancels out
(b) Multiply the horizontal component of the velocity at the end of the roof by the time it takes to fall a distance H. Note that is leaves the roof with a downward velocity component.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.