- #1
Alex126
- 84
- 5
Homework Statement
We have an object rotating inside a circular container. The rotation is vertical (see picture below).
The radius r of the container is given. Find the frequency (which then ties back to finding the centripetal acceleration) necessary, so that the objects rotating inside the container will fall down once they form a fixed/given angle α with the horizontal plane (the angle is 70°).
Homework Equations
Force (centripetal) = m*acceleration (centripetal)
Centripetal acceleration = v2/r
The Attempt at a Solution
I tried drawing the free-body diagram, and this is my best attempt:
F = centripetal force
W = weight force
R = reaction force
At first I actually thought of putting R (reaction force) perpendicular to the surface, i.e. in the same direction as F, but things just didn't add up. I watched several videos on this topic, and most of them just talked about "convenient/easy" positions inside the circle (at the very bottom, at the very top, or at "3/9 o'clock"). Just one video mentioned intermediate positions, which is the case with this problem.
That video said, and that's the way I've set up the problem, that you need to "deduce" the position of R (so R is NOT perpendicular to the tangent to the circle in the point where the object is), knowing that the sum of all forces must be equal to F. So I tried my best doing an accurate drawing, using the geometric vector sum rule (the parallelogram thing), summing F and -W to "deduce" R in the drawing.
I was then going to proceed summing the X and Y components to happily solve for a, and then I got stuck because I can't find any way to obtain the green angle in the figure, which seems necessary to calculate the Rx and Ry components.
The axis I was going to choose were +X axis in the same direction of F, and then +Y perpendicular to it and pointing "northwest" (up and left). That would have given me:
Y axis:
Ry - Wy = 0
X axis:
Rx + Wx = m*a
But, again, I can't seem to find the green angle to use for Ry and Rx.