- Homework Statement
- A circle with a radius R lies in the vertical plane. A bead falling under gravity moves from A( the top point) to B ( an antipodal point to A), Moving a long the diameter. Now consider a separate bead, such a bead leaves A at an angle W from the vertical and moves a long a cord to a point C. Prove that both beads take the same time to complete their respective journeys.
- Relevant Equations
- g=9.81ms^-2 j is the y unit vector , i the x unit vector
I can evaluate the first beads motion easily A to B is -2Rj considering the point B as y=0 the motion of the bead will be -gt^2/2+2R=0 which implies t=2√(R/G) , this is ok but what I am struggling with is A to C I can see that the angle between the beads weight and it's negative normal force is W-90 as (180=180-W + 90 + (the new angle=L), given this I can derivate that the acceleration moving down the plane is gsin(L)=gsin(W-90)=-gcos(W) now the motion of this bead need be -1/2(gcos(w))t^2+2R=C(J) I can also see that A to C= A to O + O to C= -R + O to C, I can't find the Y coordinated of C. If you see a flaw in my reason please point it out.