The conical pendulum (1 Viewer)

[YBK]

hey this is questions 4 from the cambridge book, I don't get how you get the radius of the string (if it's needed anyway) and then do the problem..

The base of a hollow cone of semi-vertical angle 30degrees is fixed to a horizontal table. Two particles each of mass m are connected by a light inextensible string which passes through a small smooth hole in the vertex C of the cone. One particle A hangs at rest inside the cone while the other particle B moves on the outer smooth surface of the cone in a horizontal circle with centre A. Find

a) the tensions in the strings and the normal reaction of the cone on B
b) the angular velocity of B


hmmm.. all i could get was that T for one of the strings is mg.

thanks for any help

 

[bboyelement]

remember that the reaction force N is always perpendicular to the surface ... hence its 90 degrees to the tension of the string at B ... also you have to take into consideration of mg straight down ...

therefore forces on B should be

vertical T(1)cos30 + Nsin30 = mg

horizontal T(1)sin30 - Ncos30 = mrw^2

forces on A is

T(2) = mg


http://users.tpg.com.au/adslvdoo/untitled.JPG - for diagram of forces on B

a) cos30 = root[3]/2 sin30 = 1/2

T(1)*root[3]/2 + N/2 = mg

since T(1) = T(2) = mg

mg*root[3]/2 + N/2 = mg

N = mg(2-root[3])

for the radius let the length from BC = L at the top its 30 degrees ... so we know that the from our exact triangle that r = L/2 and r is needed to do part b

 

[YBK]

thanks.. but I don't really understand it yet