Need help in determining normal force the question is from ss krotov

[ishanp]

cylinder of mass m and radius r rests on two supports of same height. one is fixed other slides with velocity v.determine normal force N by the cylinder on stationary support at the moment when distance between the point of contacts A and B of cylinder and support) is r√2assuming supports were very close to each other at the initial moment. friction between cylinder and support should be neglected.


my attempt;

r^2 +r^2=(r√2)^2

since friction is neglected the forces exerted on cylinder by supports are always normal to its surface they do zero work. only graviy does work on it. since the triangle formed by radii and AB is rt angled other angles are of 45 degree. work done till that moment=mg(r-r√2/2) . i think that the cylinder rolls without slipping about point of contact with stationary axis(A). moment of inertia about it is 3/2mr^2.if i take v=rω and put work equal to KE will get v of centre of mass and then since com moves in circle centered at A
mgcos45-N=mv^2/r ans is not coming
it is my first post here . thanks

 

[ishanp]

cylinder of mass m and radius r rests on two supports of same height. one is fixed other slides with velocity v.determine normal force N by the cylinder on stationary support at the moment when distance between the point of contacts A and B of cylinder and support) is r√2assuming supports were very close to each other at the initial moment. friction between cylinder and support should be neglected.


my attempt;

r^2 +r^2=(r√2)^2

since friction is neglected the forces exerted on cylinder by supports are always normal to its surface they do zero work. only graviy does work on it. since the triangle formed by radii and AB is rt angled other angles are of 45 degree. work done till that moment=mg(r-r√2/2) . i think that the cylinder rolls without slipping about point of contact with stationary axis(A). moment of inertia about it is 3/2mr^2.if i take v=rω and put work equal to KE will get v of centre of mass and then since com moves in circle centered at A
mgcos45-N=mv^2/r ans is not coming
it is my first post here . thanks

problem is 1.45
solution at back says horizontal component of cylinder's velocity is v/2 .
i don't know how