Resolving in the vertical direction and along the direction of the normal force

[influx]

Ok I know this is simple resolving but I'm a bit confused. If we resolve forces in the vertical y direction (as in the attached image), we obtain Rcos(theta)-W=0 and hence Rcos(theta) = W meaning R = W/cos(theta) [where theta = 18 degrees]

However, if we resolve forces along the direction of the normal force, R, we obtain R - Wcos(theta) = 0 and hence R = Wcos(theta) [again theta=18]. These 2 results for R appear to contradict so what have I done wrong?

Cheers

 

[PhanthomJay]

View attachment 82057
Ok I know this is simple resolving but I'm a bit confused. If we resolve forces in the vertical y direction (as in the attached image), we obtain Rcos(theta)-W=0 and hence Rcos(theta) = W meaning R = W/cos(theta) [where theta = 18 degrees]

However, if we resolve forces along the direction of the normal force, R, we obtain R - Wcos(theta) = 0 and hence R = Wcos(theta) [again theta=18]. These 2 results for R appear to contradict so what have I done wrong?

Cheers

The first approach as per the solution is correct, since there is no acceleration or component thereof in the vertical direction.

The second approach is incorrect, because if you resolve forces along the normal direction, the acceleration is not 0 in the normal direction; there is a component of the radial acceleration in that direction, so equilibrium does not apply in that direction normal to the plane.

 

[influx]

The first approach as per the solution is correct, since there is no acceleration or component thereof in the vertical direction.

The second approach is incorrect, because if you resolve forces along the normal direction, the acceleration is not 0 in the normal direction; there is a component of the radial acceleration in that direction, so equilibrium does not apply in that direction normal to the plane.

Ah I see. With radial acceleration you are referring to a_n right?

 

[PhanthomJay]

Ah I see. With radial acceleration you are referring to a_n right?

Yes, right.