Determining Normal Forces for Particle P

[songoku]

Homework Statement

Particle P has a mass of 1 kg and is confined to move along the smooth vertical slot due to the rotation of the arm AB. Assume that at the instant as shown, the acceleration of particle P is 2.46 ms^-2 upward. Determine the normal force N_rod on the particle by the rod and the normal force N_slot on the particle by the slot in the position shown. Friction forces are negligible.

Homework Equations

F = ma

The Attempt at a Solution

I think that the N_slot is directed out of the page and equals to W so N_slot = 1*9.8 = 9.8 N

Then, N_rod is directed to the top left and is perpendicular to AB. So, N_rod can be projected to N_rod cos 30^o directed vertically. Hence :
N_rod cos 30^o = m*a
N_rod = 2.84 N

But there is no such answer in the multiple choices...

Thanks

 

[ehild]

Nslot is normal to the walls of the slot, so it is in-plane and horizontal. As for Nrod, you are right, Nrod is perpendicular to AB, but there is the weight of the body which is vertical and points downward.

ehild

 

[songoku]

Hi ehild

Ok I think that Nslot is the projection of the normal force in horizontal direction and yes I forgot to take the weight into account. I think I figure out the answer

Thanks a lot !