Direction of reactions

[cipotilla]

Hello, there something that doesn't make sense to me in the attached problem, P16.3. You can see from the diagram that you will have two reculting reactions, RA and RB. According to what I know from statics, the reactions will be at the same angle theta as the incline of the plate, see my solution on page 2. Why does the book's author, solve the problem using reactions that are purely horizontal and purely vertical?

Thanks.

 

[Doc Al]

According to what I know from statics, the reactions will be at the same angle theta as the incline of the plate, see my solution on page 2.

Why do you think that?

Why does the book's author, solve the problem using reactions that are purely horizontal and purely vertical?

He doesn't. At the A end of the plate, the reaction force of the surface on the plate has both horizontal (friction, F) and vertical (normal force, $$N_A$$) components. The author identifies the horizontal component as friction, but it's still part of the overall force that the surface exerts on the plate.

At the B end, the surface is smooth so there is no vertical component of reaction force, only the horizontal normal force ($$N_B$$).