Why Do Reactions Differ in Problem P16.3 Compared to Standard Statics?

[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 ($$N_B$$).

 

[m2003]

I understand your confusion regarding the direction of reactions in problem P16.3. It is important to note that the direction of reactions can vary depending on the specific problem and the assumptions made by the author. In this case, the author may have assumed that the incline of the plate is very small and can be considered as a flat surface. In this scenario, the reactions RA and RB can be considered purely horizontal and vertical without significantly impacting the accuracy of the solution. Additionally, solving for purely horizontal and vertical reactions may simplify the solution and make it easier to understand for the intended audience. However, it is always important to critically analyze the assumptions and reasoning behind the solution presented in any problem in order to fully understand the underlying principles and concepts. I hope this explanation helps to clarify the direction of reactions in problem P16.3.