Question

Does the normal force of a block always equal the weight of the block? For example, a block on an incline?

Answer 1

Absolutely not. In the case of an inclined plane we can impose the following coordinate system and diagramThe equations of motion will be (\(\theta\) is the angle of inclination of the floor)\[\sum F_x =mg \sin \theta - f = ma\]\[\sum F_y = N-mg \cos \theta=0\] Then it is clear that the normal force is not the weight but is \(N=mg \cos \theta\). Moreover, using the usual model for the friction force \(f=\mu N\) were \(\mu\) is the coefficient of friction, the acceleration will be not g but \[a=g( sen \theta - \mu \cos \theta)\]