Question

Let F, F_N and f denote the magnitudes of the contact force, normal force and the friction exerted by one surface on the other kept in contact. If none of these is zero.
(a) F > F_N
(b) F > f
(c) F_N > f
(d) F_N − f < F < F_N + f.

Answer 1

(a) F > F_N
(b) F > f
(d) F_N − f < F < F_N + f

The system is in equilibrium condition when F = f.
Hence, the net horizontal force is zero.
f = μF_N
F > F_N
f = F_N and 0 ≤ μ ≤ 1
Therefore, we can say that F > f. So the net horizontal force is nonzero.
F > f, and so the net horizontal force is zero.
F_N > f ⇒ F_N > μF_{N ⇒} μ < 1
Here, the given relation between F and f i.e 
F > f and f = μF_N  will not be satisfied So it cannot be said that the net horizontal force is zero or nonzero.
F_N − f < F < F_N + f
∵ f = μF_N

`f/mu-f<F<f/mu+f`
`f((1-mu)/mu)<F<f((1+mu)/mu)`

For the above relation, we can say that F ≠ f and so the net horizontal force is nonzero.