Suppose F , F_N , and f represent the magnitudes of the contact force, normal force, and friction exerted by one surface on another kept in contact. If none of these values is zero,

Step-by-step solution

The contact force F is the vector sum of the normal force F_N and the friction force f . Since the normal force and friction are perpendicular to each other, the magnitude of the contact force is given by F = F_N^2 + f^2 . Since neither F_N nor f is zero, we have F^2 = F_N^2 + f^2 > f^2 F > f . Similarly, F^2 = F_N^2 + f^2 > F_N^2 F > F_N . Squaring the sum of the magnitudes gives (F_N + f)^2 = F_N^2 + f^2 + 2F_N f . Since 2F_N f > 0 , we get (F_N + f)^2 > F^2 F Squaring the difference gives (F_N - f)^2 = F_N^2 + f