In the setting of Exercise 67, show that for any the minimal force required is proportional

In the setting of Exercise 67, show that for any ƒ the minimal force required is proportional to 1/√1 + ƒ².

Data From Exercise 67 

The force F (in Newtons) required to move a box of mass m kg in motion by pulling on an attached rope (Figure 33) is

where θ is the angle between the rope and the horizontal, ƒ is the coefficient of static friction, and g = 9.8 m/s². Find the angle θ that minimizes the required force F, assuming ƒ = 0.4. Find the maximum value of cos θ + ƒ sin θ.

Transcribed Image Text:

F(0) = fmg cos 0 + f sin 0