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65. The force F (in Newtons) required to move a box of mass m kg in motion by pulling on an attached rope (Figure 32) is fmg cos 0 + f sin 0 where 0 is the angle between the rope and the horizontal, f is the coefficient of static friction, and g = 9.8 m/s?. Find the angle 0 that minimizes the required force F, assuming f = 0.4. Hint: Find the maximum value of cos 0 + f sin 0. F (0) = FIGURE 32

65. The force F (in Newtons) required to move a box of mass m kg in motion by pulling on an attached rope (Figure 32) is fmg cos 0 + f sin 0 where 0 is the angle between the rope and the horizontal, f is the coefficient of static friction, and g = 9.8 m/s?. Find the angle 0 that minimizes the required force F, assuming f = 0.4. Hint: Find the maximum value of cos 0 + f sin 0. F (0) = FIGURE 32

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.3: Vectors In The Plane
Problem 11ECP
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65. The force F (in Newtons) required to move a box of mass m kg in motion by pulling on an attached rope (Figure 32) is fmg cos 0 + f sin 0 where 0 is the angle between the rope and the horizontal, f is the coefficient of static friction, and g = 9.8 m/s?. Find the angle 0 that minimizes the required force F, assuming f = 0.4. Hint: Find the maximum value of cos 0 + f sin 0. F (0) = FIGURE 32
Transcribed Image Text:65. The force F (in Newtons) required to move a box of mass m kg in motion by pulling on an attached rope (Figure 32) is fmg cos 0 + f sin 0 where 0 is the angle between the rope and the horizontal, f is the coefficient of static friction, and g = 9.8 m/s?. Find the angle 0 that minimizes the required force F, assuming f = 0.4. Hint: Find the maximum value of cos 0 + f sin 0. F (0) = FIGURE 32
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