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A book of mass M is positioned against a vertical wall. The coefficient of friction between the book and the wall is μ. You wish to keep the book from falling by pushing on it with a force F applied at an angle θ with respect to the horizontal (−π/2 < θ < π/2), as shown in the figure. (a) For a given θ, what is the minimum F required? (b) For what θ is this minimum F the smallest? What is the corresponding minimum F? Answers a) Fmin = Mg μscos⁡θ+sin⁡θ b) θ = tan−1 ⁡1/μs, Fmin = Mg μs2+1

A book of mass M is positioned against a vertical wall. The coefficient of friction between the book and the wall is μ. You wish to keep the book from falling by pushing on it with a force F applied at an angle θ with respect to the horizontal (−π/2 < θ < π/2), as shown in the figure. (a) For a given θ, what is the minimum F required? (b) For what θ is this minimum F the smallest? What is the corresponding minimum F? Answers a) Fmin = Mg μscos⁡θ+sin⁡θ b) θ = tan−1 ⁡1/μs, Fmin = Mg μs2+1

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A book of mass M is positioned against a vertical wall. The coefficient of friction between the book and the wall is μ . You wish to keep the book from falling by pushing on it with a force F applied at an angle θ with respect to the horizontal ( − π / 2 < θ < π / 2 ) , as shown in the figure. (a) For a given θ , what is the minimum F required? (b) For what θ is this minimum F the smallest? What is the corresponding minimum F ?
Answers a) F min = M g μ s cos ⁡ θ + sin ⁡ θ b) θ = tan − 1 ⁡ 1 μ s , F min = M g μ s 2 + 1

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