Unformatted text preview: 94. (a) The x component of F tries to move the crate while its y component indirectly contributes to the inhibiting effects of friction (by increasing the normal force). Newton’s second law implies x direction: Fcosθ – fs = 0 y direction: FN – Fsinθ – mg = 0. To be “on the verge of sliding” means fs = fs,max = μsFN (Eq. 6-1). Solving these equations for F (actually, for the ratio of F to mg) yields → μs F = . mg cos θ − μ s sin θ
This is plotted on the right (θ in degrees). (b) The denominator of our expression (for F/mg) vanishes when
cos θ − μ s sin θ = 0 θinf = tan −1 1 μs 1 −1 For μ s = 0.70 , we obtain θ inf = tan μ = 55° . s (c) Reducing the coefficient means increasing the angle by the condition in part (b).
1 −1 (d) For μ s = 0.60 we have θ inf = tan μ = 59° . s ...
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