Question-159675

Question Number 159675 by Tawa11 last updated on 19/Nov/21

Commented by mr W last updated on 20/Nov/21

$${i}\:{remember}\:{this}\:{question}\:{is}\:{not}\:{asked} \\ $$$${for}\:{the}\:{first}\:{time}. \\ $$

Commented by Tawa11 last updated on 20/Nov/21

Wow, I really appreciate sir. I understand very well.

$$\mathrm{Wow},\:\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{understand}\:\mathrm{very}\:\mathrm{well}. \\ $$

Answered by mr W last updated on 20/Nov/21

Commented by mr W last updated on 20/Nov/21

(a) N=mg cos θ F=mg sin θ−μN=mg(sin θ−μ cos θ)

$$\left({a}\right) \\ $$$${N}={mg}\:\mathrm{cos}\:\theta \\ $$$${F}={mg}\:\mathrm{sin}\:\theta−\mu{N}={mg}\left(\mathrm{sin}\:\theta−\mu\:\mathrm{cos}\:\theta\right) \\ $$

Commented by mr W last updated on 20/Nov/21

Commented by mr W last updated on 20/Nov/21

(b) N=mg cos θ F=mg sin θ+μN=mg(sin θ+μ cos θ)

$$\left({b}\right) \\ $$$${N}={mg}\:\mathrm{cos}\:\theta \\ $$$${F}={mg}\:\mathrm{sin}\:\theta+\mu{N}={mg}\left(\mathrm{sin}\:\theta+\mu\:\mathrm{cos}\:\theta\right) \\ $$

Commented by mr W last updated on 20/Nov/21

Commented by mr W last updated on 20/Nov/21

(c) N=mg cos θ+F sin θ F cos θ=mg sin θ+μN=mg sin θ+μ(mg cos θ+F sin θ) F(cos θ−μ sin θ)=mg (sin θ+μcos θ) F=((mg (sin θ+μcos θ))/(cos θ−μ sin θ))

$$\left({c}\right) \\ $$$${N}={mg}\:\mathrm{cos}\:\theta+{F}\:\mathrm{sin}\:\theta \\ $$$${F}\:\mathrm{cos}\:\theta={mg}\:\mathrm{sin}\:\theta+\mu{N}={mg}\:\mathrm{sin}\:\theta+\mu\left({mg}\:\mathrm{cos}\:\theta+{F}\:\mathrm{sin}\:\theta\right) \\ $$$${F}\left(\mathrm{cos}\:\theta−\mu\:\mathrm{sin}\:\theta\right)={mg}\:\left(\mathrm{sin}\:\theta+\mu\mathrm{cos}\:\theta\right) \\ $$$${F}=\frac{{mg}\:\left(\mathrm{sin}\:\theta+\mu\mathrm{cos}\:\theta\right)}{\mathrm{cos}\:\theta−\mu\:\mathrm{sin}\:\theta} \\ $$

Commented by mr W last updated on 20/Nov/21

Commented by mr W last updated on 20/Nov/21

(d) (not asked in question) N=mg cos θ+F sin θ F cos θ=mg sin θ−μN=mg sin θ−μ(mg cos θ+F sin θ) F(cos θ+μ sin θ)=mg (sin θ−μcos θ) F=((mg (sin θ−μcos θ))/(cos θ+μ sin θ))

$$\left({d}\right)\:\left({not}\:{asked}\:{in}\:{question}\right) \\ $$$${N}={mg}\:\mathrm{cos}\:\theta+{F}\:\mathrm{sin}\:\theta \\ $$$${F}\:\mathrm{cos}\:\theta={mg}\:\mathrm{sin}\:\theta−\mu{N}={mg}\:\mathrm{sin}\:\theta−\mu\left({mg}\:\mathrm{cos}\:\theta+{F}\:\mathrm{sin}\:\theta\right) \\ $$$${F}\left(\mathrm{cos}\:\theta+\mu\:\mathrm{sin}\:\theta\right)={mg}\:\left(\mathrm{sin}\:\theta−\mu\mathrm{cos}\:\theta\right) \\ $$$${F}=\frac{{mg}\:\left(\mathrm{sin}\:\theta−\mu\mathrm{cos}\:\theta\right)}{\mathrm{cos}\:\theta+\mu\:\mathrm{sin}\:\theta} \\ $$

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