Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

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.

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

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))

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

Terms of Service

Privacy Policy

Contact: info@tinkutara.com