Question Number 74655 by TawaTawa last updated on 28/Nov/19
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Commented by TawaTawa last updated on 28/Nov/19
The force F acting along an inclined plane is just sufficient to maintain a body on the plane, the angle of friction M being less than Y, the angle of plane. prove that the least force acting along the plane, sufficient to drag the body up the plane is : F sin( M + Y )/sin( M - Y)
Answered by mr W last updated on 28/Nov/19
$${to}\:{push}: \\ $$$${F}={mg}\:\mathrm{sin}\:{Y}−{mg}\:\mathrm{cos}\:{Y}\:\mathrm{tan}\:{M}=\frac{{mg}\:\mathrm{sin}\:\left({Y}−{M}\right)}{\mathrm{cos}\:{M}} \\ $$$${to}\:{pull}: \\ $$$${T}={mg}\:\mathrm{sin}\:{Y}+{mg}\:\mathrm{cos}\:{Y}\:\mathrm{tan}\:{M}=\frac{{mg}\:\mathrm{sin}\:\left({Y}+{M}\right)}{\mathrm{cos}\:{M}}=\frac{{F}\:\mathrm{sin}\:\left({Y}+{M}\right)}{\mathrm{sin}\:\left({Y}−{M}\right)} \\ $$
Commented by TawaTawa last updated on 28/Nov/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Commented by TawaTawa last updated on 29/Nov/19
$$\mathrm{Sir},\:\:\mathrm{please}\:\mathrm{can}\:\mathrm{i}\:\mathrm{get}\:\mathrm{the}\:\mathrm{diagram}\:? \\ $$
Commented by mr W last updated on 29/Nov/19
$${i}\:{have}\:{no}\:{diagram}.\:{the}\:{question}\:{should} \\ $$$${give}\:{a}\:{diagram},\:{i}\:{think}. \\ $$
Commented by TawaTawa last updated on 29/Nov/19
$$\mathrm{Alright}\:\mathrm{sir},\:\:\mathrm{thanks}. \\ $$