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Question-80885




Question Number 80885 by ajfour last updated on 07/Feb/20
Commented by ajfour last updated on 07/Feb/20
cylinder against a wall and an  incline. Find acceleration (→)  of the system such that both   normal reactions are equal.
$${cylinder}\:{against}\:{a}\:{wall}\:{and}\:{an} \\ $$$${incline}.\:{Find}\:{acceleration}\:\left(\rightarrow\right) \\ $$$${of}\:{the}\:{system}\:{such}\:{that}\:{both} \\ $$$$\:{normal}\:{reactions}\:{are}\:{equal}. \\ $$
Commented by mr W last updated on 07/Feb/20
N cos α=mg  ⇒N=((mg)/(cos α))  N−N sin α=ma  ⇒a=((N(1−sin α))/m)=((g(1−sin α))/(cos α))
$${N}\:\mathrm{cos}\:\alpha={mg} \\ $$$$\Rightarrow{N}=\frac{{mg}}{\mathrm{cos}\:\alpha} \\ $$$${N}−{N}\:\mathrm{sin}\:\alpha={ma} \\ $$$$\Rightarrow{a}=\frac{{N}\left(\mathrm{1}−\mathrm{sin}\:\alpha\right)}{{m}}=\frac{{g}\left(\mathrm{1}−\mathrm{sin}\:\alpha\right)}{\mathrm{cos}\:\alpha} \\ $$
Commented by ajfour last updated on 08/Feb/20
Thanks sir!
$${Thanks}\:{sir}! \\ $$

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