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جستجو

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A small smooth ring $R$, of mass $0.6{\text{ }}kg$, is threaded on a light inextensible string of length $100{\text{ }}cm$.

One end of the string is attached to a fixed point $A$. A small bead $B$ of mass $0.4{\text{ }}kg$ is attached to the other end of the string, and is threaded on a fixed rough horizontal rod which passes through $A$. The system is in equilibrium with $B$ at a distance of $80{\text{ }}cm$ from $A$ (see diagram).

a) Find the tension in the string.

b) Find the frictional and normal components of the contact force acting on $B$.

c) Given that the equilibrium is limiting, find the coefficient of friction between the bead and the rod.

پاسخ تشریحی :
نمایش پاسخ

a) $2T\cos \alpha  = 0.6g$

Tension is $5N$

b) $\left[ {F = T\sin \alpha } \right]$

Frictional component is $4N$

$\left[ {N = 0.4g + T\cos \alpha } \right]$

Normal component is $7{\text{ }}N$

c) Coefficient is $4/7$ or $0.571$

Alternative for Q6 (a)/(b)

a) For finding the relevant angles and using

Lami’s theorem

$6/\sin {106.26^ \circ } = T/\sin {126.87^ \circ }$

Tension is $5N$

b) $F/\sin {126.87^ \circ } = 5/\sin {90^ \circ }$

Frictional component is $4N$

$\left( {R - 4} \right)/\sin {143.13^ \circ } = 5/\sin {90^ \circ }$

Normal component is $7{\text{ }}N$

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