an object of mass M is suspended from the end of a horizontal strut at mass m(fi

Question

an object of mass M is suspended from the end of a horizontal strut at mass m(fig.11.59). what horizontal and vertical forces does the wall exert on the strut? is the vertical force up or down?why? what coefficient of friction is needed between the wall and the strut to prevent slipping?

an object of mass M is suspended from the end of a horizontal strut at mass m(fig.11.59). what horizontal and vertical forces does the wall exert on the strut? is the vertical force up or down? why? what coefficient of friction is needed between the wall and the strut to prevent slipping?

Explanation / Answer

let the wall exert a force of K on the strut

so the friction force will be Mu*K

for vertical equilibrium of the wall

taking upward direction as positive

we have Tsin(30) - m*g +Mu*k - Mg = 0

for horizontal equilibrium

Tcos 30 = K

for equilibrium taking moments about the wall

m*g(l/2) + M*g*l - Tsin30*l = 0

T = (2M + m)g

K = (2M + m)g sqrt(3) / 2

so using

Tsin(30) - m*g +Mu*k - Mg = 0

we have

(2M + m)g(1/ 2) + Mu*(2M + m)g sqrt(3) / 2 = (M+m)g

1+Mu*sqrt(3) = 2(M+m) / (2M+m)

Mu = m/[(2M+m)*sqrt(3)]

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