As shown in the figure, a beam is supported by two pillars separated by a distan

Question

As shown in the figure, a beam is supported by two pillars separated by a distance l. The beam has a mass M, a length L, and a girl of mass m is walking from the left end toward the right. Find a symbolic expression for the normal force exerted on the beam by the pillar on the right, when the beam is on the verge of tipping. (Use the following as necessary: M, m, and g.) N2 = Find a symbolic expression for the girl's position, when the beam is on the verge of tipping. (Use the following as necessary: M, m, L and f.) Find a symbolic expression for the minimum value of l that will allow the girl to reach the end of the beam without it tipping. (Use the following as necessary: M, m, and L.)

Explanation / Answer

a) apply the equilibrium condition, we get

N2*l - m*g*x - M*g*(L/2) = 0

here N2 is normal force exerted by the second pivot

the net torque is zero when the system is in equilibrium for second pivot,

M*g*(l - L/2) - m*g*(x-l) = 0

solve the above equations, we get

N2 = (m + M)*g
the position is,

x = (M/m)*(l - L/2) + l

= (M/m)*[(M*l+m*l)/M - L/2]

b) therefore, the position is,

x = (M/m)*(l - L/2) + l

= (M/m)*[(M*l+m*l)/(M - L/2)]

c)

Let x = L, the minimum length is,

L = (M/m)*[(M*l+m*l)/M - L/2]

l = L*(m + M/2)/(m + M)

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