A beam of length L and mass M rests on two pivots. The first pivot is at the lef

Question

A beam of length L and mass M rests on two pivots. The first pivot is at the left end, taken as the origin, and the second pivot is at a distance l from the left end. A woman of mass m starts at the left end and walks toward the right end at a distance x from the first pivot. When the beam is on the verge of tipping, find symbolic expressions for (a) the normal force exerted by the second pivot in terms of M, m, and g and (b) the woman's position in terms of M, m, L, and l. (c) Find the minimum value of l that will allow the woman to reach the end of the beam without tipping.

Explanation / Answer

a) the beam is on the verge of tipping, the normal force exerted bythe first pivot = 0 vertical net force = 0 so force exerted by the second pivot = mg + Mg b) net torque about the second pivot = 0 Mg(l - L/2) = mg(x - l) x = l + M(l - L/2)/m c) let x = L L = l + M(l - L/2)/m l = L(m + M/2)/(m + M)

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