As shown in the figure, a beam is supported by two pillars separated by a distan
ID: 1473152 • Letter: A
Question
As shown in the figure, a beam is supported by two pillars separated by a distance e. 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 = (m + M) g 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.) x= (M/m) (M e + m e)/(M - L/2) Since this is an equilibrium problem we expect to use the first and second conditions of equilibrium to solve the problem. See if you can write a second condition of equilibrium statement that will allow you to obtain a symbolic expression (in terms of the given information) that can be used to determine the distance of the girl from the left end of the beam when the beam is on the verge of tipping. Find a symbolic expression for the minimum value off that will allow the girl to reach the end of the beam without it tipping. (Use the following as necessary: M, m, and L.) emin = L (m + M/2)/(m + M)Explanation / Answer
Taking up to be positive and measuring torques about the left pillar:
N*l - m*g*x - M*g*(L/2) = 0
Where N is the normal force exerted by the second pillar and x is the distance of the woman from the first pivot. M*g is multiplied by L/2 because the force of gravity acts on the center of mass, which is at L/2.
Taking sum of the torques about the second pillar,
M*g*(l - L/2) + m*g*(l-x) = 0
Solving for N and x, we obtain the following results,
N = (m + M)*g
x = (M/m)*(l - L/2) + l = (M/m)*[{(M*l+m*l)/M}- L/2] Ans
Notice that the denominator in your answer is incorrect and the correct answer is as above.
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