A man weighing 500N stands on a uniform bridge whose weight is 1200N, and whose

Question

A man weighing 500N stands on a uniform bridge whose weight is 1200N, and whose length is 100 meters. The Bridge is supported at points A and B, where A is at the left edge of the bridge and B is located 40 meters from the right edge. The man is standing 5 m. to the right of the point B. (Between point B and the right edge of the bridge {35 m from the right edge)) Draw a diagram showing the forces represented by the man, the bridge and the forces R1 at the point A and the force R2 at the point B. What are the forces R1 and R2? How far can the man walk to the right, before the bridge will tip? If the man is placed at the right most position of the bridge, what can be done to prevent the bridge from tipping.

Explanation / Answer

a)   weight of man acting downwards . weight of bridge acting downwards . Reactions at A and B are acting in upwards direction .

b)    Here,   R1 + R2 = 1700

   Also ,   1200 * 50 + 500 * 65 =   R2 * 60

=> R2 = 1541.67 N

=> R1 = 158.33 N

c)    Here,   1200 * 10 = 500 * x

=> x = 24 m

=>   man can go   19 m   towards right before bridge will trip .

d)    Here,   40 * 500 - 1200 * 10 = F * r

=> F * r = 8000 N.m

=>    weight of 800 N can be placed at distance of 10 m from left of point B .

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