A 20.0 m long uniform beam weighing 790 N rests on walls A and B, as shown n Fig

Question

A 20.0 m long uniform beam weighing 790 N rests on walls A and B, as shown n Fig. 9-80. Figure 9-80 (a) Find the maximum weight of a person who can walk to the extreme end D without tipping the beam. ____N (b) Find the forces that the walls A and B exert on the beam when the same person is standing at point D. N (wall A) _____________ N (wall B) (c)Find the forces that the walls A and B exert on the beam when the same person is standing at a point 2.0 m to the right of B. N (wall A) L N (wall B) (d) Find the forces that the walls A and B exert on the beam when the same person is standing 2.0 m to the right of A. N (wall A) N (wall B)

Explanation / Answer

Let the normal forces on the beam at A and B be N1 and N2.

N2 = 790 + W

Balancing torques about B,

790 * 12/2 = W * (20 -12) / 2

W = 1185 N

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b) 0N

forces at A and B are 0 N and (1185 + 790) = 1975 N

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(c) when the person is standing at a point 2 m to right ofB,

balancing forces, N1 + N2 = 1975 N

balancing torques about A

N2 * 12 = 790 *12/2 + 1185*14

N2 = 1778 N

N1 = 197.5 N

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(d)when the person is standing 2 m to the right of A,

N1 + N2 = 1975 N

balancing torques about A,

1185 * 2 + 790 * 12/2 = N2 * 12

N2 = 592.5 N

N1 = 1382.5N

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