As shown, a uniform beam that has a mass 33.0 k g is attached to a wall at point
ID: 2133824 • Letter: A
Question
As shown, a uniform beam that has a mass 33.0kg is attached to a wall at point A. The beam is subjected to three forces, F1 = 24.0N , F2 = 8.90N , and F3 = 14.0N . (Figure 1) The line of action of F2 passes through point A. If the wall can sustain a maximum moment of 665N?m about point A, what is the largest value for d, the beam's length, that preserves static equilibrium? The beam's width is negligible.
As shown, a uniform beam that has a mass 33.0kg is attached to a wall at point A. The beam is subjected to three forces, F1 = 24.0N , F2 = 8.90N , and F3 = 14.0N . (Figure 1) The line of action of F2 passes through point A. If the wall can sustain a maximum moment of 665N?m about point A, what is the largest value for d, the beam's length, that preserves static equilibrium? The beam's width is negligible.Explanation / Answer
Moment of F1 about A is
M1 = F1*(4/5)*d/2 (Since only the vertical component of F1 has a moment about A and horizontal component passing through A doesn't have any moment about A)
Moment of F3 about A is
M3 = F3*d.
Moment of F2 bout A is
M2 = 0 (Since the line of force passes through A)
There is also a moment due to weight of the rod which is
M4 = m*g*d/2
Total moment M = (4/10 * F1*d + F3 d +m*g*d/2) -----------(1)
Given Mmax = 665N ------------(2)
665 = (2.4*4 + 6.6*9.8 + 14)dmax
From (1 ) & (2) we get dmax = 3.588m
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