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Mechanics : Ten Problems

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Set of 10 problems on mechanics : forces, moment, springs, stress, strain, Young's modulus, shear, modulus

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(Please refer to the attachment for figs.)

1. Let the distance from end 1 at which the 800N person will not cause the plank to tip about the support A be x.

The plank will experience normal reaction of the supports as shown in the fig.. In general, NA + NB = 100+800 = 900 N. However, when the plank is on the verge of tipping about the support A, NB will become zero.

For equilibrium, net moment of all forces about support A must be zero. Hence, taking counter clockwise as +ve and clockwise -ve, we have :

800(1-x) - 100x4 = 0 or x = 0.5m

2. Force F can be resolved into components Fx = F cos20 = 0.94F and Fy = F sin20 = 0.34F

For equilibrium, net moment of forces about the hinge must be zero. Hence,

145x(3.13/2) - Fy (2.5) = 0 [Fx has no moment about the hinge as it passes through the hinge]

Or Fy = 0.34F = 90.48 or ...

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