Theory question 108
StaticsA uniform plank PQ of length 8m and mass 10 Kg is supported horizontally at the end P and at point R, 3 metres from Q. A boy of mass 20 kg walks along the plank starting from P. If the plank is in equilibrium, calculate the (a) reactions at P and R when he walked 1.5 metres; (b) distance he had walked when the two reactions are equal; (c) distance he walked before the plank tips over. [Take g = 10ms−2].
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Weights: plank 100 N at 4 m from P, boy 200 N; R is 5 m from P; RP + RR = 300 N
(a) Moments about P: 5RR = 100 × 4 + 200 × 1.5 = 700, RR = 140 N, RP = 160 N
(b) Equal reactions: 150 N each; 150 × 5 = 400 + 200x, x = 1.75 m
(c) About to tip about R when RP = 0: 200(x − 5) = 100 × 1, x = 5.5 m from P
Take moments about a support to remove one unknown reaction.