A uniform plank PQ of length 8 m and mass 10kg is supported horizontally at the
end P and at point R, 3 meters from Q. A boy of mass 20 kg walks along the
plank starting from P. If the plank is in equilibrium, calculate the
(a) reaction at P and R when he has walked 1.5 meters;

(b) distance he had walked when the two reactions are equal;

(c) distance he walked before the plank tips over. (Take g = 10 ms")

Majority of the candidates' responses to this question were reportedly poor. A
good number of the candidates who attempted this question were not able to draw
the diagram correctly. Many of the candidates were reported to have shown a
poor understanding of the demands of the question. They were expected to draw
the diagram of the plank showing all the reactions at P and Q and direction of the
masses as shown.

RJ?.! il.5mL
P 200N

RR ~~m---r----lm----~1--3m---+~Q
lOON R

Taking moments about P gave 200 x 1.5 + 100 x 4 = 5RR which gave
RR = 140N. Taking moments about R gave 200 x 3.5 + 100 = 5 Rp, hence
Rp = l60N. In part (b), suppose the distance is d, since their reactions were the
same, then each reaction = 160 + 140 = 150 N.
2

Taking moments about P gave 150 (5) = 200(d) + 4(100). Therefore, d = 1.75m
In part (c), the boy's position would be at a point, dcm from R and between Q and
R. Hence taking moments about R gave 100 = 200d. Therefore d = O.5m. This
implied that the boy would have worked 5.5m from P.