Further Mathematics Paper 2, May/June. 2010  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments

Question 8

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.

P        200N

          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.

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.
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