A-LevelMathematicsMechanics9709/51 · Oct/Nov 2018 · Q68 Marks

Fig. 1 shows the cross-section ABCDE through the centre of mass G of a uniform prism. The cross-section consists of a rectangle ABCF from which a triangle DEF has been removed; AB = 0.6m, BC = 0.7 m and DF = EF = 0.3 m.

(i)Show that the distance of G from BC is 0.276 m, and find the distance of G from AB.[5]
(ii)The prism is placed with CD on a rough horizontal surface. A force of magnitude 2 N acting in the plane of the cross-section is applied to the prism. The line of action of the force passes through G and is perpendicular to DE (see Fig. 2). The prism is on the point of toppling about the edge through D. Calculate the weight of the prism.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[B1] Area of cross-section of prism = 0.5×0.6 – 0.3×0.3/2 = 0.375 m² (Area of cross-section of prism = area of rectangle – area of triangle)
[M1] 0.375y = 0.42×0.6/2 -0.045(0.6 – 0.3/3) (Take moments about BC)
[A1] y = 0.276 m (AG)
[M1] 0.375x = 0.42×0.7/2 – 0.045(0.7 – 0.3/3) (Take moments about AB)
[A1] x = 0.32 m
[M1] Attempt to take moments about D
[A1] 2cos45× (0.7 – 0.32) = 2cos45× (0.3 – 0.276) + W(0.3 – 0.276)
[A1] W = 21(.0) N

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