A-LevelMathematicsMechanics9709/52 · May/June 2019 · Q712 Marks
Fig. 1 shows an object made from a uniform wire of length 0.8 m. The object consists of a straight part AB, and a semicircular part BC such that A, B and C lie in the same straight line. The radius of the semicircle is r m and the centre of mass of the object is 0.1 m from line ABC.
- (i)Show that r = 0.2.[3]
- (ii)The object is freely suspended at A and a horizontal force of magnitude 7 N is applied to the object at C so that the object is in equilibrium with ABC vertical (see Fig. 2). Calculate the weight of the object.[3]
- (iii)The 7 N force is removed and the object hangs in equilibrium with ABC at an angle of θ° with the vertical. Find θ.[6]
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Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] X = 2r/π (distance of centre of mass of the arc from ABC)
- [M1] Take moments about ABC
- [A1]
- [B1] AC=0.8+2×0.2-0.2π (= 0.57168...)
- [M1] AC must be a numerical value. Take moments about A
- [A1] W=40(0.) N
- [B1] (0.8-0.2π+0.2) [= 0.37168...]
- [M1A1] 0.8Y = (0.8-0.2π)×(0.8-0.2π)/2 + (0.2π)×(0.8-0.2π +0.2)
- [A1] Y=0.310(338)
- [M1] tanθ = 0.1 / 0.310338
- [A1] θ=17.9
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