A-LevelMathematicsMechanics9709/52 · May/June 2018 · Q35 Marks
ABC is an object made from a uniform wire consisting of two straight portions AB and BC, in which AB = a, BC = x and angle ABC = 90°. When the object is freely suspended from A and in equilibrium, the angle between AB and the horizontal is θ [Figure 3.1].
- (i)Show that x² tan θ – 2ax – a² = 0.[3]
- (ii)Given that tan θ = 1.25, calculate the length of the wire in terms of a.[2]
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Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] (i) d = xsinθ/2 – acosθ or equivalent
- [M1] (i) a(acosθ)/2 = x(xsinθ/2 – acosθ)
- [A1] (i) x² tanθ – 2ax – a² = 0
- [M1] (ii) 1.25 x² – 2ax – a² = 0 [x = 2a and x = - 2a/5]
- [A1] (ii) Length (= 2a + a ) = 3a
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