A-LevelMathematicsMechanics9709/52 · May/June 2017 · Q68 Marks
The end A of a non-uniform rod AB of length 0.6 m and weight 8 N rests on a rough horizontal plane, with AB inclined at 60° to the horizontal. Equilibrium is maintained by a force of magnitude 3 N applied to the rod at B. This force acts at 30° above the horizontal in the vertical plane containing the rod [Figure 6.1].
- (i)Find the distance of the centre of mass of the rod from A.[2]
- (ii)The 3 N force is removed, and the rod is held in equilibrium by a force of magnitude P N applied at B, acting in the vertical plane containing the rod, at an angle of 30° below the horizontal. Calculate P.[2]
- (iii)In one of the two situations described, the rod AB is in limiting equilibrium. Find the coefficient of friction at A.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [M1] Takes moments about A
- [A1] x = 0.45 m
- [M1] Takes moments about A
- [A1] P = 6 N
- [M1] Uses F = µR used
- [M1]
- [A1] µ = 0.4 or 0.472
- [A1] µ = 0.472 accept 0.47
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