Further Mathematics Paper 2, Nov/Dec. 2010
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength
Question 8

A body of mass 6 kg is hung from a fixed point by a light inextensible string. A horizontal force is applied to the body such that the body is in equilibrium when the string is inclined at 350 to the vertical. Find, correct to one decimal place, the:
(a) horizontal force;
(b) tension in the string.
[Take g = 10 ms-²]

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Observation

The Chief Examiner observed that this question was not popular among the candidates and the few who attempted this question were reported not to have drawn the diagram correctly and this also affected their performance. Candidates should represent the forces as indicated below

Using Lami's theorem,     F/Sin 145° = 60/Sin 125° ⇒60xSin145°
Sin 125°
= 42.0N

Similarly,  T    =    60/125°  =>T = 60Sin900
Sin90                              Sin125°
= 73.2N
The solution could also be obtained by resolving the forces into its horizontal and vertical components. In which case, we would obtain:

[0,-60] +[Fcos0,Fsin0] + [-Tcos55,Tsin55] = [0,0] i.e [0,-60] + [f,0] +[-0.5736T,0.8192T] = [0,0]