Further Mathematics Paper 2, Nov/Dec. 2014
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Main
Weakness/Remedies
Strength

Question 15

(a)  PQRS is a square. Calculate the magnitude and direction of the resultant of the
forces 5 N acting along PQ, 3 N acting along PR and 3 N acting along PS.

(b)  A book of mass 0.8 kg is placed on a plane inclined at 30o to the horizontal.  Find       the frictional force, if the book:

1. does not slide;

(ii)   slides with an acceleration of 1.2 ms-2
[Take g = 10 ms-2]

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Observation

This question was reported to be the most unpopular question in the paper and it was also poorly attempted by majority of those who attempted it.  Candidates were encouraged to put in more effort at studying this topic.

In part (a), candidates were expected to represent the given information in a diagram

S

R

Resolving the forces vertically gave (3 + 3 sin 45o) N = 6 N.
Resolving the forces horizontally gave (5 + 3o) N = 8 N.
Therefore, magnitude of the resultant force =   = 10 N. The direction of the
resultant force = θ = 90o  - tan –1()  = 053o, i.e. the resultant force, R, = (10 N, 053o).

In part (b), candidates were also expected to represent the given information in a diagram.

From the diagram, if the book does not slide, then the frictional force FR = 8sin 30o = 4 N.
If the book is sliding with an acceleration of 1.2 ms-2, then the effective force, F = ma = 8 sin 30o – frictional force, FR.  i.e. 0.8 ´ 1.2 = 8sin 30o – FR.  Therefore, FR =

8sin 30O – 0.96 = 4 – 0.96