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Further Mathematics Paper 2, Nov/Dec. 2009  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength
Question 18

  1. (a)      A body of mass 8kg is placed on a smooth plane inclined at an angle of 40o to the horizontal.  Find the magnitude of the force

    • acting perpendicular to the plane;
    • required to keep the body in equilibrium.

    [Take g = 10.0ms-2]

    (b)     A particle of mass 800g is moving in a straight line with a velocity of      (5i + 3j)ms-1.  It is acted upon by a force that changes the velocity to
              (5i + 12j)ms-1.
             

    • Find the impulse.
    • If the force acted for 2s, find the acceleration with which the body begins to move.

    [Take g = 10.0 ms-2]

_____________________________________________________________________________________________________
Observation

This question was reportedly very unpopular as it was attempted by only very few candidates.  In part (a), candidates were expected to sketch the diagram for easier understanding of what needed to be done.

 

From the diagram, R = mg cosq = 8 cos 40o = 6.13N
The required force F = mg sinq = 0.8 x 10 x sin 40o = 5.14N

In part (b), mass = 0.8kg, u = 5i + 3j; and v = 5i + 12j.  Impulse ft = m(v – u) = 0.8[(5i + 12j) – (5i + 3j)] = 0.8[0 + 9j] = 7.2j Kg ms-2.

To find the acceleration, ft = mat = 7.2 kgms-2 ⇒  a =   =    =  4.5ms-2.

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