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ZIMSEC A Level · 9164/4 · J2017

Mechanics Paper 4 June 2017

Questions
11
Total marks
24
Syllabus code
9164/4

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Questions
11
Pass mark
7
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Section b

Section b, Question 5

[2 marks]Projectiles

A particle is projected horizontally from a point O at a height of 45 m vertically above a point P on level ground. It hits the ground at a point Q with PQ = 15 m. Take g=9.81g = 9.81 ms−2^{-2}.

Calculate the time taken by the particle to reach the point Q.

Answer this when you sit the paper.

[2 marks]Projectiles

A particle is projected horizontally from a point O at a height of 45 m vertically above a point P on level ground. It hits the ground at a point Q with PQ = 15 m, taking 3.03 s to do so.

Calculate the horizontal component of the particle's velocity at Q, in ms−1^{-1}.

Answer this when you sit the paper.

[2 marks]Projectiles

A particle projected horizontally reaches the ground at a point Q after 3.03 s. At Q its horizontal component of velocity is 4.95 ms−1^{-1} and its vertical component is 29.72 ms−1^{-1} downwards.

Calculate the speed of the particle at the point Q, in ms−1^{-1}.

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Section b, Question 6

[1 marks]Newton's second law

A particle B of mass 2.5 kg is accelerated from rest along a smooth horizontal surface at 4 ms−2^{-2}.

Find the value of the force acting on particle B, in newtons.

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[3 marks]Kinematics under gravity

A particle A is dropped from rest from a point (9g2)\left(\dfrac{9g}{2}\right) metres vertically above a point R on a horizontal surface.

Calculate the time taken by A to reach R, in seconds.

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[2 marks]Kinematics

A particle B of mass 2.5 kg is accelerated from rest along a smooth horizontal surface at 4 ms−2^{-2} towards a point R, reaching R after 3 s.

Calculate the distance covered by particle B to reach R, in metres.

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[2 marks]Kinematics

A particle B starts from rest and is accelerated along a smooth horizontal surface at a constant 4 ms−2^{-2}.

Which equation gives the displacement s of B, in metres, after t seconds?

  1. As=2t2s = 2t^{2}
  2. Bs=4t2s = 4t^{2}
  3. Cs=4.905t2s = 4.905t^{2}
  4. Ds=t2s = t^{2}

Section b, Question 7

[3 marks]Friction on an inclined plane

A particle of mass 0.5 kg rests in limiting equilibrium on a rough plane inclined to the horizontal at 35∘^{\circ}. Take g=9.81g = 9.81 ms−2^{-2}.

Calculate the coefficient of friction between the particle and the plane, correct to three decimal places.

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[2 marks]Friction on an inclined plane

A particle of mass 0.5 kg rests on a rough plane inclined to the horizontal at 65∘^{\circ}. Take g=9.81g = 9.81 ms−2^{-2}.

Calculate the normal reaction between the particle and the plane, in newtons.

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[3 marks]Friction on an inclined plane

A particle of mass 0.5 kg is released from rest on a rough plane inclined to the horizontal at 65∘^{\circ}. The coefficient of friction is 0.700 and the normal reaction is 2.07 N. Take g=9.81g = 9.81 ms−2^{-2}.

Calculate the acceleration of the particle down the plane, in ms−2^{-2}.

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[2 marks]Friction on an inclined plane

A particle is released from rest and slides 0.8 m down a plane inclined at 65∘^{\circ} with a constant acceleration of 5.99 ms−2^{-2}, taking 0.517 s to reach the horizontal surface.

Calculate the velocity of the particle when it reaches the horizontal surface, in ms−1^{-1}.

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