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4 marksCoplanar Forces and Equilibrium

CAPE Applied Mathematics Unit 2 · 2014 · Paper 2 · Question 5(b)(i)

A particle of mass m kg rests on a horizontal plane. Resultant force S of the normal and frictional forces is at angle λ to the normal. Force P inclined at angle α to the plane is applied until it is just about to move.

Draw a force diagram to illustrate this information.

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Other parts of this question

  1. 5(a)(i)On the answer sheet provided as an insert, draw a displacement time graph for 0 ≤ t ≤ 8.[4 marks]
  2. 5(a)(ii)a)From your graph calculate the total distance travelled in the period 0 ≤ t ≤ 5.[3 marks]
  3. 5(a)(ii)b)From your graph calculate the average velocity over the period 0 ≤ t ≤ 5.[3 marks]
  4. 5(a)(ii)c)From your graph calculate the time at which the velocity is zero.[2 marks]
  5. 5(b)(ii)Find the LEAST value of P and the value of α when P is least.[7 marks]
  6. 5(b)(iii)Determine the LEAST value of P in terms of m when α = 30°.[2 marks]

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