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4 marksKinematics and Dynamics

CAPE Applied Mathematics Unit 2 · 2016 · Paper 2 · Question 5(b)(ii)

A wrecker (mass 1050 kg) pulls buses (mass 3550 kg) down an incline of gradient 1 in 5 (sin θ = 1/5) against 250 N resistance. Engine is shut off and braking force is 10 kN, reducing speed from 80 km/h to 44 km/h. Take g = 10 m s⁻².

Determine the decelerating force acting on the system.

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Other parts of this question

  1. 5(a)(i)Use Lami's theorem, or otherwise, to show that the weight of the fixture is 50((cos θ)/√3 + sin θ).[9 marks]
  2. 5(a)(ii)Show that the tension in string B is TB = (100/√3) cos θ.[3 marks]
  3. 5(b)(i)Draw a clearly labelled diagram showing all the forces acting on the system after the engine is shut off.[3 marks]
  4. 5(b)(iii)Determine the time taken to reduce speed from 80 km h⁻¹ to 44 km h⁻¹.[6 marks]

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