Edexcel M2 2003 January — Question 1

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2003
SessionJanuary
TopicCentre of Mass 1

  1. Three particles of mass \(3 m , 5 m\) and \(\lambda m\) are placed at points with coordinates (4, 0), (0, -3) and \(( 4,2 )\) respectively. The centre of mass of the system of three particles is at \(( 2 , k )\).
    1. Show that \(\lambda = 2\).
    2. Calculate the value of \(k\).
    3. A car of mass 1000 kg is moving along a straight horizontal road with a constant acceleration of \(f \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The resistance to motion is modelled as a constant force of magnitude 1200 N . When the car is travelling at \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the power generated by the engine of the car is 24 kW .
    4. Calculate the value of \(f\).
    When the car is travelling at \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the engine is switched off and the car comes to rest, without braking, in a distance of \(d\) metres. Assuming the same model for resistance,
  2. use the work-energy principle to calculate the value of \(d\).
  3. Give a reason why the model used for the resistance to motion may not be realistic. \section*{3.} \section*{Figure 1}
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    A uniform ladder \(A B\), of mass \(m\) and length \(2 a\), has one end \(A\) on rough horizontal ground. The other end \(B\) rests against a smooth vertical wall. The ladder is in a vertical plane perpendicular to the wall. The ladder makes an angle \(\alpha\) with the horizontal, where \(\tan \alpha = \frac { 4 } { 3 }\). A child of mass \(2 m\) stands on the ladder at \(C\) where \(A C = \frac { 1 } { 2 } a\), as shown in Fig. 1. The ladder and the child are in equilibrium. By modelling the ladder as a rod and the child as a particle, calculate the least possible value of the coefficient of friction between the ladder and the ground.