Edexcel M2 2010 June — Question 1

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2010
SessionJune
TopicWork, energy and Power 1
  1. A particle \(P\) moves on the \(x\)-axis. The acceleration of \(P\) at time \(t\) seconds, \(t \geqslant 0\), is \(( 3 t + 5 ) \mathrm { m } \mathrm { s } ^ { - 2 }\) in the positive \(x\)-direction. When \(t = 0\), the velocity of \(P\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the positive \(x\)-direction. When \(t = T\), the velocity of \(P\) is \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the positive \(x\)-direction. Find the value of \(T\).
  2. A particle \(P\) of mass 0.6 kg is released from rest and slides down a line of greatest slope of a rough plane. The plane is inclined at \(30 ^ { \circ }\) to the horizontal. When \(P\) has moved 12 m , its speed is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Given that friction is the only non-gravitational resistive force acting on \(P\), find
    1. the work done against friction as the speed of \(P\) increases from \(0 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\),
    2. the coefficient of friction between the particle and the plane.
    \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{0e4552e0-7737-439b-a337-789c83c5258c-04_430_624_297_658} \captionsetup{labelformat=empty} \caption{Figure 1}
    \end{figure} A triangular frame is formed by cutting a uniform rod into 3 pieces which are then joined to form a triangle \(A B C\), where \(A B = A C = 10 \mathrm {~cm}\) and \(B C = 12 \mathrm {~cm}\), as shown in Figure 1.
  3. Find the distance of the centre of mass of the frame from \(B C\). The frame has total mass \(M\). A particle of mass \(M\) is attached to the frame at the mid-point of \(B C\). The frame is then freely suspended from \(B\) and hangs in equilibrium.
  4. Find the size of the angle between \(B C\) and the vertical.
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