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Edexcel M2 2024 January Q2
6 marks Moderate -0.8
  1. \hspace{0pt} [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal perpendicular unit vectors.]
A particle \(Q\) of mass 0.5 kg is moving on a smooth horizontal surface. Particle \(Q\) is moving with velocity \(( 3 \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse of \(( 2 \mathbf { i } + 5 \mathbf { j } ) \mathrm { Ns }\).
  1. Find the speed of \(Q\) immediately after receiving the impulse. As a result of receiving the impulse, the direction of motion of \(Q\) is turned through an angle \(\theta ^ { \circ }\)
  2. Find the value of \(\theta\)
Edexcel M2 2024 January Q3
9 marks Standard +0.3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f06fe7-4d9c-4009-8931-3ecbc31fa5e5-06_323_1043_255_513} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A rough ramp is fixed to horizontal ground.
The ramp is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 3 } { 7 }\) The line \(A B\) is a line of greatest slope of the ramp, with \(B\) above \(A\) and \(A B = 6 \mathrm {~m}\), as shown in Figure 1. A block \(P\) of mass 2 kg is pushed, with constant speed, in a straight line up the slope from \(A\) to \(B\). The force pushing \(P\) acts parallel to \(A B\). The coefficient of friction between \(P\) and the ramp is \(\frac { 1 } { 3 }\) The block is modelled as a particle and air resistance is negligible.
  1. Use the model to find the total work done in pushing the block from \(A\) to \(B\). The block is now held at \(B\) and released from rest.
  2. Use the model and the work-energy principle to find the speed of the block at the instant it reaches \(A\).
Edexcel M2 2024 January Q4
9 marks Challenging +1.2
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f06fe7-4d9c-4009-8931-3ecbc31fa5e5-10_552_680_255_447} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f06fe7-4d9c-4009-8931-3ecbc31fa5e5-10_547_494_255_1165} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} The uniform rectangular lamina \(A B C D\), shown in Figure 2, has \(D C = 4 a\) and \(A D = 5 a\) The points \(S\) on \(A B\) and \(T\) on \(B C\) are such that \(S B = B T = 3 a\) The lamina is folded along \(S T\) to form the folded lamina \(L\), shown in Figure 3.
The distance of the centre of mass of \(L\) from \(A D\) is \(d\).
  1. Show that \(d = \frac { 71 } { 40 } a\) The weight of \(L\) is \(4 W\). A particle of weight \(W\) is attached to \(L\) at \(C\).
    The folded lamina \(L\) is freely suspended from \(S\).
    A force of magnitude \(F\), acting parallel to \(D C\), is applied to \(L\) at \(D\) so that \(A D\) is vertical.
  2. Find \(F\) in terms of \(W\)
Edexcel M2 2024 January Q5
9 marks Standard +0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f06fe7-4d9c-4009-8931-3ecbc31fa5e5-14_355_1230_244_422} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} A van of mass 600 kg is moving up a straight road inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 14 }\). The van is towing a trailer of mass 200 kg . The trailer is attached to the van by a rigid towbar which is parallel to the direction of motion of the van and the trailer, as shown in Figure 4. The resistance to the motion of the van from non-gravitational forces is modelled as a constant force of magnitude 250 N . The resistance to the motion of the trailer from non-gravitational forces is modelled as a constant force of magnitude 150 N . The towbar is modelled as a light rod.
At the instant when the speed of the van is \(16 \mathrm {~ms} ^ { - 1 }\), the engine of the van is working at a rate of 10 kW .
  1. Find the deceleration of the van at this instant.
  2. Find the tension in the towbar at this instant.
Edexcel M2 2024 January Q6
9 marks Standard +0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f06fe7-4d9c-4009-8931-3ecbc31fa5e5-18_424_990_255_539} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} A uniform beam \(A B\), of weight 40 N and length 7 m , rests with end \(A\) on rough horizontal ground. The beam rests on a smooth horizontal peg at \(C\), with \(A C = 5 \mathrm {~m}\), as shown in Figure 5.
The beam is inclined at an angle \(\theta\) to the ground, where \(\sin \theta = \frac { 3 } { 5 }\) The beam is modelled as a rod that lies in a vertical plane perpendicular to the peg.
The normal reaction between the beam and the peg at \(C\) has magnitude \(P\) newtons.
Using the model,
  1. show that \(P = 22.4\)
  2. find the magnitude of the resultant force acting on the beam at \(A\).
Edexcel M2 2024 January Q7
14 marks Standard +0.8
  1. Particle \(P\) has mass \(m\) and particle \(Q\) has mass \(5 m\).
The particles are moving in the same direction along the same straight line on a smooth horizontal surface. Particle \(P\) collides directly with particle \(Q\).
Immediately before the collision, the speed of \(P\) is \(6 u\) and the speed of \(Q\) is \(u\).
Immediately after the collision, the speed of \(P\) is \(x\) and the speed of \(Q\) is \(y\).
The direction of motion of \(P\) is reversed as a result of the collision.
The coefficient of restitution between \(P\) and \(Q\) is \(e\).
  1. Find the complete range of possible values of \(e\). Given that \(e = \frac { 3 } { 5 }\)
  2. find the total kinetic energy lost in the collision between \(P\) and \(Q\). After the collision, \(Q\) hits a smooth fixed vertical wall that is perpendicular to the direction of motion of \(Q\). Particle \(Q\) rebounds.
    The coefficient of restitution between \(Q\) and the wall is \(f\).
    Given that there is a second collision between \(P\) and \(Q\),
  3. find the complete range of possible values of \(f\).
Edexcel M2 2024 January Q8
11 marks Standard +0.3
  1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors, with \(\mathbf { i }\) horizontal and \(\mathbf { j }\) vertical.]
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f06fe7-4d9c-4009-8931-3ecbc31fa5e5-26_273_889_296_589} \captionsetup{labelformat=empty} \caption{Figure 6}
\end{figure} The fixed points \(A\) and \(B\) lie on horizontal ground.
At time \(t = 0\), a particle \(P\) is projected from \(A\) with velocity \(( 4 \mathbf { i } + 7 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) Particle \(P\) moves freely under gravity and hits the ground at \(B\), as shown in Figure 6 .
  1. Find the distance \(A B\). The speed of \(P\) is less than \(5 \mathrm {~ms} ^ { - 1 }\) for an interval of length \(T\) seconds.
  2. Find the value of \(T\) At the instant when the direction of motion of \(P\) is perpendicular to the initial direction of motion of \(P\), the particle is \(h\) metres above the ground.
  3. Find the value of \(h\).
Edexcel M2 2014 June Q1
11 marks Moderate -0.3
  1. A particle \(P\) moves on the \(x\)-axis. The acceleration of \(P\), in the positive \(x\) direction at time \(t\) seconds, is \(( 2 t - 3 ) \mathrm { m } \mathrm { s } ^ { - 2 }\). The velocity of \(P\), in the positive \(x\) direction at time \(t\) seconds, is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). When \(t = 0 , v = 2\)
    1. Find \(v\) in terms of \(t\).
    The particle is instantaneously at rest at times \(t _ { 1 }\) seconds and \(t _ { 2 }\) seconds, where \(t _ { 1 } < t _ { 2 }\).
  2. Find the values \(t _ { 1 }\) and \(t _ { 2 }\).
  3. Find the distance travelled by \(P\) between \(t = t _ { 1 }\) and \(t = t _ { 2 }\).
Edexcel M2 2014 June Q2
10 marks Standard +0.3
2. A trailer of mass 250 kg is towed by a car of mass 1000 kg . The car and the trailer are travelling down a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 20 }\) The resistance to motion of the car is modelled as a single force of magnitude 300 N acting parallel to the road. The resistance to motion of the trailer is modelled as a single force of magnitude 100 N acting parallel to the road. The towbar joining the car to the trailer is modelled as a light rod which is parallel to the direction of motion. At a given instant the car and the trailer are moving down the road with speed \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and acceleration \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  1. Find the power being developed by the car's engine at this instant.
  2. Find the tension in the towbar at this instant.
Edexcel M2 2014 June Q3
9 marks Standard +0.3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f79f83-ccfb-47a5-8100-88db81fd0862-05_1102_732_118_651} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A uniform \(\operatorname { rod } A B\) of weight \(W\) is freely hinged at end \(A\) to a vertical wall. The rod is supported in equilibrium at an angle of \(60 ^ { \circ }\) to the wall by a light rigid strut \(C D\). The strut is freely hinged to the rod at the point \(D\) and to the wall at the point \(C\), which is vertically below \(A\), as shown in Figure 1. The rod and the strut lie in the same vertical plane, which is perpendicular to the wall. The length of the rod is \(4 a\) and \(A C = A D = 2.5 a\).
  1. Show that the magnitude of the thrust in the strut is \(\frac { 4 \sqrt { 3 } } { 5 } W\).
  2. Find the magnitude of the force acting on the \(\operatorname { rod }\) at \(A\).
Edexcel M2 2014 June Q4
10 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f79f83-ccfb-47a5-8100-88db81fd0862-07_728_748_214_639} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The uniform square lamina \(A B C D\) shown in Figure 2 has sides of length 4a. The points \(E\) and \(F\), on \(D A\) and \(D C\) respectively, are both at a distance \(3 a\) from \(D\). The portion \(D E F\) of the lamina is folded through \(180 ^ { \circ }\) about \(E F\) to form the folded lamina \(A B C F E\) shown in Figure 3 below. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5f79f83-ccfb-47a5-8100-88db81fd0862-07_709_730_1395_639} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure}
  1. Show that the distance from \(A B\) of the centre of mass of the folded lamina is \(\frac { 55 } { 32 } a\).
    (6) The folded lamina is freely suspended from \(E\) and hangs in equilibrium.
  2. Find the size of the angle between \(E D\) and the downward vertical.
Edexcel M2 2014 June Q5
7 marks Moderate -0.3
5. A particle of mass 0.5 kg is moving on a smooth horizontal surface with velocity \(12 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it receives an impulse \(K ( \mathbf { i } + \mathbf { j } ) \mathrm { N } \mathrm { s }\), where \(K\) is a positive constant. Immediately after receiving the impulse the particle is moving with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a direction which makes an acute angle \(\theta\) with the vector \(\mathbf { i }\). Find
  1. the value of \(K\),
  2. the size of angle \(\theta\).
Edexcel M2 2014 June Q6
14 marks Standard +0.3
6. Three particles \(P , Q\) and \(R\) have masses \(3 m , k m\) and 7.5m respectively. The three particles lie at rest in a straight line on a smooth horizontal table with \(Q\) between \(P\) and \(R\). Particle \(P\) is projected towards \(Q\) with speed \(u\) and collides directly with \(Q\). The coefficient of restitution between \(P\) and \(Q\) is \(\frac { 1 } { 9 }\).
  1. Show that the speed of \(Q\) immediately after the collision is \(\frac { 10 u } { 3 ( 3 + k ) }\).
  2. Find the range of values of \(k\) for which the direction of motion of \(P\) is reversed as a result of the collision. Following the collision between \(P\) and \(Q\) there is a collision between \(Q\) and \(R\). Given that \(k = 7\) and that \(Q\) is brought to rest by the collision with \(R\),
  3. find the total kinetic energy lost in the collision between \(Q\) and \(R\).
Edexcel M2 2014 June Q7
14 marks Standard +0.8
7. A particle \(P\) is projected from a fixed point \(A\) with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) above the horizontal and moves freely under gravity. When \(P\) passes through the point \(B\) on its path, it has speed \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  1. By considering energy, find the vertical distance between \(A\) and \(B\). The minimum speed of \(P\) on its path from \(A\) to \(B\) is \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  2. Find the size of angle \(\alpha\).
  3. Find the horizontal distance between \(A\) and \(B\).
Edexcel M2 2015 June Q1
6 marks Moderate -0.3
  1. A particle of mass 0.3 kg is moving with velocity \(( 5 \mathbf { i } + 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse \(( - 3 \mathbf { i } + 3 \mathbf { j } ) \mathrm { N } \mathrm { s }\). Find the change in the kinetic energy of the particle due to the impulse.
    (6)
  2. At time \(t\) seconds, \(t \geqslant 0\), a particle \(P\) has velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\), where
$$\mathbf { v } = \left( 27 - 3 t ^ { 2 } \right) \mathbf { i } + \left( 8 - t ^ { 3 } \right) \mathbf { j }$$ When \(t = 1\), the particle \(P\) is at the point with position vector \(\mathbf { r } \mathrm { m }\) relative to a fixed origin \(O\), where \(\mathbf { r } = - 5 \mathbf { i } + 2 \mathbf { j }\) Find
  1. the magnitude of the acceleration of \(P\) at the instant when it is moving in the direction of the vector \(\mathbf { i }\),
  2. the position vector of \(P\) at the instant when \(t = 3\)
Edexcel M2 2015 June Q3
10 marks Standard +0.8
  1. A thin uniform wire of mass \(12 m\) is bent to form a right-angled triangle \(A B C\). The lengths of the sides \(A B , B C\) and \(A C\) are \(3 a , 4 a\) and \(5 a\) respectively. A particle of mass \(2 m\) is attached to the triangle at \(B\) and a particle of mass \(3 m\) is attached to the triangle at \(C\). The bent wire and the two particles form the system \(S\).
The system \(S\) is freely suspended from \(A\) and hangs in equilibrium.
Find the size of the angle between \(A B\) and the downward vertical.
Edexcel M2 2015 June Q4
11 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3f2bf524-ee27-4eef-8c54-48be61c11677-07_531_1194_118_374} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A particle \(P\) of mass 6.5 kg is projected up a fixed rough plane with initial speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(X\) on the plane, as shown in Figure 1. The particle moves up the plane along the line of greatest slope through \(X\) and comes to instantaneous rest at the point \(Y\), where \(X Y = d\) metres. The plane is inclined at an angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 5 } { 12 }\). The coefficient of friction between \(P\) and the plane is \(\frac { 1 } { 3 } \cdot\)
  1. Use the work-energy principle to show that, to 2 significant figures, \(d = 2.7\) After coming to rest at \(Y\), the particle \(P\) slides back down the plane.
  2. Find the speed of \(P\) as it passes through \(X\).
Edexcel M2 2015 June Q5
13 marks Standard +0.3
  1. Three particles \(A , B\) and \(C\) lie at rest in a straight line on a smooth horizontal table with \(B\) between \(A\) and \(C\). The masses of \(A , B\) and \(C\) are \(3 m\), 4m, and 5m respectively. Particle \(A\) is projected with speed \(u\) towards particle \(B\) and collides directly with \(B\). The coefficient of restitution between \(A\) and \(B\) is \(\frac { 1 } { 3 }\).
    1. Show that the impulse exerted by \(A\) on \(B\) in this collision has magnitude \(\frac { 16 } { 7 } m u\)
    After the collision between \(A\) and \(B\) there is a direct collision between \(B\) and \(C\).
    After this collision between \(B\) and \(C\), the kinetic energy of \(C\) is \(\frac { 72 } { 245 } m u ^ { 2 }\)
  2. Find the coefficient of restitution between \(B\) and \(C\).
Edexcel M2 2015 June Q6
12 marks Standard +0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3f2bf524-ee27-4eef-8c54-48be61c11677-11_684_1022_114_479} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A uniform \(\operatorname { rod } A B\) has length \(4 a\) and weight \(W\). A particle of weight \(k W , k < 1\), is attached to the rod at \(B\). The rod rests in equilibrium against a fixed smooth horizontal peg. The end \(A\) of the rod is on rough horizontal ground, as shown in Figure 2. The rod rests on the peg at \(C\), where \(A C = 3 a\), and makes an angle \(\alpha\) with the ground, where \(\tan \alpha = \frac { 1 } { 3 }\). The peg is perpendicular to the vertical plane containing \(A B\).
  1. Give a reason why the force acting on the rod at \(C\) is perpendicular to the rod.
  2. Show that the magnitude of the force acting on the rod at \(C\) is $$\frac { \sqrt { 10 } } { 5 } W ( 1 + 2 k )$$ The coefficient of friction between the rod and the ground is \(\frac { 3 } { 4 }\).
  3. Show that for the rod to remain in equilibrium \(k \leqslant \frac { 2 } { 11 }\).
Edexcel M2 2015 June Q7
13 marks Standard +0.3
  1. \hspace{0pt} [In this question, the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a vertical plane, \(\mathbf { i }\) being horizontal and \(\mathbf { j }\) being vertically upwards.]
At time \(t = 0\), a particle \(P\) is projected with velocity ( \(4 \mathbf { i } + 9 \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\) from a fixed point \(O\) on horizontal ground. The particle moves freely under gravity. When \(P\) is at the point \(H\) on its path, \(P\) is at its greatest height above the ground.
  1. Find the time taken by \(P\) to reach \(H\). At the point \(A\) on its path, the position vector of \(P\) relative to \(O\) is \(( k \mathbf { i } + k \mathbf { j } ) \mathrm { m }\), where \(k\) is a positive constant.
  2. Find the value of \(k\).
    (4)
  3. Find, in terms of \(k\), the position vector of the other point on the path of \(P\) which is at the same vertical height above the ground as the point \(A\).
    (3) At time \(T\) seconds the particle is at the point \(B\) and is moving perpendicular to \(( 4 \mathbf { i } + 9 \mathbf { j } )\)
  4. Find the value of \(T\).
Edexcel M2 2016 June Q1
8 marks Moderate -0.3
  1. A particle of mass 3 kg is moving with velocity \(( 3 \mathbf { i } + 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse \(( - 4 \mathbf { i } + 3 \mathbf { j } ) \mathrm { N }\) s.
Find
  1. the speed of the particle immediately after receiving the impulse,
  2. the kinetic energy gained by the particle as a result of the impulse.
Edexcel M2 2016 June Q2
10 marks Standard +0.3
2. A truck of mass 1800 kg is moving along a straight horizontal road. The engine of the truck is working at a constant rate of 10 kW . The non-gravitational resistance to motion is modelled as a constant force of magnitude \(R\) newtons. At the instant when the truck is moving with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the acceleration of the truck is \(0.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  1. Find the value of \(R\).
    (4) The truck now moves up a straight road at a constant speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The road is inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 14 }\). The non-gravitational resistance to motion is now modelled as a constant force of magnitude 30 V newtons. The engine of the truck is now working at a constant rate of 12 kW .
  2. Find the value of \(V\).
    DO NOT WIRITE IN THIS AREA
    \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{790546bf-38a4-4eb7-876e-941fe58f4a48-05_529_1040_118_450} \captionsetup{labelformat=empty} \caption{Figure 1}
    \end{figure}
Edexcel M2 2016 June Q3
9 marks Standard +0.3
3. Two particles \(P\) and \(Q\), of mass \(2 m\) and \(3 m\) respectively, are connected by a light inextensible string. Initially \(P\) is held at rest on a fixed rough plane inclined at \(\theta\) to the horizontal ground, where \(\sin \theta = \frac { 2 } { 5 }\). The string passes over a small smooth pulley fixed at the top of the plane. The particle \(Q\) hangs freely below the pulley, as shown in Figure 1. The part of the string from \(P\) to the pulley lies along a line of greatest slope of the plane. At time \(t = 0\) the system is released from rest with the string taut. When \(P\) moves the friction between \(P\) and the plane is modelled as a constant force of magnitude \(\frac { 3 } { 5 } m g\). At the instant when each particle has moved a distance \(d\), they are both moving with speed \(v\), particle \(P\) has not reached the pulley and \(Q\) has not reached the ground.
  1. Show that the total potential energy lost by the system when each particle has moved a distance \(d\) is \(\frac { 11 } { 5 } m g d\).
  2. Use the work-energy principle to find \(v ^ { 2 }\) in terms of \(g\) and \(d\). When \(t = T\) seconds, \(d = 1.5 \mathrm {~m}\).
  3. Find the value of \(T\).
    DO NOT WIRITE IN THIS AREA
Edexcel M2 2016 June Q4
10 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{790546bf-38a4-4eb7-876e-941fe58f4a48-07_671_661_239_635} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The uniform lamina \(A B C D E\) is made by joining a rectangular lamina \(A B D E\) to a triangular lamina \(B C D\) along the edge \(B D\). The rectangle has length \(6 a\) and width \(3 a\). The triangle is isosceles, with \(B C = C D\), and the distance from \(C\) to \(B D\) is \(3 a\), as shown in Figure 2.
  1. Find the distance of the centre of mass of the lamina, \(A B C D E\), from \(A E\). The lamina \(A B C D E\) is freely suspended from \(A\). A horizontal force of magnitude \(F\) newtons is applied to the lamina at \(D\). The line of action of the force lies in the vertical plane containing the lamina. The lamina is in equilibrium with \(A E\) vertical. The mass of the lamina is 4 kg .
  2. Find the magnitude of the force exerted on the lamina at \(A\).
    DO NOT WIRITE IN THIS AREA
Edexcel M2 2016 June Q5
11 marks Standard +0.8
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{790546bf-38a4-4eb7-876e-941fe58f4a48-09_952_664_246_712} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A uniform rod \(A B\) has mass 6 kg and length 2 m . The end \(A\) of the rod rests against a rough vertical wall. One end of a light string is attached to the rod at \(B\). The other end of the string is attached to the wall at \(C\), which is vertically above \(A\). The angle between the rod and the string is \(30 ^ { \circ }\) and the angle between the rod and the wall is \(70 ^ { \circ }\), as shown in Figure 3. The rod is in a vertical plane perpendicular to the wall and rests in limiting equilibrium. Find
  1. the tension in the string,
  2. the coefficient of friction between the rod and the wall,
  3. the direction of the force exerted on the rod by the wall at \(A\).
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