Questions M1 (1912 questions)

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Edexcel M1 2012 June Q3
9 marks Standard +0.3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c908e75-73df-46be-93bb-09dba2cb3b7e-04_432_780_210_584} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A box of mass 5 kg lies on a rough plane inclined at \(30 ^ { \circ }\) to the horizontal. The box is held in equilibrium by a horizontal force of magnitude 20 N , as shown in Figure 2. The force acts in a vertical plane containing a line of greatest slope of the inclined plane.
The box is in equilibrium and on the point of moving down the plane. The box is modelled as a particle. Find
  1. the magnitude of the normal reaction of the plane on the box,
  2. the coefficient of friction between the box and the plane.
Edexcel M1 2012 June Q4
13 marks Moderate -0.8
  1. A car is moving on a straight horizontal road. At time \(t = 0\), the car is moving with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is at the point \(A\). The car maintains the speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for 25 s . The car then moves with constant deceleration \(0.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), reducing its speed from \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The car then moves with constant speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for 60 s . The car then moves with constant acceleration until it is moving with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the point \(B\).
    1. Sketch a speed-time graph to represent the motion of the car from \(A\) to \(B\).
    2. Find the time for which the car is decelerating.
    Given that the distance from \(A\) to \(B\) is 1960 m ,
  2. find the time taken for the car to move from \(A\) to \(B\).
Edexcel M1 2012 June Q5
12 marks Standard +0.3
  1. A particle \(P\) is projected vertically upwards from a point \(A\) with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The point \(A\) is 17.5 m above horizontal ground. The particle \(P\) moves freely under gravity until it reaches the ground with speed \(28 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Show that \(u = 21\)
    At time \(t\) seconds after projection, \(P\) is 19 m above \(A\).
  2. Find the possible values of \(t\). The ground is soft and, after \(P\) reaches the ground, \(P\) sinks vertically downwards into the ground before coming to rest. The mass of \(P\) is 4 kg and the ground is assumed to exert a constant resistive force of magnitude 5000 N on \(P\).
  3. Find the vertical distance that \(P\) sinks into the ground before coming to rest.
Edexcel M1 2012 June Q6
13 marks Moderate -0.8
6. [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors due east and due north respectively and position vectors are given with respect to a fixed origin.] A ship \(S\) is moving with constant velocity \(( - 12 \mathbf { i } + 7.5 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\).
  1. Find the direction in which \(S\) is moving, giving your answer as a bearing. At time \(t\) hours after noon, the position vector of \(S\) is \(\mathbf { s } \mathrm { km }\). When \(t = 0 , \mathbf { s } = 40 \mathbf { i } - 6 \mathbf { j }\).
  2. Write down \(\mathbf { s }\) in terms of \(t\). A fixed beacon \(B\) is at the point with position vector \(( 7 \mathbf { i } + 12.5 \mathbf { j } ) \mathrm { km }\).
  3. Find the distance of \(S\) from \(B\) when \(t = 3\)
  4. Find the distance of \(S\) from \(B\) when \(S\) is due north of \(B\).
Edexcel M1 2012 June Q7
15 marks Moderate -0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5c908e75-73df-46be-93bb-09dba2cb3b7e-12_150_1104_255_422} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Two particles \(P\) and \(Q\), of mass 0.3 kg and 0.5 kg respectively, are joined by a light horizontal rod. The system of the particles and the rod is at rest on a horizontal plane. At time \(t = 0\), a constant force \(\mathbf { F }\) of magnitude 4 N is applied to \(Q\) in the direction \(P Q\), as shown in Figure 3. The system moves under the action of this force until \(t = 6 \mathrm {~s}\). During the motion, the resistance to the motion of \(P\) has constant magnitude 1 N and the resistance to the motion of \(Q\) has constant magnitude 2 N . Find
  1. the acceleration of the particles as the system moves under the action of \(\mathbf { F }\),
  2. the speed of the particles at \(t = 6 \mathrm {~s}\),
  3. the tension in the rod as the system moves under the action of \(\mathbf { F }\). At \(t = 6 \mathrm {~s} , \mathbf { F }\) is removed and the system decelerates to rest. The resistances to motion are unchanged. Find
  4. the distance moved by \(P\) as the system decelerates,
  5. the thrust in the rod as the system decelerates.
Edexcel M1 2013 June Q1
6 marks Moderate -0.8
  1. Two particles \(A\) and \(B\), of mass 2 kg and 3 kg respectively, are moving towards each other in opposite directions along the same straight line on a smooth horizontal surface. The particles collide directly. Immediately before the collision the speed of \(A\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The magnitude of the impulse exerted on \(B\) by \(A\) is 14 N s . Find
    1. the speed of \(A\) immediately after the collision,
    2. the speed of \(B\) immediately after the collision.
    \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{278c8424-38aa-48c2-bc82-af4be9234f71-03_359_1298_219_413} \captionsetup{labelformat=empty} \caption{Figure 1}
    \end{figure} A particle of weight 8 N is attached at \(C\) to the ends of two light inextensible strings \(A C\) and \(B C\). The other ends, \(A\) and \(B\), are attached to a fixed horizontal ceiling. The particle hangs at rest in equilibrium, with the strings in a vertical plane. The string \(A C\) is inclined at \(35 ^ { \circ }\) to the horizontal and the string \(B C\) is inclined at \(25 ^ { \circ }\) to the horizontal, as shown in Figure 1. Find
    (i) the tension in the string \(A C\),
    (ii) the tension in the string \(B C\).
Edexcel M1 2013 June Q3
9 marks Standard +0.3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{278c8424-38aa-48c2-bc82-af4be9234f71-04_589_1027_248_440} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A fixed rough plane is inclined at \(30 ^ { \circ }\) to the horizontal. A small smooth pulley \(P\) is fixed at the top of the plane. Two particles \(A\) and \(B\), of mass 2 kg and 4 kg respectively, are attached to the ends of a light inextensible string which passes over the pulley \(P\). The part of the string from \(A\) to \(P\) is parallel to a line of greatest slope of the plane and \(B\) hangs freely below \(P\), as shown in Figure 2. The coefficient of friction between \(A\) and the plane is \(\frac { 1 } { \sqrt { } 3 }\). Initially \(A\) is held at rest on the plane. The particles are released from rest with the string taut and \(A\) moves up the plane. Find the tension in the string immediately after the particles are released.
Edexcel M1 2013 June Q4
7 marks Standard +0.3
4. At time \(t = 0\), two balls \(A\) and \(B\) are projected vertically upwards. The ball \(A\) is projected vertically upwards with speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point 50 m above the horizontal ground. The ball \(B\) is projected vertically upwards from the ground with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At time \(t = T\) seconds, the two balls are at the same vertical height, \(h\) metres, above the ground. The balls are modelled as particles moving freely under gravity. Find
  1. the value of \(T\),
  2. the value of \(h\).
Edexcel M1 2013 June Q5
10 marks Moderate -0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{278c8424-38aa-48c2-bc82-af4be9234f71-07_520_1143_116_406} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A particle \(P\) of mass 0.6 kg slides with constant acceleration down a line of greatest slope of a rough plane, which is inclined at \(25 ^ { \circ }\) to the horizontal. The particle passes through two points \(A\) and \(B\), where \(A B = 10 \mathrm {~m}\), as shown in Figure 3. The speed of \(P\) at \(A\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The particle \(P\) takes 3.5 s to move from \(A\) to \(B\). Find
  1. the speed of \(P\) at \(B\),
  2. the acceleration of \(P\),
  3. the coefficient of friction between \(P\) and the plane.
Edexcel M1 2013 June Q6
11 marks Moderate -0.3
6. [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors due east and due north respectively. Position vectors are given with respect to a fixed origin \(O\).] A ship \(S\) is moving with constant velocity \(( 3 \mathbf { i } + 3 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\). At time \(t = 0\), the position vector of \(S\) is \(( - 4 \mathbf { i } + 2 \mathbf { j } ) \mathrm { km }\).
  1. Find the position vector of \(S\) at time \(t\) hours. A ship \(T\) is moving with constant velocity \(( - 2 \mathbf { i } + n \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\). At time \(t = 0\), the position vector of \(T\) is \(( 6 \mathbf { i } + \mathbf { j } ) \mathrm { km }\). The two ships meet at the point \(P\).
  2. Find the value of \(n\).
  3. Find the distance \(O P\).
Edexcel M1 2013 June Q7
11 marks Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{278c8424-38aa-48c2-bc82-af4be9234f71-11_216_1335_207_306} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} A truck of mass 1750 kg is towing a car of mass 750 kg along a straight horizontal road. The two vehicles are joined by a light towbar which is inclined at an angle \(\theta\) to the road, as shown in Figure 4. The vehicles are travelling at \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) as they enter a zone where the speed limit is \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The truck's brakes are applied to give a constant braking force on the truck. The distance travelled between the instant when the brakes are applied and the instant when the speed of each vehicle is \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is 100 m .
  1. Find the deceleration of the truck and the car. The constant braking force on the truck has magnitude \(R\) newtons. The truck and the car also experience constant resistances to motion of 500 N and 300 N respectively. Given that \(\cos \theta = 0.9\), find
  2. the force in the towbar,
  3. the value of \(R\).
Edexcel M1 2013 June Q8
13 marks Moderate -0.3
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{278c8424-38aa-48c2-bc82-af4be9234f71-13_259_1367_228_294} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} A uniform rod \(A B\) has length 2 m and mass 50 kg . The rod is in equilibrium in a horizontal position, resting on two smooth supports at \(C\) and \(D\), where \(A C = 0.2\) metres and \(D B = x\) metres, as shown in Figure 5. Given that the magnitude of the reaction on the rod at \(D\) is twice the magnitude of the reaction on the rod at \(C\),
  1. find the value of \(x\). The support at \(D\) is now moved to the point \(E\) on the rod, where \(E B = 0.4\) metres. A particle of mass \(m \mathrm {~kg}\) is placed on the rod at \(B\), and the rod remains in equilibrium in a horizontal position. Given that the magnitude of the reaction on the rod at \(E\) is four times the magnitude of the reaction on the rod at \(C\),
  2. find the value of \(m\). \includegraphics[max width=\textwidth, alt={}, center]{278c8424-38aa-48c2-bc82-af4be9234f71-14_77_74_2480_1836}
Edexcel M1 2013 June Q1
6 marks Moderate -0.8
\begin{enumerate} \item Particle \(P\) has mass 3 kg and particle \(Q\) has mass \(m \mathrm {~kg}\). The particles are moving in opposite directions along a smooth horizontal plane when they collide directly. Immediately before the collision, the speed of \(P\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(Q\) is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). In the collision the direction of motion of \(P\) is unchanged and the direction of motion of \(Q\) is reversed. Immediately after the collision, the speed of \(P\) is \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(Q\) is \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  1. Find the magnitude of the impulse exerted on \(P\) in the collision.
  2. Find the value of \(m\).
    \item A woman travels in a lift. The mass of the woman is 50 kg and the mass of the lift is 950 kg . The lift is being raised vertically by a vertical cable which is attached to the top of the lift. The lift is moving upwards and has constant deceleration of \(2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). By modelling the cable as being light and inextensible, find
Edexcel M1 2013 June Q4
9 marks Standard +0.3
  1. A lorry is moving along a straight horizontal road with constant acceleration. The lorry passes a point \(A\) with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 } , ( u < 34 )\), and 10 seconds later passes a point \(B\) with speed \(34 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Given that \(A B = 240 \mathrm {~m}\), find
    1. the value of \(u\),
    2. the time taken for the lorry to move from \(A\) to the mid-point of \(A B\).
    3. A car is travelling along a straight horizontal road. The car takes 120 s to travel between two sets of traffic lights which are 2145 m apart. The car starts from rest at the first set of traffic lights and moves with constant acceleration for 30 s until its speed is \(22 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The car maintains this speed for \(T\) seconds. The car then moves with constant deceleration, coming to rest at the second set of traffic lights.
    4. Sketch, in the space below, a speed-time graph for the motion of the car between the two sets of traffic lights.
    5. Find the value of \(T\).
    A motorcycle leaves the first set of traffic lights 10 s after the car has left the first set of traffic lights. The motorcycle moves from rest with constant acceleration, a \(\mathrm { m } \mathrm { s } ^ { - 2 }\), and passes the car at the point \(A\) which is 990 m from the first set of traffic lights. When the motorcycle passes the car, the car is moving with speed \(22 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  2. Find the time it takes for the motorcycle to move from the first set of traffic lights to the point \(A\).
  3. Find the value of \(a\).
Edexcel M1 2013 June Q6
14 marks Standard +0.8
6. A beam \(A B\) has length 15 m . The beam rests horizontally in equilibrium on two smooth supports at the points \(P\) and \(Q\), where \(A P = 2 \mathrm {~m}\) and \(Q B = 3 \mathrm {~m}\). When a child of mass 50 kg stands on the beam at \(A\), the beam remains in equilibrium and is on the point of tilting about \(P\). When the same child of mass 50 kg stands on the beam at \(B\), the beam remains in equilibrium and is on the point of tilting about \(Q\). The child is modelled as a particle and the beam is modelled as a non-uniform rod.
    1. Find the mass of the beam.
    2. Find the distance of the centre of mass of the beam from \(A\). When the child stands at the point \(X\) on the beam, it remains horizontal and in equilibrium. Given that the reactions at the two supports are equal in magnitude,
  2. find \(A X\).
Edexcel M1 2013 June Q7
11 marks Moderate -0.8
  1. \hspace{0pt} [In this question, the horizontal unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed due east and due north respectively.]
The velocity, \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\), of a particle \(P\) at time \(t\) seconds is given by $$\mathbf { v } = ( 1 - 2 t ) \mathbf { i } + ( 3 t - 3 ) \mathbf { j }$$
  1. Find the speed of \(P\) when \(t = 0\)
  2. Find the bearing on which \(P\) is moving when \(t = 2\)
  3. Find the value of \(t\) when \(P\) is moving
    1. parallel to \(\mathbf { j }\),
    2. parallel to \(( - \mathbf { i } - 3 \mathbf { j } )\).
Edexcel M1 2013 June Q8
10 marks Standard +0.3
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3c8dce6f-367a-42bb-be60-d03d0a23664f-13_526_945_258_502} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Two particles \(A\) and \(B\) have masses \(2 m\) and \(3 m\) respectively. The particles are attached to the ends of a light inextensible string. Particle \(A\) is held at rest on a smooth horizontal table. The string passes over a small smooth pulley which is fixed at the edge of the table. Particle \(B\) hangs at rest vertically below the pulley with the string taut, as shown in Figure 2. Particle \(A\) is released from rest. Assuming that \(A\) has not reached the pulley, find
  1. the acceleration of \(B\),
  2. the tension in the string,
  3. the magnitude and direction of the force exerted on the pulley by the string.
Edexcel M1 2014 June Q1
6 marks Moderate -0.8
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b896c631-00a0-46c5-bce9-16d65f6e3095-02_586_506_285_708} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A particle \(P\) of weight \(W\) newtons is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point \(O\). A horizontal force of magnitude 5 N is applied to \(P\). The particle \(P\) is in equilibrium with the string taut and with \(O P\) making an angle of \(25 ^ { \circ }\) to the downward vertical, as shown in Figure 1. Find
  1. the tension in the string,
  2. the value of \(W\).
Edexcel M1 2014 June Q2
10 marks Moderate -0.8
  1. Two forces \(( 4 \mathbf { i } - 2 \mathbf { j } ) \mathrm { N }\) and \(( 2 \mathbf { i } + q \mathbf { j } ) \mathrm { N }\) act on a particle \(P\) of mass 1.5 kg . The resultant of these two forces is parallel to the vector \(( 2 \mathbf { i } + \mathbf { j } )\).
    1. Find the value of \(q\).
    At time \(t = 0 , P\) is moving with velocity \(( - 2 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
  2. Find the speed of \(P\) at time \(t = 2\) seconds.
Edexcel M1 2014 June Q3
13 marks Moderate -0.3
3. A car starts from rest and moves with constant acceleration along a straight horizontal road. The car reaches a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in 20 seconds. It moves at constant speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for the next 30 seconds, then moves with constant deceleration \(\frac { 1 } { 2 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it has speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It moves at speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for the next 15 seconds and then moves with constant deceleration \(\frac { 1 } { 3 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it comes to rest.
  1. Sketch, in the space below, a speed-time graph for this journey. In the first 20 seconds of this journey the car travels 140 m . Find
  2. the value of \(V\),
  3. the total time for this journey,
  4. the total distance travelled by the car.
Edexcel M1 2014 June Q4
8 marks Moderate -0.8
  1. At time \(t = 0\), a particle is projected vertically upwards with speed \(u\) from a point \(A\). The particle moves freely under gravity. At time \(T\) the particle is at its maximum height \(H\) above \(A\).
    1. Find \(T\) in terms of \(u\) and \(g\).
    2. Show that \(H = \frac { u ^ { 2 } } { 2 g }\)
    The point \(A\) is at a height \(3 H\) above the ground.
  2. Find, in terms of \(T\), the total time from the instant of projection to the instant when the particle hits the ground.
Edexcel M1 2014 June Q5
14 marks Standard +0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b896c631-00a0-46c5-bce9-16d65f6e3095-09_364_422_269_753} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Two particles \(A\) and \(B\) have masses \(2 m\) and \(3 m\) respectively. The particles are connected by a light inextensible string which passes over a smooth light fixed pulley. The system is held at rest with the string taut. The hanging parts of the string are vertical and \(A\) and \(B\) are above a horizontal plane, as shown in Figure 2. The system is released from rest.
  1. Show that the tension in the string immediately after the particles are released is \(\frac { 12 } { 5 } m g\). After descending \(1.5 \mathrm {~m} , B\) strikes the plane and is immediately brought to rest. In the subsequent motion, \(A\) does not reach the pulley.
  2. Find the distance travelled by \(A\) between the instant when \(B\) strikes the plane and the instant when the string next becomes taut. Given that \(m = 0.5 \mathrm {~kg}\),
  3. find the magnitude of the impulse on \(B\) due to the impact with the plane.
Edexcel M1 2014 June Q6
11 marks Standard +0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b896c631-00a0-46c5-bce9-16d65f6e3095-11_600_969_127_491} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A non-uniform beam \(A D\) has weight \(W\) newtons and length 4 m . It is held in equilibrium in a horizontal position by two vertical ropes attached to the beam. The ropes are attached to two points \(B\) and \(C\) on the beam, where \(A B = 1 \mathrm {~m}\) and \(C D = 1 \mathrm {~m}\), as shown in Figure 3. The tension in the rope attached to \(C\) is double the tension in the rope attached to \(B\). The beam is modelled as a rod and the ropes are modelled as light inextensible strings.
  1. Find the distance of the centre of mass of the beam from \(A\). A small load of weight \(k W\) newtons is attached to the beam at \(D\). The beam remains in equilibrium in a horizontal position. The load is modelled as a particle. Find
  2. an expression for the tension in the rope attached to \(B\), giving your answer in terms of \(k\) and \(W\),
  3. the set of possible values of \(k\) for which both ropes remain taut.
Edexcel M1 2014 June Q7
13 marks Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b896c631-00a0-46c5-bce9-16d65f6e3095-13_364_833_269_561} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} A particle \(P\) of mass 2.7 kg lies on a rough plane inclined at \(40 ^ { \circ }\) to the horizontal. The particle is held in equilibrium by a force of magnitude 15 N acting at an angle of \(50 ^ { \circ }\) to the plane, as shown in Figure 4. The force acts in a vertical plane containing a line of greatest slope of the plane. The particle is in equilibrium and is on the point of sliding down the plane. Find
  1. the magnitude of the normal reaction of the plane on \(P\),
  2. the coefficient of friction between \(P\) and the plane. The force of magnitude 15 N is removed.
  3. Determine whether \(P\) moves, justifying your answer.
Edexcel M1 2014 June Q1
6 marks Moderate -0.8
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ed659098-c1cf-4ee1-a12a-bf8b6c42db95-02_332_921_260_516} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A particle of weight \(W\) newtons is attached at \(C\) to two light inextensible strings \(A C\) and \(B C\). The other ends of the strings are attached to fixed points \(A\) and \(B\) on a horizontal ceiling. The particle hangs in equilibrium with \(A C\) and \(B C\) inclined to the horizontal at \(30 ^ { \circ }\) and \(50 ^ { \circ }\) respectively, as shown in Figure 1. Given that the tension in \(B C\) is 6 N , find
  1. the tension in \(A C\),
  2. the value of \(W\).