Questions — Edexcel M1 (599 questions)

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Edexcel M1 2017 January Q2
  1. A particle \(P\) of mass 0.5 kg moves under the action of a single constant force ( \(2 \mathbf { i } + 3 \mathbf { j }\) )N.
    1. Find the acceleration of \(P\).
    At time \(t\) seconds, \(P\) has velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\). When \(t = 0 , \mathbf { v } = 4 \mathbf { i }\)
  2. Find the speed of \(P\) when \(t = 3\) Given that \(P\) is moving parallel to the vector \(2 \mathbf { i } + \mathbf { j }\) at time \(t = T\)
  3. find the value of \(T\).
Edexcel M1 2017 January Q3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-05_520_730_264_607} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Two forces \(\mathbf { P }\) and \(\mathbf { Q }\) act on a particle at a point \(O\). Force \(\mathbf { P }\) has magnitude 6 N and force \(\mathbf { Q }\) has magnitude 7 N . The angle between the line of action of \(\mathbf { P }\) and the line of action of \(\mathbf { Q }\) is \(120 ^ { \circ }\), as shown in Figure 1. The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(\mathbf { R }\). Find
  1. the magnitude of \(\mathbf { R }\),
  2. the angle between the line of action of \(\mathbf { R }\) and the line of action of \(\mathbf { P }\).
Edexcel M1 2017 January Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-06_266_1440_239_251} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A plank \(A B\) of mass 20 kg and length 8 m is resting in a horizontal position on two supports at \(C\) and \(D\), where \(A C = 1.5 \mathrm {~m}\) and \(D B = 2 \mathrm {~m}\). A package of mass 8 kg is placed on the plank at \(C\), as shown in Figure 2. The plank remains horizontal and in equilibrium. The plank is modelled as a uniform rod and the package is modelled as a particle.
  1. Find the magnitude of the normal reaction
    1. between the plank and the support at \(C\),
    2. between the plank and the support at \(D\).
      (6) The package is now moved along the plank to the point \(E\). When the package is at \(E\), the magnitude of the normal reaction between the plank and the support at \(C\) is \(R\) newtons and the magnitude of the normal reaction between the plank and the support at \(D\) is \(2 R\) newtons.
  2. Find the distance \(A E\).
  3. State how you have used the fact that the package is modelled as a particle.
Edexcel M1 2017 January Q5
  1. Two particles \(P\) and \(Q\) have masses \(4 m\) and \(k m\) respectively. They are moving towards each other in opposite directions along the same straight line on a smooth horizontal table when they collide directly. Immediately before the collision the speed of \(P\) is \(3 u\) and the speed of \(Q\) is \(u\). Immediately after the collision both particles have speed \(2 u\) and the direction of motion of \(Q\) has been reversed.
    1. Find, in terms of \(k , m\) and \(u\), the magnitude of the impulse received by \(Q\) in the collision.
    2. Find the two possible values of \(k\).
Edexcel M1 2017 January Q6
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-10_609_1013_118_456} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A particle \(P\) of mass 4 kg is held at rest at the point \(A\) on a rough plane which is inclined at \(30 ^ { \circ }\) to the horizontal. The point \(B\) lies on the line of greatest slope of the plane that passes through \(A\). The point \(B\) is 5 m down the plane from \(A\), as shown in Figure 3. The coefficient of friction between the plane and \(P\) is 0.3 The particle is released from rest at \(A\) and slides down the plane.
  1. Find the speed of \(P\) at the instant it reaches \(B\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-10_478_1011_1343_456} \captionsetup{labelformat=empty} \caption{Figure 4}
    \end{figure} The particle is now returned to \(A\) and is held in equilibrium by a horizontal force of magnitude \(H\) newtons, as shown in Figure 4. The line of action of the force lies in the vertical plane containing the line of greatest slope of the plane through \(A\). The particle is on the point of moving up the plane.
  2. Find the value of \(H\).
Edexcel M1 2017 January Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-12_524_586_274_696} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} Two particles \(P\) and \(Q\) have masses 3 kg and \(m \mathrm {~kg}\) respectively ( \(m > 3\) ). 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 and the hanging parts of the string vertical. The particle \(Q\) is at a height of 10.5 m above the horizontal ground, as shown in Figure 5. The system is released from rest and \(Q\) moves downwards. In the subsequent motion \(P\) does not reach the pulley. After the system is released, the tension in the string is 33.6 N .
  1. Show that the magnitude of the acceleration of \(P\) is \(1.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  2. Find the value of \(m\). The system is released from rest at time \(t = 0\). At time \(T _ { 1 }\) seconds after release, \(Q\) strikes the ground and does not rebound. The string goes slack and \(P\) continues to move upwards.
  3. Find the value of \(T _ { 1 }\) At time \(T _ { 2 }\) seconds after release, \(P\) comes to instantaneous rest.
  4. Find the value of \(T _ { 2 }\) At time \(T _ { 3 }\) seconds after release ( \(T _ { 3 } > T _ { 1 }\) ) the string becomes taut again.
  5. Sketch a velocity-time graph for the motion of \(P\) in the interval \(0 \leqslant t \leqslant T _ { 3 }\)
Edexcel M1 2018 January Q1
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-02_297_812_240_567} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A particle of weight \(W\) 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 the strings in a vertical plane and with \(A C\) and \(B C\) inclined to the horizontal at \(30 ^ { \circ }\) and \(45 ^ { \circ }\) respectively, as shown in Figure 1. Find, in terms of \(W\),
  1. the tension in \(A C\),
  2. the tension in \(B C\).
    VILLI SIHI NITIIIUM ION OC
    VILV SIHI NI JAHM ION OC
    VI4V SIHI NI JIIIM ION OC
Edexcel M1 2018 January Q2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-06_241_768_214_589} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A particle \(P\) of weight 40 N lies at rest in equilibrium on a fixed rough horizontal surface. A force of magnitude 20 N is applied to \(P\). The force acts at angle \(\theta\) to the horizontal, as shown in Figure 2. The coefficient of friction between \(P\) and the surface is \(\mu\). Given that the particle remains at rest, show that $$\mu \geqslant \frac { \cos \theta } { 2 + \sin \theta }$$ \includegraphics[max width=\textwidth, alt={}, center]{04b73f81-3316-4f26-ad98-a7be3a4b738f-07_119_167_2615_1777}
Edexcel M1 2018 January Q3
3. Two particles \(A\) and \(B\) have mass \(2 m\) and \(k m\) respectively. The particles are moving in opposite directions along the same straight smooth horizontal line so that the particles collide directly. Immediately before the collision \(A\) has speed \(2 u\) and \(B\) has speed \(u\). The direction of motion of each particle is reversed by the collision. Immediately after the collision the speed of \(A\) is \(\frac { u } { 2 }\).
  1. Find, in terms of \(m\) and \(u\), the magnitude of the impulse exerted by \(B\) on \(A\) in the collision.
  2. Show that \(k < 5\)
Edexcel M1 2018 January Q4
  1. A package of mass 6 kg is held at rest at a fixed point \(A\) on a rough plane. The plane is inclined at \(30 ^ { \circ }\) to the horizontal. The package is released from rest and slides down a line of greatest slope of the plane. The coefficient of friction between the package and the plane is \(\frac { 1 } { 4 }\). The package is modelled as a particle.
    1. Find the magnitude of the acceleration of the package.
    As it slides down the slope the package passes through the point \(B\), where \(A B = 10 \mathrm {~m}\).
  2. Find the speed of the package as it passes through \(B\).
Edexcel M1 2018 January Q5
5. A cyclist is travelling along a straight horizontal road. The cyclist starts from rest at point \(A\) on the road and accelerates uniformly at \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for 20 seconds. He then moves at constant speed for \(4 T\) seconds, where \(T < 20\). He then decelerates uniformly at \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and after \(T\) seconds passes through point \(B\) on the road. The distance from \(A\) to \(B\) is 705 m .
  1. Sketch a speed-time graph for the motion of the cyclist between points \(A\) and \(B\).
  2. Find the value of \(T\). The cyclist continues his journey, still decelerating uniformly at \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), until he comes to rest at point \(C\) on the road.
  3. Find the total time taken by the cyclist to travel from \(A\) to \(C\).
Edexcel M1 2018 January Q6
  1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors.]
A particle \(P\) of mass 2 kg moves under the action of two forces, \(( 2 \mathbf { i } + 3 \mathbf { j } ) \mathrm { N }\) and \(( 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { N }\).
  1. Find the magnitude of the acceleration of \(P\). At time \(t = 0 , P\) has velocity ( \(- u \mathbf { i } + u \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\), where \(u\) is a positive constant. At time \(t = T\) seconds, \(P\) has velocity \(( 10 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
  2. Find
    1. the value of \(T\),
    2. the value of \(u\).
Edexcel M1 2018 January Q7
7. A non-uniform rod \(A B\) has length 6 m and mass 8 kg . The rod rests in equilibrium, in a horizontal position, on two smooth supports at \(C\) and at \(D\), where \(A C = 1 \mathrm {~m}\) and \(D B = 1 \mathrm {~m}\), as shown in Figure 3. The magnitude of the reaction between the rod and the support at \(D\) is twice the magnitude of the reaction between the rod and the support at \(C\). The centre of mass of the rod is at \(G\), where \(A G = x \mathrm {~m}\).
  1. Show that \(x = \frac { 11 } { 3 }\). The support at \(C\) is moved to the point \(F\) on the rod, where \(A F = 2 \mathrm {~m}\). A particle of mass 3 kg is placed on the rod at \(A\). The rod remains horizontal and in equilibrium. The magnitude of the reaction between the rod and the support at \(D\) is \(k\) times the magnitude of the reaction between the rod and the support at \(F\).
  2. Find the value of \(k\).
    7. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-20_223_1262_127_338}
    \end{figure}
Edexcel M1 2018 January Q8
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-24_496_1143_121_404} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} One end of a light inextensible string is attached to a block \(A\) of mass 3 kg . Block \(A\) is held at rest on a smooth fixed plane. The plane is inclined at \(40 ^ { \circ }\) to the horizontal ground. The string lies along a line of greatest slope of the plane and passes over a small smooth pulley which is fixed at the top of the plane. The other end of the string is attached to a block \(B\) of mass 5 kg . Block \(B\) hangs freely at rest below the pulley, as shown in Figure 4. The system is released from rest with the string taut. By modelling the two blocks as particles,
  1. find the tension in the string as \(B\) descends. After falling for 1.5 s , block \(B\) hits the ground and is immediately brought to rest. In its subsequent motion, \(A\) does not reach the pulley.
  2. Find the speed of \(B\) at the instant it hits the ground.
  3. Find the total distance moved up the plane by \(A\) before it comes to instantaneous rest. \includegraphics[max width=\textwidth, alt={}, center]{04b73f81-3316-4f26-ad98-a7be3a4b738f-28_97_141_2519_1804}
    \includegraphics[max width=\textwidth, alt={}, center]{04b73f81-3316-4f26-ad98-a7be3a4b738f-28_125_161_2624_1779}
Edexcel M1 2019 January Q1
  1. Two particles, \(A\) and \(B\), have masses \(2 m\) and \(3 m\) respectively. They are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane when they collide directly. Immediately before they collide, the speed of \(A\) is \(3 u\) and the speed of \(B\) is \(u\). As a result of the collision, the speed of \(A\) is halved and the direction of motion of each particle is reversed.
    1. Find the speed of \(B\) immediately after the collision.
    2. Find the magnitude of the impulse exerted on \(A\) by \(B\) in the collision.
Edexcel M1 2019 January Q2
2. [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors due east and due north respectively and position vectors are given relative to a fixed origin \(O\).] At time \(t = 0\), a bird \(A\) leaves its nest, that is located at the point with position vector \(( 20 \mathbf { i } - 17 \mathbf { j } ) \mathrm { m }\), and flies with constant velocity \(( - 6 \mathbf { i } + 7 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). At the same time a second bird \(B\) leaves its nest which is located at the point with position vector \(( - 8 \mathbf { i } + 9 \mathbf { j } ) \mathrm { m }\) and flies with constant velocity ( \(p \mathbf { i } + 2 p \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\), where \(p\) is a constant. At time \(t = 4 \mathrm {~s}\), bird \(B\) is south west of bird \(A\).
  1. Find the direction of motion of \(A\), giving your answer as a bearing to the nearest degree.
  2. Find the speed of \(B\).
Edexcel M1 2019 January Q3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0d5a56ba-6a33-4dc8-b612-d2957211124f-08_387_204_251_872} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A lift of mass \(M \mathrm {~kg}\) is being raised by a vertical cable attached to the top of the lift. A person of mass \(m \mathrm {~kg}\) stands on the floor inside the lift, as shown in Figure 1. The lift ascends vertically with constant acceleration \(1.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The tension in the cable is 2800 N and the person experiences a constant normal reaction of magnitude 560 N from the floor of the lift. The cable is modelled as being light and inextensible, the person is modelled as a particle and air resistance is negligible.
  1. Write down an equation of motion for the person only.
  2. Write down an equation of motion for the lift only.
  3. Hence, or otherwise, find
    1. the value of \(m\),
    2. the value of \(M\).
Edexcel M1 2019 January Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0d5a56ba-6a33-4dc8-b612-d2957211124f-10_410_1143_258_404} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A boy sees a box on the end \(Q\) of a plank \(P Q\) which overhangs a swimming pool. The plank has mass 30 kg , is 5 m long and rests in a horizontal position on two bricks. The bricks are modelled as smooth supports, one acting on the rod at \(P\) and one acting on the rod at \(R\), where \(P R = 3 \mathrm {~m}\). The support at \(R\) is on the edge of the swimming pool, as shown in Figure 2. The boy has mass 40 kg and the box has mass 2.5 kg . The plank is modelled as a uniform rod and the boy and the box are modelled as particles. The boy steps on to the plank at \(P\) and begins to walk slowly along the plank towards the box.
  1. Find the distance he can walk along the plank from \(P\) before the plank starts to tilt.
  2. State how you have used, in your working, the fact that the box is modelled as a particle. A rock of mass \(M \mathrm {~kg}\) is placed on the plank at \(P\). The boy is then able to walk slowly along the plank to the box at the end \(Q\) without the plank tilting. The rock is modelled as a particle.
  3. Find the smallest possible value of \(M\).
Edexcel M1 2019 January Q5
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0d5a56ba-6a33-4dc8-b612-d2957211124f-14_451_551_255_699} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A small metal box of mass 6 kg is attached at \(B\) to two ropes \(B P\) and \(B Q\). The fixed points \(P\) and \(Q\) are on a horizontal ceiling and \(P Q = 3.5 \mathrm {~m}\). The box hangs in equilibrium at a vertical distance of 2 m below the line \(P Q\), with the ropes in a vertical plane and with angle \(B Q P = 45 ^ { \circ }\), as shown in Figure 3. The box is modelled as a particle and the ropes are modelled as light inextensible strings. Find
  1. the tension in \(B P\),
  2. the tension in \(B Q\).
Edexcel M1 2019 January Q6
6. A train travels for a total of 270 s along a straight horizontal track between two stations \(A\) and \(B\). The train starts from rest at \(A\) and moves with constant acceleration for 60 s until it reaches a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The train then travels at this constant speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) before it moves with constant deceleration for 30 s , coming to rest at \(B\).
  1. Sketch below a speed-time graph for the journey of the train between the two stations \(A\) and \(B\). Given that the distance between the two stations is 4.5 km ,
  2. find the value of \(V\),
  3. find how long it takes the train to travel from station \(A\) to the point that is exactly halfway between the two stations. The train is travelling at speed \(\frac { 1 } { 4 } V \mathrm {~ms} ^ { - 1 }\) at times \(T _ { 1 }\) seconds and \(T _ { 2 }\) seconds after leaving station \(A\).
  4. Find the value of \(T _ { 1 }\) and the value of \(T _ { 2 }\)
Edexcel M1 2019 January Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0d5a56ba-6a33-4dc8-b612-d2957211124f-20_410_1091_258_440} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Two particles \(A\) and \(B\) have masses \(m\) and \(3 m\) respectively. The particles are attached to the ends of a light inextensible string. Particle \(A\) is held at rest on a rough horizontal table. The coefficient of friction between particle \(A\) and the table is \(\frac { 1 } { 5 }\). The string lies along the table and passes over a small smooth light pulley that is fixed at the edge of the table. Particle \(B\) is at rest on a rough plane that is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 4 } { 3 }\), as shown in Figure 4. The coefficient of friction between particle \(B\) and the inclined plane is \(\frac { 1 } { 3 }\). The string lies in the vertical plane that contains the pulley and a line of greatest slope of the inclined plane. The system is released from rest with the string taut and \(B\) slides down the inclined plane. Given that \(A\) does not reach the pulley,
  1. find the tension in the string,
  2. state where in your working you have used the fact that the string is modelled as being light,
  3. find the magnitude of the force exerted on the pulley by the string.
    \includegraphics[max width=\textwidth, alt={}, center]{0d5a56ba-6a33-4dc8-b612-d2957211124f-24_172_1824_2581_123}
    \includegraphics[max width=\textwidth, alt={}, center]{0d5a56ba-6a33-4dc8-b612-d2957211124f-24_157_85_2595_1966}
Edexcel M1 2020 January Q1
  1. Two particles, \(P\) and \(Q\), of mass \(m _ { 1 }\) and \(m _ { 2 }\) respectively, are moving on a smooth horizontal plane. The particles are moving towards each other in opposite directions along the same straight line when they collide directly. Immediately before the collision, both particles are moving with speed \(u\).
The direction of motion of each particle is reversed by the collision.
Immediately after the collision, the speed of \(Q\) is \(\frac { 1 } { 3 } u\).
  1. Find, in terms of \(m _ { 2 }\) and \(u\), the magnitude of the impulse exerted by \(P\) on \(Q\) in the collision.
  2. Find, in terms of \(m _ { 1 } , m _ { 2 }\) and \(u\), the speed of \(P\) immediately after the collision.
  3. Hence show that \(m _ { 2 } > \frac { 3 } { 4 } m _ { 1 }\)
Edexcel M1 2020 January Q2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{916543cb-14f7-486c-ba3c-eda9be134045-04_473_1254_221_346} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A non-uniform beam \(A B\) has length 6 m and weight \(W\) newtons. The beam is supported in equilibrium in a horizontal position by two vertical ropes, one attached to the beam at \(A\) and the other attached to the beam at \(C\), where \(C B = 1.5 \mathrm {~m}\), as shown in Figure 1 . The centre of mass of the beam is 2.625 m from \(A\). The ropes are modelled as light strings. The beam is modelled as a non-uniform rod. Given that the tension in the rope attached at \(C\) is 20 N greater than the tension in the rope attached at \(A\),
  1. find the value of \(W\).
  2. State how you have used the fact that the beam is modelled as a rod.
Edexcel M1 2020 January Q3
3. A particle, \(P\), is projected vertically upwards with speed \(U\) from a fixed point \(O\). At the instant when \(P\) reaches its greatest height \(H\) above \(O\), a second particle, \(Q\), is projected with speed \(\frac { 1 } { 2 } U\) vertically upwards from \(O\).
  1. Find \(H\) in terms of \(U\) and \(g\).
  2. Find, in terms of \(U\) and \(g\), the time between the instant when \(Q\) is projected and the instant when the two particles collide.
  3. Find where the two particles collide. DO NOT WRITEIN THIS AREA
    \includegraphics[max width=\textwidth, alt={}, center]{916543cb-14f7-486c-ba3c-eda9be134045-08_2666_99_107_1957}
Edexcel M1 2020 January Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{916543cb-14f7-486c-ba3c-eda9be134045-10_633_1237_258_356} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Two identical small rings, \(A\) and \(B\), each of mass \(m\), are threaded onto a rough horizontal wire. The rings are connected by a light inextensible string. A particle \(C\) of mass \(3 m\) is attached to the midpoint of the string. The particle \(C\) hangs in equilibrium below the wire with angle \(B A C = \beta\), as shown in Figure 2. The tension in each of the parts, \(A C\) and \(B C\), of the string is \(T\)
  1. By considering particle \(C\), find \(T\) in terms of \(m , g\) and \(\beta\)
  2. Find, in terms of \(m\) and \(g\), the magnitude of the normal reaction between the wire and \(A\). The coefficient of friction between each ring and the wire is \(\frac { 4 } { 5 }\)
    The two rings, \(A\) and \(B\), are on the point of sliding along the wire towards each other.
  3. Find the value of \(\tan \beta\)
    \includegraphics[max width=\textwidth, alt={}, center]{916543cb-14f7-486c-ba3c-eda9be134045-11_2255_50_314_34}
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