Questions — Edexcel (9685 questions)

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Edexcel M1 Q1
6 marks Moderate -0.8
  1. A tennis ball, moving horizontally, hits a wall at \(25 \mathrm {~ms} ^ { - 1 }\) and rebounds along the same straight line at \(15 \mathrm {~ms} ^ { - 1 }\). The impulse exerted by the wall on the ball has magnitude 12 Ns .
    1. Calculate the mass of the ball.
    2. State any modelling assumptions that you have made.
    \includegraphics[max width=\textwidth, alt={}]{977c24cc-8280-4881-8a62-65b7efd336ac-1_278_337_751_434}
    Forces of magnitude \(4 \mathrm {~N} , 5 \mathrm {~N}\) and 8 N act on a particle in directions whose bearings are \(000 ^ { \circ } , 090 ^ { \circ }\) and \(210 ^ { \circ }\) respectively. Find the magnitude of the resultant force and the bearing of the direction in which it acts.
Edexcel M1 Q3
9 marks Moderate -0.3
3. A packing-case, of mass 60 kg , is standing on the floor of a lift. The mass of the lift-cage is 200 kg . The lift-cage is raised and lowered by means of a cable attached to its roof. In each of the following cases, find the magnitude of the force exerted by the floor of the liftcage on the packing-case and the tension in the cable supporting the lift:
  1. The lift is descending with constant speed.
  2. The lift is ascending and accelerating at \(1.2 \mathrm {~ms} ^ { - 2 }\).
  3. State any modelling assumptions you have made.
Edexcel M1 Q4
12 marks Standard +0.3
4. \(A B\) is a light rod. Forces \(\mathbf { F } , \mathbf { G }\) and \(\mathbf { H }\), of magnitudes \(3 \mathrm {~N} , 2 \mathrm {~N}\) and 6 N respectively, act upwards at right angles to the rod in a vertical plane at points dividing \includegraphics[max width=\textwidth, alt={}, center]{977c24cc-8280-4881-8a62-65b7efd336ac-1_186_586_1741_1329} \(A B\) in the ratio \(1 : 4 : 2 : 4\), as shown.
A single force \(\mathbf { P }\) is applied downwards at the point \(C\) to keep the rod horizontal in equilibrium.
  1. State the magnitude of \(\mathbf { P }\).
  2. Show that \(A C : C B = 5 : 6\). Two particles, of weights 3 N and \(k \mathrm {~N}\), are now placed on the rod at \(A\) and \(B\) respectively, while the same upward forces \(\mathbf { F } , \mathbf { G }\) and \(\mathbf { H }\) act as before. It is found that a single downward force at the same point \(C\) as before keeps \(A B\) horizontal under gravity.
  3. Find the value of \(k\). \section*{MECHANICS 1 (A) TEST PAPER 4 Page 2}
Edexcel M1 Q5
13 marks Standard +0.3
  1. Two smooth spheres \(A\) and \(B\), of masses \(2 m\) and \(m\) respectively, are connected by a light inextensible string which passes over a smooth fixed pulley as shown. \(A\) is initially at rest on the rough horizontal surface of a table, the coefficient of friction between \(A\) \includegraphics[max width=\textwidth, alt={}, center]{977c24cc-8280-4881-8a62-65b7efd336ac-2_253_323_255_1622}
    and the table being \(\frac { 2 } { 7 }\). \(B\) hangs freely on the end of the vertical portion of the string. \(A\) is now given an impulse, directed away from the pulley, of magnitude 5 m Ns.
    1. Show that the system starts to move with speed \(2.5 \mathrm {~ms} ^ { - 1 }\).
    2. State which modelling assumption ensures that the tensions in the two sections of the string can be taken to be equal.
    Given that \(A\) comes to rest before it reaches the edge of the table and before \(B\) hits the pulley,
  2. find the time taken for the system to come to rest.
  3. Find the distance travelled by \(A\) before it first comes to rest.
Edexcel M1 Q6
14 marks Standard +0.3
6. The diagram shows the velocity-time graph for a cyclist's journey. Each section has constant acceleration or deceleration and the three sections are of equal duration \(x\) seconds each.
Given that the total distance travelled is 792 m , \includegraphics[max width=\textwidth, alt={}, center]{977c24cc-8280-4881-8a62-65b7efd336ac-2_337_647_1128_1284}
  1. find the value of \(x\) and the acceleration for the first section of the journey. Another cyclist covers the same journey in three sections of equal duration, accelerating at \(\frac { 1 } { 11 } \mathrm {~ms} ^ { - 2 }\) for the first section, travelling at constant speed for the second section and decelerating at \(\frac { 1 } { 11 } \mathrm {~ms} ^ { - 2 }\) for the third section.
  2. Find the time taken by this cyclist to complete the journey.
  3. Show that the maximum speeds of both cyclists are the same.
Edexcel M1 Q7
14 marks Moderate -0.3
7. Relative to a fixed origin \(O\), the points \(X\) and \(Y\) have position vectors \(( 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { m }\) and \(( 12 \mathbf { i } + \mathbf { j } ) \mathbf { m }\) respectively, where \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors.
  1. Find the distance \(X Y\). A particle \(P\) of mass 2 kg moves from \(X\) to \(Y\) in 4 seconds, in a straight line at a constant speed.
  2. Show that the velocity vector of \(P\) is \(( 2 \mathbf { i } + 1 \cdot 5 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\). The particle continues beyond \(Y\) with the same constant velocity.
  3. Write down an expression for the position vector of \(P t\) seconds after leaving \(X\).
  4. Find the value of \(t\) when \(P\) is at the point with position vector \(( 16 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m }\). When it is moving with the same constant speed, \(P\) collides directly with another particle \(Q\), of mass 4 kg , which is at rest. \(P\) and \(Q\) coalesce and move together as a single particle.
  5. Find the velocity vector of the combined particle after the collision.
    (5 marks)
Edexcel M1 Q1
5 marks Moderate -0.8
  1. Two forces, both of magnitude 5 N , act on a particle in the directions with bearings \(000 ^ { \circ }\) and \(070 ^ { \circ }\), as shown. Calculate
    1. the magnitude of the resultant force on the particle,
    2. the bearing on which this resultant force acts.
    3. A uniform plank \(X Y\) has length 7 m and mass 2 kg . It is placed with the portion \(Z Y\) in contact with a \includegraphics[max width=\textwidth, alt={}, center]{38e355b0-9d75-40ad-b450-bd74c5135c7f-1_149_616_843_1334}
      horizontal surface, where \(Z Y = 2.8 \mathrm {~m}\). To prevent the \includegraphics[max width=\textwidth, alt={}, center]{38e355b0-9d75-40ad-b450-bd74c5135c7f-1_207_253_404_1505}
    \section*{MECHANICS 1 (A) TEST PAPER 5 Page 2}
Edexcel M1 Q5
15 marks Standard +0.3
  1. \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors. The point \(A\) has position vector \(6 \mathbf { j } \mathrm {~m}\) relative to an origin \(O\). At time \(t = 0\) a particle \(P\) starts from \(O\) and moves with constant velocity ( \(5 \mathbf { i } + 2 \mathbf { j }\) ) \(\mathrm { ms } ^ { - 1 }\). At the same instant a particle \(Q\) starts from \(A\) and moves with constant velocity \(4 \mathrm { ims } ^ { - 1 }\).
    1. Write down the position vectors of \(P\) and of \(Q\) at time \(t\) seconds.
    2. Show that the distance \(d \mathrm {~m}\) between \(P\) and \(Q\) at time \(t\) seconds is such that
    $$d ^ { 2 } = 5 t ^ { 2 } - 24 t + 36 .$$
  2. Find the value of \(t\) for which \(d ^ { 2 }\) is a minimum.
  3. Hence find the minimum distance between \(P\) and \(Q\), and state the position vector of each particle when they are closest together.
Edexcel M1 Q6
15 marks Standard +0.3
6. \(A , B\) and \(C\) are three small spheres of equal radii and masses \(2 m , m\) and \(5 m\) respectively. They are placed in a straight line on a smooth horizontal surface. \(A\) is projected with speed \(6 \mathrm {~ms} ^ { - 1 }\) towards \(B\), which is at rest. When \(A\) hits \(B\) it exerts an impulse of magnitude 8 m Ns on \(B\).
  1. Find the speed with which \(B\) starts to move.
  2. Show that the speed of \(A\) after it collides with \(B\) is \(2 \mathrm {~ms} ^ { - 1 }\). After travelling \(3 \mathrm {~m} , B\) hits \(C\), which is then travelling towards \(B\) at \(2 \cdot 2 \mathrm {~ms} ^ { - 1 } . C\) is brought to rest by this impact.
  3. Show that the direction of \(B\) 's motion is reversed and find its new speed.
  4. Find how far \(B\) now travels before it collides with \(A\) again.
  5. State a modelling assumption that you have made about the spheres.
Edexcel M1 Q7
16 marks Standard +0.8
7. A particle \(P\), of mass \(m\), is in contact with a rough plane inclined at \(30 ^ { \circ }\) to the horizontal as shown. A light string is attached to \(P\) and makes an angle of \(30 ^ { \circ }\) with the plane. When the tension in this string has magnitude \(k m g , P\) is \includegraphics[max width=\textwidth, alt={}, center]{38e355b0-9d75-40ad-b450-bd74c5135c7f-2_268_474_1759_1407}
just on the point of moving up the plane.
  1. Show that \(\mu\), the coefficient of friction between \(P\) and the plane, is \(\frac { k \sqrt { } 3 - 1 } { \sqrt { } 3 - k }\).
  2. Given further that \(k = \frac { 3 \sqrt { } 3 } { 7 }\), deduce that \(\mu = \frac { \sqrt { } 3 } { 6 }\). The string is now removed.
  3. Determine whether \(P\) will move down the plane and, if it does, find its acceleration.
  4. Give a reason why the way in which \(P\) is shown in the diagram might not be consistent with the modelling assumptions that have been made.
Edexcel M1 Q1
6 marks Standard +0.3
1. \includegraphics[max width=\textwidth, alt={}, center]{31efa627-5114-4797-9d46-7f1311c18ff8-1_490_254_354_347} A vertical pole \(X Y\), of length 2.5 m and mass 0.5 kg , has its lower end \(Y\) free to move in a smooth horizontal groove. Forces of magnitude 0.2 N and 0.14 N are applied to the pole horizontally at the points \(V\) and \(W\) respectively, where \(X V = 1.5 \mathrm {~m}\) and \(V W = 0.5 \mathrm {~m}\).
Find, to the nearest cm , the distance from \(X\) at which an opposing horizontal force must be applied to keep the pole at rest in equilibrium, and state the magnitude of this force.
Edexcel M1 Q2
7 marks Standard +0.3
2. A particle passes through a point \(O\) with speed \(9 \mathrm {~ms} ^ { - 1 }\) and moves in a straight line with constant acceleration \(3.6 \mathrm {~ms} ^ { - 2 }\) for \(t\) seconds until it reaches the point \(P\). The acceleration is then reduced to \(2 \mathrm {~ms} ^ { - 2 }\) and this is maintained for another \(t\) seconds until the particle passes the point \(Q\) with speed \(16 \mathrm {~ms} ^ { - 1 }\). Calculate
  1. the time taken by the particle to travel from \(O\) to \(Q\),
  2. the distance \(O Q\).
Edexcel M1 Q3
9 marks Standard +0.3
3. A lump of clay, of mass 0.8 kg , is attached to the end \(A\) of a light \(\operatorname { rod } A B\), which is pivoted at its other end \(B\) so that it can rotate smoothly in a vertical plane. A force is applied to \(A\) at an angle of \(60 ^ { \circ }\) to the vertical, as shown, the magnitude \(F \mathrm {~N}\) of this force being just enough to hold the lump of clay in equilibrium with \(A B\) inclined \includegraphics[max width=\textwidth, alt={}, center]{31efa627-5114-4797-9d46-7f1311c18ff8-1_309_335_1453_1590}
at an angle of \(30 ^ { \circ }\) to the upward vertical.
  1. Find the value of \(F\),
  2. Find the magnitude of the force in the \(\operatorname { rod } A B\).
  3. State the modelling assumption that you have made about the lump of clay.
    (6 marks)
    (2 marks)
    (1 mark)
Edexcel M1 Q4
10 marks Standard +0.3
4. Two particles \(A\) and \(B\), of masses 50 grams and \(y\) grams, are moving in the same straight line, in opposite directions, with speeds \(7 \mathrm {~ms} ^ { - 1 }\) and \(4 \mathrm {~ms} ^ { - 1 }\) respectively, and collide. \includegraphics[max width=\textwidth, alt={}, center]{31efa627-5114-4797-9d46-7f1311c18ff8-1_218_508_2143_1382}
In each of the following separate cases, find the value of \(y\) and the magnitude of the impulse exerted by each particle on the other:
  1. after impact the particles move together with speed \(2.25 \mathrm {~ms} ^ { - 1 }\);
  2. after impact the particles move in opposite directions with speed \(5 \mathrm {~ms} ^ { - 1 }\). \section*{MECHANICS 1 (A) TEST PAPER 6 Page 2}
Edexcel M1 Q5
12 marks Standard +0.3
5.
\includegraphics[max width=\textwidth, alt={}]{31efa627-5114-4797-9d46-7f1311c18ff8-2_262_597_276_356}
A small stone is projected with speed \(7 \mathrm {~ms} ^ { - 1 }\) from \(P\), the bottom of a rough plane inclined at \(25 ^ { \circ }\) to the horizontal, and moves up a line of greatest slope of the plane until it comes to instantaneous rest at \(Q\), where \(P Q = 4 \mathrm {~m}\).
  1. Show that the deceleration of the stone as it moves up the plane has magnitude \(\frac { 49 } { 8 } \mathrm {~ms} ^ { - 2 }\).
  2. Find the coefficient of friction between the stone and the plane,
  3. Find the speed with which the stone returns to \(P\).
  4. Name one force which you have ignored in your mathematical model, and state whether the answer to part (c) would be larger or smaller if that force were taken into account.
Edexcel M1 Q6
14 marks Standard +0.3
6. The points \(A\) and \(B\) have position vectors \(( 30 \mathbf { i } - 60 \mathbf { j } ) \mathrm { m }\) and \(( - 20 \mathbf { i } + 60 \mathbf { j } ) \mathrm { m }\) respectively relative to an origin \(O\), where \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors. A cyclist, Chris, starts at \(A\) and cycles towards \(B\) with constant speed \(2.6 \mathrm {~ms} ^ { - 1 }\). Another cyclist, Doug, starts at \(O\) and cycles towards \(B\) with constant speed \(k \sqrt { } 10 \mathrm {~ms} ^ { - 1 }\).
  1. Show that Chris's velocity vector is \(( - \mathbf { i } + 2 \cdot 4 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\).
  2. Find Doug's velocity vector in the form \(k ( a \mathbf { i } + b \mathbf { j } ) \mathrm { ms } ^ { - 1 }\). Given that Chris and Doug arrive at \(B\) at the same time,
  3. find the value of \(k\).
Edexcel M1 Q7
17 marks Standard +0.3
7. \includegraphics[max width=\textwidth, alt={}, center]{31efa627-5114-4797-9d46-7f1311c18ff8-2_456_380_1862_395} A particle \(P\), of mass 4 kg , rests on horizontal ground and is attached by a light, inextensible string to another particle \(Q\) of mass 4.5 kg . The string passes over a smooth pulley whose centre is 3 m above the ground. Initially \(Q\) is 1.1 m below the level of the centre of the pulley. The system is released from rest in this position.
  1. Find the acceleration of the two particles.
  2. Find the speed with which \(Q\) hits the ground. Assuming that \(Q\) does not rebound from the ground while the string is slack,
  3. show that \(P\) does not reach the pulley before \(Q\) starts to move again.
  4. Find the speed with which \(Q\) leaves the ground when the string again becomes taut.
    (3 marks)
Edexcel M1 Q1
4 marks Moderate -0.3
  1. Briefly define the following terms used in modelling in Mechanics:
    1. lamina,
    2. uniform rod,
    3. smooth surface,
    4. particle.
      (4 marks)
    5. Two forces \(\mathbf { F }\) and \(\mathbf { G }\) are given by \(\mathbf { F } = ( 6 \mathbf { i } - 5 \mathbf { j } ) \mathbf { N } , \mathbf { G } = ( 3 \mathbf { i } + 17 \mathbf { j } ) \mathrm { N }\), where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors in the \(x\) and \(y\) directions respectively and the unit of length on each axis is 1 cm .
      (a) Find the magnitude of \(\mathbf { R }\), the resultant of \(\mathbf { F }\) and \(\mathbf { G }\).
      (b) Find the angle between the direction of \(\mathbf { R }\) and the positive \(x\)-axis. \(\mathbf { R }\) acts through the point \(P ( - 4,3 )\). \(O\) is the origin \(( 0,0 )\).
      (c) Use the fact that \(O P\) is perpendicular to the line of action of \(\mathbf { R }\) to calculate the moment of \(\mathbf { R }\) about an axis through the origin and perpendicular to the \(x - y\) plane.
    6. A string is attached to a packing case of mass 12 kg , which is at rest on a rough horizontal plane. When a force of magnitude 50 N is applied at the other end of the string, and \includegraphics[max width=\textwidth, alt={}, center]{6fbe12d6-9a46-4602-a7b9-63d50b02ff28-1_183_522_1106_1421}
      the string makes an angle of \(35 ^ { \circ }\) with the vertical as shown, the case is on the point of moving.
      (a) Find the coefficient of friction between the case and the plane.
    The force is now increased, with the string at the same angle, and the case starts to move along the plane with constant acceleration, reaching a speed of \(2 \mathrm {~ms} ^ { - 1 }\) after 4 seconds.
    (b) Find the magnitude of the new force.
    (c) State any modelling assumptions you have made about the case and the string.
Edexcel M1 Q4
12 marks Moderate -0.3
4. A uniform yoke \(A B\), of mass 4 kg and length \(4 a \mathrm {~m}\), rests on the shoulders \(S\) and \(T\) of two oxen. \includegraphics[max width=\textwidth, alt={}, center]{6fbe12d6-9a46-4602-a7b9-63d50b02ff28-1_131_679_1800_1275} \(A S = T B = a \mathrm {~m}\). A bucket of mass \(x \mathrm {~kg}\) is suspended from \(A\).
  1. Show that the vertical force on the yoke at \(T\) has magnitude \(\left( 2 - \frac { 1 } { 2 } x \right) g \mathrm {~N}\) and find, in terms of \(x\) and \(g\), the vertical force on the yoke at \(S\).
  2. If the ratio of these vertical forces is \(5 : 1\), find the value of \(x\).
  3. Find the maximum value of \(x\) for which the yoke will remain horizontal.
Edexcel M1 Q5
12 marks Standard +0.3
5. Two small smooth spheres \(A\) and \(B\), of equal radius but masses \(m \mathrm {~kg}\) and km kg respectively, where \(k > 1\), move towards each other along a straight line and collide directly. Immediately before the collision, \(A\) has speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(B\) has speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). In the collision, the impulse exerted by \(A\) on \(B\) has magnitude 7 km Ns.
Q. 5 continued on next page ... \section*{MECHANICS 1 (A) TEST PAPER 7 Page 2}
  1. continued ...
    1. Find the speed of \(B\) after the impact.
    2. Show that the speed of \(A\) immediately after the collision is \(( 7 k - 5 ) \mathrm { ms } ^ { - 1 }\) and deduce that the direction of \(A\) 's motion is reversed. \(B\) is now given a further impulse of magnitude \(m u \mathrm { Ns }\), as a result of which a second collision between it and \(A\) occurs.
    3. Show that \(u > k ( 7 k - 1 )\).
    \includegraphics[max width=\textwidth, alt={}]{6fbe12d6-9a46-4602-a7b9-63d50b02ff28-2_422_787_815_340}
    The velocity-time graph illustrates the motion of a particle which accelerates from rest to \(8 \mathrm {~ms} ^ { - 1 }\) in \(x\) seconds and then to \(24 \mathrm {~ms} ^ { - 1 }\) in a further 4 seconds. It then travels at a constant speed for another \(y\) seconds before decelerating to \(12 \mathrm {~ms} ^ { - 1 }\) over the next \(y\) seconds and then to rest in the final 7 seconds of its motion. Given that the total distance travelled by the particle is 496 m ,
  2. show that \(2 x + 21 y = 195\). Given also that the average speed of the particle during its motion is \(15 \cdot 5 \mathrm {~ms} ^ { - 1 }\),
  3. show that \(x + 2 y = 21\).
  4. Hence find the values of \(x\) and \(y\),
  5. Write down the acceleration for each section of the motion.
Edexcel M1 Q7
14 marks Standard +0.3
7. Two particles \(P\) and \(Q\), of masses \(2 m\) and \(3 m\) respectively, are connected by a light string. Initially, \(P\) is at rest on a smooth horizontal table. The string passes over a small smooth pulley and \(Q\) rests on a rough plane inclined at an \includegraphics[max width=\textwidth, alt={}, center]{6fbe12d6-9a46-4602-a7b9-63d50b02ff28-2_241_483_1818_1407}
angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 4 } { 3 }\). The coefficient of friction between \(Q\) and the inclined plane is \(\frac { 1 } { 6 }\).
The system is released from rest with \(Q\) at a distance of 0.8 metres above a horizontal floor.
  1. Show that the acceleration of \(P\) and \(Q\) is \(\frac { 21 g } { 50 }\), stating a modelling assumption which you must make to ensure that both particles have the same acceleration.
  2. Find the speed with which \(Q\) hits the floor. After \(Q\) hits the floor and does not rebound, \(P\) moves a further 0.2 m until it hits the pulley.
  3. Find the total time after the system is released before \(P\) hits the pulley.
Edexcel M1 Q1
5 marks Easy -1.2
  1. A golf ball and a table tennis ball are dropped together from the top of a building. The golf ball hits the ground after 1.7 seconds.
    1. Calculate the height of the top of the building above the ground.
    According to a simple model, the two balls hit the ground at the same time.
  2. State why this may not be true in practice and describe a refinement to the model which could lead to a more realistic solution.
Edexcel M1 Q2
5 marks Standard +0.3
2. A plank of wood \(X Y\) has length \(5 a\) m and mass 5 kg . It rests on a support at \(Q\), where \(X Q = 3 a\) m . When a kitten of mass 8 kg sits on the plank at \(P\), where \(P Y = a \mathrm {~m}\), the plank just remains horizontal. By modelling the plank as a non-uniform rod and the kitten as a particle, find
  1. the magnitude of the reaction at the support,
  2. the distance from \(X\) to the centre of mass of the plank, in terms of \(a\).
Edexcel M1 Q3
9 marks Moderate -0.3
3. A particle is in equilibrium under the action of three forces \(\mathbf { P } , \mathbf { Q }\) and \(\mathbf { R }\) acting in the same horizontal plane. \(P\) has magnitude 9 N and acts on a bearing of \(030 ^ { \circ } . Q\) has magnitude 12 N . and acts on a bearing of \(225 ^ { \circ }\).
  1. Find the values of \(a\) and \(b\) such that \(\mathbf { R } = ( a \mathbf { i } + b \mathbf { j } ) \mathrm { N }\), where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors in the directions due East and due North respectively.
  2. Calculate the magnitude and direction of \(\mathbf { R }\)
Edexcel M1 Q4
13 marks Standard +0.3
4. \(X\) and \(Y\) are two points 1 m apart on a line of greatest slope of a smooth plane inclined at \(60 ^ { \circ }\) to the horizontal. A particle \(P\) of mass 1 kg is released from rest at \(X\).
  1. Find the speed with which \(P\) reaches \(Y\). \(P\) is now connected to another particle \(Q\), of mass \(M \mathrm {~kg}\), by a light inextensible string. The system is placed with \(P\) at \(Y\) on the plane and \(Q\) hanging vertically at the other end of the string, which passes over a fixed pulley at the top of the plane.
    The system is released from rest and \(P\) moves up the plane with acceleration \(\frac { g } { 5 }\). \includegraphics[max width=\textwidth, alt={}, center]{cc75a4a5-1c3a-4e36-acfd-21f6246f2a38-1_358_321_2024_1597}
  2. Show that \(M = \frac { 5 \sqrt { } 3 + 2 } { 8 }\).
  3. State a modelling assumption that you have made about the pulley. Briefly state what would be implied if this assumption were not made. \section*{MECHANICS 1 (A) TEST PAPER 8 Page 2}