3.04b Equilibrium: zero resultant moment and force

9. \begin{figure}[h] \end{figure} A plank, \(A B\), of mass \(M\) and length \(2 a\), rests with its end \(A\) against a rough vertical wall. The plank is held in a horizontal position by a rope. One end of the rope is attached to the plank at \(B\) and the other end is attached to the wall at the point \(C\), which is vertically above \(A\). A small block of mass \(3 M\) is placed on the plank at the point \(P\), where \(A P = x\). The plank is in equilibrium in a vertical plane which is perpendicular to the wall. The angle between the rope and the plank is \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\), as shown in Figure 3 .
The plank is modelled as a uniform rod, the block is modelled as a particle and the rope is modelled as a light inextensible string.

1. Using the model, show that the tension in the rope is \(\frac { 5 M g ( 3 x + a ) } { 6 a }\) The magnitude of the horizontal component of the force exerted on the plank at \(A\) by the wall is \(2 M g\).
2. Find \(x\) in terms of \(a\). The force exerted on the plank at \(A\) by the wall acts in a direction which makes an angle \(\beta\) with the horizontal.
3. Find the value of \(\tan \beta\) The rope will break if the tension in it exceeds \(5 M g\).
4. Explain how this will restrict the possible positions of \(P\). You must justify your answer carefully.

9. Figure 1 A uniform ladder \(A B\), of length \(2 a\) and weight \(W\), has its end \(A\) on rough horizontal ground. The coefficient of friction between the ladder and the ground is \(\frac { 1 } { 4 }\).
The end \(B\) of the ladder is resting against a smooth vertical wall, as shown in Figure 1.
A builder of weight \(7 W\) stands at the top of the ladder.
To stop the ladder from slipping, the builder's assistant applies a horizontal force of magnitude \(P\) to the ladder at \(A\), towards the wall.
The force acts in a direction which is perpendicular to the wall.
The ladder rests in equilibrium in a vertical plane perpendicular to the wall and makes an angle \(\alpha\) with the horizontal ground, where \(\tan \alpha = \frac { 5 } { 2 }\).
The builder is modelled as a particle and the ladder is modelled as a uniform rod.

1. Show that the reaction of the wall on the ladder at \(B\) has magnitude \(3 W\).
2. Find, in terms of \(W\), the range of possible values of \(P\) for which the ladder remains in equilibrium. Often in practice, the builder's assistant will simply stand on the bottom of the ladder.
3. Explain briefly how this helps to stop the ladder from slipping.

9 Two blocks have square cross sections. One block has mass 9 kg and its cross section has sides of length 20 cm
The other block has mass 1 kg and its cross section has sides of length 4 cm
The blocks are fixed together to form the composite body shown in Figure 1. \begin{figure}[h] \end{figure} 9

1. Find the distance of the centre of mass of the composite body from \(A F\) [0pt] [2 marks]
   Question 9 continues on the next page 9
2. A uniform rod has mass 12 kg and length 1 metre. One end of the rod rests against a smooth vertical wall.
   The other end of the rod rests on the composite body at point \(B\) The composite body is on a horizontal surface.
   The coefficient of friction between the composite body and the horizontal surface is 0.3 The angle between the rod and \(A B\) is \(60 ^ { \circ }\) A particle of mass \(m \mathrm {~kg}\) is fixed to the rod at a distance of 75 cm from \(B\) The rod, particle and composite body are shown in Figure 2. \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{0afe3ff2-0af5-4aeb-98c5-1346fa803388-14_939_1020_1133_511}
   \end{figure} 9 (b) (i) Write down the magnitude of the vertical reaction force acting on the rod at \(B\) in terms of \(m\) and \(g\) [0pt] [1 mark] 9 (b) (ii) Show that the magnitude of the horizontal reaction force acting on the rod at \(B\) is $$\frac { g ( 6 + 0.75 m ) } { \sqrt { 3 } }$$ 9 (b) (iii) Find the maximum value of \(m\) for which the composite body does not slide or topple. Fully justify your answer.

6 Nm
8 Nm
10 Nm
14 Nm 3 A uniform disc has mass 6 kg and diameter 8 cm A uniform rectangular lamina, \(A B C D\), has mass 4 kg , width 8 cm and length 20 cm
The disc is fixed to the lamina to form a composite body as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-03_448_881_587_577} The sides \(A B , A D\) and \(C D\) are tangents to the disc.
Calculate the distance of the centre of mass of the composite body from \(A D\) Circle your answer.
4 cm
5.6 cm
6.4 cm
8.8 cm 4 A car of mass 1400 kg drives around a horizontal circular bend of radius 60 metres.
The car has a constant speed of \(12 \mathrm {~ms} ^ { - 1 }\) on the bend.
Calculate the magnitude of the resultant force acting on the car.
[0pt] [2 marks] \(5 \quad\) A region bounded by the curve with equation \(y = 4 - x ^ { 2 }\), the \(x\)-axis and the \(y\)-axis is shown below. \includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-04_641_380_408_831} The region is rotated through \(360 ^ { \circ }\) around the \(x\)-axis to create a uniform solid.
5

1. Show that the distance of the centre of mass of the solid from the circular face is \(\frac { 5 } { 8 }\) [0pt] [5 marks]
   5
2. The solid is suspended in equilibrium from a point on the edge of the circular face.
   Find the angle between the circular face and the horizontal, giving your answer to the nearest degree.
   6 In this question use \(g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) A sphere of mass 0.8 kg is attached to one end of a string of length 2 metres.
   The other end of the string is attached to a fixed point \(O\) The sphere is released from rest with the string taut and at an angle of \(30 ^ { \circ }\) to the vertical, as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-06_464_218_676_909} 6
   1. Find the speed of the sphere when it is directly below \(O\) 6
   2. State one assumption that you made about the string.
      6
   3. As the sphere moves, the string makes an angle \(\theta\) with the downward vertical. By finding an expression for the tension in the string in terms of \(\theta\), show that the tension is a maximum when the sphere is directly below \(O\) 6
   4. A physics student conducts an experiment and uses a device to measure the tension in the string when the sphere is directly below \(O\) They find that the tension is 9.5 newtons.
      Explain why this result is reasonable, showing any calculations that you make.

14 Nm 3 A uniform disc has mass 6 kg and diameter 8 cm A uniform rectangular lamina, \(A B C D\), has mass 4 kg , width 8 cm and length 20 cm
The disc is fixed to the lamina to form a composite body as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-03_448_881_587_577} The sides \(A B , A D\) and \(C D\) are tangents to the disc.
Calculate the distance of the centre of mass of the composite body from \(A D\) Circle your answer.
4 cm
5.6 cm
6.4 cm
8.8 cm 4 A car of mass 1400 kg drives around a horizontal circular bend of radius 60 metres.
The car has a constant speed of \(12 \mathrm {~ms} ^ { - 1 }\) on the bend.
Calculate the magnitude of the resultant force acting on the car.
[0pt] [2 marks] \(5 \quad\) A region bounded by the curve with equation \(y = 4 - x ^ { 2 }\), the \(x\)-axis and the \(y\)-axis is shown below. \includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-04_641_380_408_831} The region is rotated through \(360 ^ { \circ }\) around the \(x\)-axis to create a uniform solid.
5

1. Show that the distance of the centre of mass of the solid from the circular face is \(\frac { 5 } { 8 }\) [0pt] [5 marks]
   5
2. The solid is suspended in equilibrium from a point on the edge of the circular face.
   Find the angle between the circular face and the horizontal, giving your answer to the nearest degree.
   6 In this question use \(g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) A sphere of mass 0.8 kg is attached to one end of a string of length 2 metres.
   The other end of the string is attached to a fixed point \(O\) The sphere is released from rest with the string taut and at an angle of \(30 ^ { \circ }\) to the vertical, as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-06_464_218_676_909} 6
   1. Find the speed of the sphere when it is directly below \(O\) 6
   2. State one assumption that you made about the string.
      6
   3. As the sphere moves, the string makes an angle \(\theta\) with the downward vertical. By finding an expression for the tension in the string in terms of \(\theta\), show that the tension is a maximum when the sphere is directly below \(O\) 6
   4. A physics student conducts an experiment and uses a device to measure the tension in the string when the sphere is directly below \(O\) They find that the tension is 9.5 newtons.
      Explain why this result is reasonable, showing any calculations that you make.
      7 Two particles, \(A\) and \(B\), are moving on a smooth horizontal surface. A straight line has been marked on the surface and the particles are on opposite sides of the line. Particle \(A\) has mass 2 kg and moves with velocity \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) to the line. Particle \(B\) has mass 3 kg and moves with velocity \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(45 ^ { \circ }\) to the line. The particles and their velocities are shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-08_451_739_858_653} The particles collide when they reach the line and then move together as a single combined particle. 7
   5. Show that the magnitude of the impulse on particle \(A\) during the collision is 7.55 Ns correct to three significant figures.
      7
   6. State the magnitude of the impulse on \(B\) during the collision, giving a reason for your answer. 7
   7. Find the size of the angle between the straight line and the impulse acting on \(B\), giving your answer to the nearest degree. 7
   8. During the collision, one particle crosses the straight line.
      State which particle crosses the line, giving a reason for your answer.
      [0pt] [1 mark] 8 In this question use \(g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) A block has mass 10 kg and is at rest 1 metre from a fixed point \(O\) on a horizontal surface. One end of an elastic string is attached to the block and the other end of the elastic string is attached to the point \(O\) The elastic string has modulus of elasticity 40 newtons and natural length 2 metres.
      The coefficient of friction between the block and the surface is 0.6 A force is applied to the block so that it starts to move towards a vertical wall.
      The block moves on a line that is perpendicular to the wall.
      The force has magnitude 100 newtons and acts at an angle of \(30 ^ { \circ }\) to the horizontal.
      The situation is shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-10_239_1339_1176_354} 8
   9. Show that the distance that the block has moved, when the forces acting on it are in equilibrium, is 3.9 metres correct to two significant figures.
      [0pt] [4 marks]
      8
   10. State one limitation of the model that you have used. 8
   11. Find the maximum speed of the block.
       8
   12. The vertical wall is 8.7 metres from \(O\) Determine whether the block reaches the wall, showing any calculations that you make. \includegraphics[max width=\textwidth, alt={}, center]{cd0d239b-ab92-4d17-9cb8-45722e2894cb-13_2492_1721_217_150}

2. \begin{figure}[h] \end{figure} A non-uniform beam \(A B\) has length 6 m and mass 50 kg . The beam rests horizontally on two supports at \(C\) and \(D\), where \(A C = 0.9 \mathrm {~m}\) and \(D B = 1.8 \mathrm {~m}\). A child of mass 25 kg stands on the beam at \(E\), where \(A E = E B = 3 \mathrm {~m}\), as shown in Figure 1. The beam is in equilibrium.
The magnitude of the normal reaction between the beam and the support at \(C\) is \(R _ { C }\) newtons. The magnitude of the normal reaction between the beam and the support at \(D\) is \(R _ { D }\) newtons. The beam is modelled as a rod and the child is modelled as a particle.
The centre of mass of the beam is between \(C\) and \(D\) and is a distance \(x\) metres from \(D\).
Given that \(2 R _ { D } = 3 R _ { C }\)

1. show that \(x = 1.38\) The child remains at \(E\) and a block of mass \(M \mathrm {~kg}\) is placed on the beam at \(B\).
   The block is modelled as a particle.
   Given that the beam is on the point of tilting,
2. find the value of \(M\).

6. \begin{figure}[h] \end{figure} A uniform beam \(A B\), of weight \(5 W\) and length \(12 a\), rests with end \(A\) on rough horizontal ground.
A package of weight \(W\) is attached to the beam at \(B\).
The beam rests in equilibrium on a smooth horizontal peg at \(C\), with \(A C = 9 a\), as shown in Figure 5.
The beam is inclined at an angle \(\theta\) to the ground, where \(\tan \theta = \frac { 5 } { 12 }\) The beam is modelled as a rod that lies in a vertical plane perpendicular to the peg. The package is modelled as a particle. The normal reaction between the beam and the peg at \(C\) has magnitude \(k W\) Using the model,

1. show that \(k = \frac { 56 } { 13 }\) The coefficient of friction between \(A\) and the ground is \(\mu\) Given that the beam is resting in limiting equilibrium,
2. find the value of \(\mu\)

10 A uniform ladder \(A B\) of length 5 m and mass 8 kg is placed at an angle \(\theta\) to the horizontal, with \(A\) on rough horizontal ground and \(B\) against a smooth vertical wall. The coefficient of friction between the ladder and the ground is 0.4 .

1. By taking moments, find the smallest value of \(\theta\) for which the ladder is in equilibrium.
2. A man of mass 75 kg stands on the ladder when \(\theta = 60 ^ { \circ }\). Find the greatest distance from \(A\) that he can stand without the ladder slipping.

8 The diagram shows a uniform rod \(A B\) of length 40 cm and mass 2 kg placed with the end \(A\) resting against a smooth vertical wall and the end \(B\) on rough horizontal ground. The angle between \(A B\) and the horizontal is \(60 ^ { \circ }\). \includegraphics[max width=\textwidth, alt={}, center]{a19fab61-da1c-4803-9dbc-38d618a0c58e-4_657_655_1128_705}

1. Given that the value of the coefficient of friction between the rod and the ground is 0.2 , determine whether the rod slips.
2. Explain why it is impossible for the rod to be in equilibrium with one end on smooth horizontal ground and the other against a rough vertical wall.

9 The diagram shows a uniform rod \(A B\) of length 40 cm and mass 2 kg placed with the end \(A\) resting against a smooth vertical wall and the end \(B\) on rough horizontal ground. The angle between \(A B\) and the horizontal is \(60 ^ { \circ }\). \includegraphics[max width=\textwidth, alt={}, center]{c4bbba86-2968-4247-b300-357217cf213b-4_657_647_1923_708} Given that the value of the coefficient of friction between the rod and the ground is 0.2 , determine whether the rod slips.

11 \includegraphics[max width=\textwidth, alt={}, center]{22640c3b-792f-4003-a4f8-78220efd73b0-4_280_1002_1722_568} A non-uniform \(\operatorname { rod } A B\) of mass 1.6 kg and length 1.25 m has its centre of mass at \(G\) where \(A G = 0.4 \mathrm {~m}\). The rod rests on a rough horizontal table. A force \(P \mathrm {~N}\) is applied at \(B\), acting at an angle \(\alpha\) above the horizontal, such that the rod is in equilibrium but about to rotate about \(A\) (see diagram).

1. Assume that the rod is in contact with the table only at \(A\). By taking moments about \(A\), show that \(P \sin \alpha = 5.12\).
2. The coefficient of friction between the rod and the table is \(\frac { 6 } { 17 }\). Show that \(P \leqslant 6.4\).

9 The diagram shows a uniform \(\operatorname { rod } A B\) of length 40 cm and mass 2 kg placed with the end \(A\) resting against a smooth vertical wall and the end \(B\) on rough horizontal ground. The angle between \(A B\) and the horizontal is \(60 ^ { \circ }\). \includegraphics[max width=\textwidth, alt={}, center]{adf5bd3c-5408-421d-b7d5-dea2d0f0185b-5_661_655_390_705} Given that the value of the coefficient of friction between the rod and the ground is 0.2 , determine whether the rod slips.

11 Three light inextensible strings \(A C , C D\) and \(D B\), each of length 10 cm , are joined as shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{85043199-527d-4105-aa0b-c913dec0e35b-5_300_670_475_699} The ends \(A\) and \(B\) are fixed to points 20 cm apart on the same horizontal level. Two heavy particles, each of mass 2 kg , are attached at \(C\) and \(D\). The system remains in a vertical plane.

1. Determine the tension in each string.
2. The string \(C D\) is replaced by one of length \(L \mathrm {~cm}\), made of the same material. If the tension in \(A C\) is 50 N , show that \(L = 20 - 4 \sqrt { 21 }\).

\includegraphics{figure_5} Two uniform rods \(AB\) and \(BC\) are smoothly jointed at \(B\) and rest in equilibrium with \(C\) on a rough horizontal floor and with \(A\) against a rough vertical wall. The rod \(AB\) is horizontal and the rods are in a vertical plane perpendicular to the wall. The rod \(AB\) has mass \(3m\) and length \(3a\), the rod \(BC\) has mass \(5m\) and length \(5a\), and \(C\) is at a distance \(6a\) from the wall (see diagram). Show that the normal reaction exerted by the floor on the rod \(BC\) at \(C\) has magnitude \(\frac{1}{2}mg\). [5] The coefficient of friction at both \(A\) and \(C\) is \(\mu\). Find the least possible value of \(\mu\) for which the rods do not slip at either \(A\) or \(C\). [7]

\includegraphics{figure_5} Two uniform rods \(AB\) and \(BC\) are smoothly jointed at \(B\) and rest in equilibrium with \(C\) on a rough horizontal floor and with \(A\) against a rough vertical wall. The rod \(AB\) is horizontal and the rods are in a vertical plane perpendicular to the wall. The rod \(AB\) has mass \(3m\) and length \(3a\), the rod \(BC\) has mass \(5m\) and length \(5a\), and \(C\) is at a distance \(6a\) from the wall (see diagram). Show that the normal reaction exerted by the floor on the rod \(BC\) at \(C\) has magnitude \(\frac{14}{5}mg\). [5] The coefficient of friction at both \(A\) and \(C\) is \(\mu\). Find the least possible value of \(\mu\) for which the rods do not slip at either \(A\) or \(C\). [7]

\includegraphics{figure_2} A uniform smooth disc with centre \(O\) and radius \(a\) is fixed at the point \(D\) on a horizontal surface. A uniform rod of length \(3a\) and weight \(W\) rests on the disc with its end \(A\) in contact with a rough vertical wall. The rod and the disc lie in a vertical plane that is perpendicular to the wall. The wall meets the horizontal surface at the point \(E\) such that \(AE = a\) and \(ED = \frac{5}{4}a\). A particle of weight \(kW\) is hung from the rod at \(B\) (see diagram). The coefficient of friction between the rod and the wall is \(\frac{1}{8}\) and the system is in limiting equilibrium. Find the value of \(k\). [8]

\includegraphics{figure_2} A uniform smooth disc with centre \(O\) and radius \(a\) is fixed at the point \(D\) on a horizontal surface. A uniform rod of length \(3a\) and weight \(W\) rests on the disc with its end \(A\) in contact with a rough vertical wall. The rod and the disc lie in a vertical plane that is perpendicular to the wall. The wall meets the horizontal surface at the point \(E\) such that \(AE = a\) and \(ED = \frac{3}{4}a\). A particle of weight \(kW\) is hung from the rod at \(B\) (see diagram). The coefficient of friction between the rod and the wall is \(\frac{1}{8}\) and the system is in limiting equilibrium. Find the value of \(k\). [8]

\includegraphics{figure_4} A uniform rod \(AB\) of length \(3a\) and weight \(W\) is freely hinged to a fixed point at the end \(A\). The end \(B\) is below the level of \(A\) and is attached to one end of a light elastic string of natural length \(4a\). The other end of the string is attached to a point \(O\) on a vertical wall. The horizontal distance between \(A\) and the wall is \(5a\). The string and the rod make angles \(\theta\) and \(2\theta\) respectively with the horizontal (see diagram). The system is in equilibrium with the rod and the string in the same vertical plane. It is given that \(\sin \theta = \frac{3}{5}\) and you may use the fact that \(\cos 2\theta = \frac{7}{25}\).

1. Find the tension in the string in terms of \(W\). [3]
2. Find the modulus of elasticity of the string in terms of \(W\). [4]
3. Find the angle that the force acting on the rod at \(A\) makes with the horizontal. [3]

\includegraphics{figure_1} A uniform ladder \(AB\), of length \(3a\) and weight \(W\), rests with the end \(A\) in contact with smooth horizontal ground and the end \(B\) against a smooth vertical wall. One end of a light inextensible rope is attached to the ladder at the point \(C\), where \(AC = a\). The other end of the rope is fixed to the point \(D\) at the base of the wall and the rope \(DC\) is in the same vertical plane as the ladder \(AB\). The ladder rests in equilibrium in a vertical plane perpendicular to the wall, with the ladder making an angle \(\theta\) with the horizontal and the rope making an angle \(\alpha\) with the horizontal (see diagram). It is given that \(\tan \alpha = 2\tan \theta\). Find, in terms of \(W\) and \(\alpha\), the tension in the rope and the magnitudes of the forces acting on the ladder at \(A\) and at \(B\). [9]

A uniform rod \(AB\) of length \(4a\) and weight \(W\) is smoothly hinged to a vertical wall at the end \(A\). The rod is held at an angle \(\theta\) above the horizontal by a light elastic string. One end of the string is attached to the point \(C\) on the rod, where \(AC = 3a\). The other end of the string is attached to a point \(D\) on the wall, with \(D\) vertically above \(A\) and such that angle \(ACD = 2\theta\). A particle of weight \(\frac{1}{4}W\) is attached to the rod at \(B\). It is given that \(\tan \theta = \frac{5}{12}\).

1. Show that the tension in the string is \(\frac{17}{12}W\). [4]
2. Find the magnitude and direction of the reaction at the hinge. [5]
3. Given that the natural length of the string is \(2a\), find its modulus of elasticity. [2]

\includegraphics{figure_4} A uniform rod \(AB\) of length \(2a\) and weight \(W\) rests against a smooth horizontal peg at a point \(C\) on the rod, where \(AC = x\). The lower end \(A\) of the rod rests on rough horizontal ground. The rod is in equilibrium inclined at an angle of \(45°\) to the horizontal (see diagram). The coefficient of friction between the rod and the ground is \(\mu\). The rod is about to slip at \(A\). \begin{enumerate}[label=(\roman*)] \item Find an expression for \(x\) in terms of \(a\) and \(\mu\). [5] \item Hence show that \(\mu \geqslant \frac{1}{3}\). [2] \item Given that \(x = \frac{5}{3}a\), find the value of \(\mu\) and the magnitude of the resultant force on the rod at \(A\). [4] \end{enumerate]

\includegraphics{figure_2} A uniform square lamina \(ABCD\) of side \(4a\) and weight \(W\) rests in a vertical plane with the edge \(AB\) inclined at angle \(\theta\) to the horizontal, where \(\tan \theta = \frac{1}{4}\). The vertex \(B\) is in contact with a rough horizontal surface for which the coefficient of friction is \(\mu\). The lamina is supported by a smooth peg at the point \(E\) on \(AB\), where \(BE = 3a\) (see diagram).

1. Find expressions in terms of \(W\) for the normal reaction forces at \(E\) and \(B\). [5]
2. Given that the lamina is about to slip, find the value of \(\mu\). [3]

\includegraphics{figure_5} The diagram shows a block \(D\) of mass 100 kg supported by two sloping struts \(AD\) and \(BD\), each attached at an angle of \(45°\) to fixed points \(A\) and \(B\) respectively on a horizontal floor. The block is also held in place by a vertical rope \(CD\) attached to a fixed point \(C\) on a horizontal ceiling. The tension in the rope \(CD\) is 500 N and the block rests in equilibrium.

1. Find the magnitude of the force in each of the struts \(AD\) and \(BD\). [3] A horizontal force of magnitude \(F\) N is applied to the block in a direction parallel to \(AB\).
2. Find the value of \(F\) for which the magnitude of the force in the strut \(AD\) is zero. [3]

\includegraphics{figure_5} A uniform rod AB has length \(2\) m and weight \(20\) N. The rod rests horizontally in equilibrium on two supports at points C and D, where AC = \(0.4\) m and BD = \(0.6\) m.

1. Find the reaction at each support. [4]
2. State what happens if the support at D is removed. [2]