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Moments At angles

Learn how to calculate moments of forces, use SOHCAHTOA, solve problems on uniform beams, and find coefficients of friction in equilibrium conditions using trigonometry. Includes practical examples and examination questions.

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Moments At angles

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  1. Moments At angles

  2. Moments: At an angle KUS objectives BAT solve problems using moments and friction at angles to a rod/ object using sohCahToa Starter: Spot the mistake

  3. Moments The moment of a force measures the turning effect of the force on the body on which it is acting The moment of a force F about a point P is the product of the magnitude of the force and the perpendicular distance of the line of action of the force from the point P Moment of F about P = Fd clockwise The magnitude of the force is measured in newtons (N) and the distance is measured in metres (m), so the moment of the force is measured in newton-metres (Nm) Moment of F about P = 15 Nm anticlockwise

  4. Using Trigonometry You may need to use trigonometry to find the perpendicular distance Moment of F about P = clockwise e.g. Moment of the force about P = = clockwise

  5. WB 1 Calculate the moment about point A of each of these forces acting on a Lamina ,

  6. WB 2 Given the moment about point A of each of these forces is 20 Nm, Find the magnitude of each force

  7. WB 3a Two forces act on a lamina as shown. Calculate the resultant moment about the point A a) Moment of Moment of Moment of and

  8. WB 3b Two forces act on a lamina as shown. Calculate the resultant moment about the point A b) Moment of Moment of Moment of and

  9. Moment on a uniform beam / rod WB4 review A light rod AB is 4 m long and can rotate in a vertical plane about fixed point C where AC = 1 m. A vertical force F of 8 N acts on the rod downwards. Find the moment of F about C when F acts a) at A b) at B c) at C a) Taking moments about C acw 1 m 3 m A C B b) Taking moments about C cw c) Taking moments about C cw

  10. WB 5The diagram shows a set of forces acting on a uniform rod of mass 3 kg. Calculate the resultant moment about point A (including direction) Taking moments about A clockwise

  11. Equilibrium

  12. WB6 A uniform rod PQ is hinged at point P, and is held in equilibrium at an angle of 50 to the horizontal by a force of magnitude F acting perpendicular to the rod at Q. Given that the rod has a length of 3 m and mass of 8 kg, find the value of F Taking moments about P

  13. WB 7A uniform rod PQ of mass 40 kg and length 10 m rests with the end P on rough horizontal ground. The rod rests against a smooth peg C where AC = 8 m The rod is in limiting equilibrium at an angle of 15 to the horizontal. Find The magnitude of the reaction at C The coefficient of friction between the rod and the ground distance a) Taking moments about P reaction at C b) Equilibrium in horizontal direction Equilibrium in vertical direction Coefficient friction

  14. WB 8A ladder PQ of mass m kg and length 3a m rests with the end P on rough horizontal ground. The other end Q rests against a smooth vertical wall. A load of mass 2m is fixed on the ladder at point C, where AC = a. The ladder is modelled as a uniform rod in a vertical plane perpendicular to the wall and the load as a particle. The ladder rests in limiting equilibrium at an angle of 60with the ground. Find the coefficient of friction between the rod and the ground N Add all the forces to the diagram Wall smooth No friction Equilibrium in horizontal direction R Equilibrium in vertical direction Friction

  15. WB 8(cont)A ladder PQ of mass m kg and length 3a m rests with the end P on rough horizontal ground. The other end Q rests against a smooth vertical wall. A load of mass 2m is fixed on the ladder at point C, where AC = a. The ladder is modelled as a uniform rod in a vertical plane perpendicular to the wall and the load as a particle. The ladder rests in limiting equilibrium at an angle of 60with the ground. Find the coefficient of friction between the rod and the ground Taking moments about Q (to get an equation with Friction and R) N Wall smooth No friction Substituting and R Cancel bymgaand rearrange to Friction

  16. WB 9(exam Q) A plank, AB, of mass M and length 2a, 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 3M is placed on the plank at the point P, where AP = 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 α, where 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 Using the model, show that the tension in the rope is T Friction R Mg 3Mg

  17. WB 9a(exam Q cont) Using the model, show that the tension in the rope is a) Taking moments about A Rearranges to Rearranges to Friction R a Mg 3Mg

  18. WB 9b(exam Q cont) The magnitude of the horizontal component of the force exerted on the plank at A by the wall is 2Mg Find x in terms of a b) Horizontally forces are in equilibrium Substituting result from a) gives Friction R=2Mg Cancel by 2Mg to simplify gives a Rearranges to then to Mg 3Mg

  19. WB 9c(exam Q cont) The force exerted on the plank at A by the wall acts in a direction which makes an angle β with the horizontal c) Find the value of c) Resolve forces vertically Rearranges using Friction R=2Mg Now find tan  a Friction Mg 3Mg R=2Mg

  20. WB 9d(exam Q cont) The rope will break if the tension in it exceeds 5 Mg d) Explain how this will restrict the possible positions of P. You must justify your answer carefully previous results: we know: simplify by cancelling and rearrange Friction R=2Mg 5 So the distance AP must be less than For the rope NOT to break a Mg 3Mg

  21. KUS objectives BAT solve problems using moments and friction at angles to a rod/ object using sohCahToa self-assess One thing learned is – One thing to improve is –

  22. END

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