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Moments At angles

Moments At angles. 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. Moments. The moment of a force measures the turning effect of the force on the body on which it is acting.

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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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