Moments

Starter: Spot the mistake Moments KUS objectives BAT understand moment and solve problems using moments when a rod is at a tipping point / about to Tilt around a picot Starter: Spot the mistake Moment at A 2 x R = 30g +

WB5 A plank of wood AB has mass 10 kg and length 4 m WB5 A plank of wood AB has mass 10 kg and length 4 m. It rests in a horizontal position on two smooth supports. One support is at the end A. The other is at the point C, 0.4 m from B, as shown. A weight of mass 30 kg stands at B with the plank in equilibrium. By modelling the plank as a uniform rod and the girl as a particle,   find the reaction on the plank at A. b) Explain what you expect to happen to the reaction at A if the weight at B is steadily increased

𝑅 𝐴 + 𝑅 𝐶 =40 𝑔 3.6× 𝑅 𝐴 +0.4 ×30𝑔=1.6 ×10𝑔 𝑅 𝐴 =10.89 𝑁 𝑹 𝑪 𝑹 𝑨 WB5 𝟐 𝒎 𝟑𝟎𝒈 𝟏𝟎𝒈 a) Resolving the Forces: 𝑅 𝐴 + 𝑅 𝐶 =40 𝑔 3.6× 𝑅 𝐴 +0.4 ×30𝑔=1.6 ×10𝑔 Take moments at C: 𝑅 𝐴 =10.89 𝑁 b) As the weight at B is steadily increased the plank will reach a ‘tipping point’ after which the weight will be too great for the plank to remain in equilibrium The reaction at A decreases until it reaches zero at the tipping point

WB6 A plank of wood AB has mass 10 kg and length 4 m WB6 A plank of wood AB has mass 10 kg and length 4 m. It rests in a horizontal position on two smooth supports. One support is at the end A. The other is at the point C, 0.4 m from B, as shown. A boulder of mass m kg is placed on the plank at A and a man of mass 80 kg stands on the plank at B   find the reaction on the plank at A. The plank remains in equilibrium and is on the point of tilting about C. b) By modelling the plank again as a uniform rod, and the man and the boulder as particles, find the value of m

𝑅 𝐴 + 𝑅 𝐶 =(90+𝑚) 𝑔 0.4 ×80𝑔=1.6 ×10𝑔+ 3.6×𝑚𝑔 313.6=156.8+ 35.28𝑚 WB6 𝑹 𝑪 𝑹 𝑨 =𝟎 𝟐 𝒎 𝒎𝒈 8𝟎𝒈 𝟏𝟎𝒈 Resolving the Forces: 𝑅 𝐴 + 𝑅 𝐶 =(90+𝑚) 𝑔 Take moments at C: 0.4 ×80𝑔=1.6 ×10𝑔+ 3.6×𝑚𝑔 313.6=156.8+ 35.28𝑚 𝑚= 40 9 =4.44 𝑘𝑔

The edge of the platform is at the point C. WB7a A plank AB has length 4 m. It lies on a horizontal platform, with the end A lying on the platform and the end B projecting over the edge, as shown below. The edge of the platform is at the point C. Jack and Jill are experimenting with the plank. Jack has mass 40 kg and Jill has mass 25 kg. They discover that, if Jack stands at B and Jill stands at A and BC = 1.6 m, the plank is in equilibrium and on the point of tilting about C. By modelling the plank as a uniform rod, and Jack and Jill as particles, (a) Find the mass of the plank. Taking moments about C Jill Jack 2m 1.6m

(b) Find the distance BC in this position. WB7b They now alter the position of the plank in relation to the platform so that, when Jill stands at B and Jack stands at A, the plank is again in equilibrium and on the point of tilting about C. (b) Find the distance BC in this position. Taking moments about C Jack Jill x (c) State how you have used the modelling assumptions that (i) the plank is uniform, (ii) the plank is a rod, (iii) Jack and Jill are particles. Weight acts at centre of plank Plank remains straight Weights act at the ends of the plank

𝟏𝟎𝒎 𝑿 𝒀 𝟒 𝒎 WB8 A non-uniform plank XY of length 10 m and mass 40 kg rests on a horizontal table with the end Y projecting 4 m over the edge of the table as shown. When a package of mass 25 kg is placed on the plank 1 m from X and a package of mass 90 kg is placed on the plank 1.5 m from Y is in limiting equilibrium Find the distance of the centre of mass of the plank from X Find the magnitude of the force which the edge of the table exerts on the plank, giving your answer in terms of g The 25 kg package is removed and the 90 kg package is moved so that the plank is again in limiting equilibrium Find how far the package is from Y 3.5 m 155g 2.89 m

One thing to improve is – KUS objectives BAT understand moment and solve problems using moments on a Non- Uniform rod and/or when a rod is at a tipping point self-assess One thing learned is – One thing to improve is –

END