# Download PDF by R. Haines;B. Haines: Work Out Applied Mathematics: ‘A’ Level

By R. Haines;B. Haines

ISBN-10: 0333397673

ISBN-13: 9780333397671

ISBN-10: 1349082139

ISBN-13: 9781349082131

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Sample text

AtE: T5 cos a+ T6 cosa = T 4 => T 6 = 10 N (tension). Force of 18 N added at CmakesRA =Rn = 36 N. By symmetry, T 6 = 0 => zero force in BE. Alternatively, use Bow's notation. (c) Resolving: AtD: At F: A~o 30t~~t24 36 18 6 Scale 1 em to 10 N 46 4 Friction. Equilibrium of Bodies in Contact The laws of friction. Equilibrium of systems of particles and rigid bodies under the action of coplanar forces including friction. 1 Fact Sheet (a) Laws of Friction (i) Friction F opposes the movement of an object across a rough surface.

Given that all the contacts are smooth, find the magnitudes of thereactions at all points of contact, A, B, C and D. 8 Two smooth planes inclined at angles a, {3 to the horizontal intersect in a horizontal line. A non-uniform thin heavy bar AB rests with end A on the plane of inclination a and the end B on the plane of inclination {3, with AB perpendicular to the line intersection of the planes. The mass of the bar isM and the mass centre at distances a and b from A and B respectively. Prove that, if () is the inclination of the bar to the vertical in equilibrium, (a + b) cot () = I a cot a - b cot {31 and find the reaction at A in terms of a and {3.

Therefore AX= 1; a. 3 Taking moments about P, T= 30yl3 ~52. T (21) cos 60° :; 60 (I) sin 60°. 4 Moments about A: P(3a) = S (a)+ W (2a) cos()+ 2W ( 4a) cos(). Resolving vertically, 3 W + S cos() = P cos(). 2W Solving, P= W (10cos 2 S= w00cos 2 0- 9)' 2 cos () ()- 2 cos () 3). 5 (a) For equilibrium all forces must pass through N w acts atM. NY = 2a cos (), Wa MY=--w+W' w () ;;;;:. 9 . TO resultant of W and => cos2 MY NY' cos()=-- cos2 () __ = _ _W 2 (w + W) w Alternatively, take moments about N. Length of string=~ = 2a cos() J (b) Taking moments about X: T = 2w + W = 2 sin() j( 2 (w + W W)) .