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Term 1
Statics prerequisites: friction, the resultant reaction and the angle of friction, equilibrium on rough horizontal and inclined planes; Unit 1 Moments: the moment of a force about a point, Varignon’s principle and the theorem of moments; Unit 2 Coplanar forces: the resultant of parallel forces, equilibrium of a rigid body under coplanar forces (boards, rods, ladders); Unit 3 Couples: the couple and its moment, equivalent couples, a system equivalent to a couple and the resultant couple
1
Friction revisited: rough surfaces, μ and the angle of friction
Statics prerequisites (Sec 2 friction revisited): smooth and rough surfaces, static friction and its limit, the coefficient of friction, kinetic friction, the resultant reaction and the angle of friction, equilibrium of a body on a rough horizontal plane and on a rough inclined plane
2
The moment of a force: turning effect, coordinates and Varignon
Moments: the turning effect of a force about a point, moment arm and sign, the moment from coordinates, and Varignon’s principle
3
Theorem of moments, forces along rectangle sides, and two-point conclusions
Moments: the theorem of moments for forces meeting at a point, forces along the sides of a rectangle or square, and equal or opposite moments about two points
4
Moments of any coplanar system, machines and mixed problems
Moments: the general statement for a system of coplanar forces, moments in machines and mixed problems with unknowns
5
Parallel forces: like, unlike and the theorem of moments
Parallel coplanar forces: the resultant of two like forces, of two unlike forces, and the theorem of moments for parallel forces
6
Several parallel forces and their resultant
Parallel coplanar forces: an unknown force from the resultant, sums of moments of parallel forces, and the resultant of several parallel forces
7
Moving a force, forces as vectors and practice
Parallel coplanar forces: moving one force, parallel forces given as vectors, and practice with resultants and balance points
8
The two conditions of equilibrium: boards, rods and strings
Equilibrium of coplanar forces: the two conditions (zero resultant and zero moment), a board on two supports, and a rod on two strings
9
Non-uniform boards, loaded rods and a bar on a wedge
Equilibrium of coplanar forces: a non-uniform board, rods and loads with unknown forces, and a bar on rough ground and a smooth wedge
10
Ladders and rods against a wall
Equilibrium of coplanar forces: ladders on rough ground and a smooth wall, a ladder held by a rope, and a rod about to slip
11
Couples and their moments
Couples: two equal opposite forces, the moment of a couple, its independence of the point, and equilibrium under several couples
12
Cancelling couples, hung bodies and equivalent couples
Couples: cancelling a couple, a hanging body with a couple acting on it, equivalent couples and the exercises of Lesson 3-1
13
Systems equivalent to a couple
Resultant couple: a system equivalent to a couple, forces along the sides of a triangle, and of a closed polygon
14
The three-point rule and resultant couples
Resultant couple: the three-point rule, the sum of several couples, and the exercises of Lesson 3-2
15
Term 1 review: moments, parallel forces, equilibrium and couples
Term 1 review: moments, parallel forces and equilibrium of rods and ladders, couples
☰ Year plan · Applied Mathematics
Egypt
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Secondary 3
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Applied Mathematics
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Week 9
Non-uniform boards, loaded rods and a bar on a wedge
Week 9 · Equilibrium of coplanar forces: a non-uniform board, rods and loads with unknown forces, and a bar on rough ground and a smooth wedge · 3 lessons
Lesson 1
Lesson 2
Lesson 3
Quiz
8
Homework
5
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A bar resting on rough ground at one end and on a smooth wedge at a point: the wedge’s reaction and the coefficient of friction
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Week 9 · Homework
