SS3 Second Term Further Mathematics Lesson Note – Statics II

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WEEK 2

TOPIC: STATICS 2

CONTENT:

1. Moment of A Force (2 and 3 Forces) Acting at a Point
2. Resolution of Forces of Friction

SUB TOPIC 1:  MOMENT OF A FORCE

MOMENT OF FORCE is the turning effect of a force about a point. It is otherwise called torque about a given point. In other words, it is a measure of the turning power of a force about a given point. Mathematically, moment of a force about an axis is the product of the magnitude of the force and the perpendicular distance of the line of action of the force from the axis. Conventionally, counter clockwise moments are taken as positive while clockwise moments are taken as negative.

PRINCIPLE OF MOMENTS states that if a body is in equilibrium under the action of forces then:  (i)the sum of the clockwise moments is equal to the sum of anticlockwise moments.(ii)the sum of upward forces is equal to the sum of downward forces.

NOTE: The resultant moment about a point in the plane of the body is the algebraic sum of the moments of each the forces about the point.

EXAMPLE 4: A uniform plank AB of mass 3kg and length16m is suspended at the ends by two inelastic strings AP and BQ, where P AND Q are two fixed points on the ceiling such that <PAB = 150⁰ and <QAB = 120⁰.The plank is held in equilibrium in an horizontal position, with strings taut, by a vertical upward force , F acting at a point C, 5m from the end A. Find correct to two decimal places the: (a)the tension in the strings  (b) force F. (take g = 10m/s²)                                                                                                      WAEC

Solution:

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