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## Chapter 2 Statics of Particles

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**→P**→Q + →R = A Addition of Forces Parallelogram Rule: The addition of two forces P and Q : Draw two parallel lines of vectors to form a parallelogram Draw the diagonal vector represent the resultant force →P →Q**→P**→Q + →R = A Addition of Forces Triangle Rule: Alternative method to Parallelogram Rule Arrange two vectors in tip-to-tail fashion Draw the vector from starting point to the tip of second vector →P →Q**→P**→P →Q →Q + + →R = A →Q →P + = Addition of Forces Triangle Rule: The order of the vectors does not matter →P →Q Addition of two forces is commutative**→S**→R + = →P →Q + A Addition of Forces More than two forces: Arrange the given vectors in tip-to-tail fashion Connect the tail of first vector to the tip of last vector →S →P →Q**→S**→R + = →P →Q + A A →P →Q →S + + = Addition of Forces More than two forces: The order of the vectors does not matter →Q →P →P →S →S →Q →S →P →Q →Q →S →P + = + + +**Rectangular Components of a Force**→F →Fx →Fy + = →Fx →F →Fy , Rectangular components of θ : Angle between x-axis and F measured from positive side of x-axis**Rectangular Components of a ForceUnit Vectors**→i , →j Unit vectors**Rectangular Components of a ForceUnit Vectors**→i , →j Unit vectors**Rectangular Components of a ForceExample**A Force of 800 N is applied on a bolt A. Determine the horizontal and vertical components of the force**Rectangular Components of a ForceExample**A man pulls with a force of 300 N on a rope attached to a building. Determine the horizontal and vertical components of the force applied by the rope at point A**→S**→R + = →P →Q + A Addition of Forces by Summing Their components →P →S →Q**Addition of Forces by Summing Their components - Example**Problem 2.22 on page 33 Determine the resultant force applied on the bolt 7 kN 5 kN 9 kN**Equilibrium of Particle**When the resultant of all the forces acting on a particle is zero, the particle is in equilibrium**Equilibrium of Particle - Example**Determine the resultant force applied on point A N N N N 200*cos(240) = -100 200*sin(240) = -173.2**Equilibrium of Particle – Newton’s First Law**• If the resultant force acting on a particle is zero, • the particle remains at rest (if originally at rest) • the particle moves with a constant speed in a straight line ( if originally in motion) Equilibrium State**Equilibrium of Particle - Example**Load with mass of 75 kg Determine the tensions in each ropes of AB and AC Since the load is in equilibrium state, The resultant force at A is zero. N N N 200*cos(240) = -100 200*sin(240) = -173.2**Equilibrium of Particle – Example (continued)**(1) N (2) N N 200*cos(240) = -100 200*sin(240) = -173.2**Equilibrium of Particle – Example-2**Two cables are tied together at C and they are loaded as shown Determine the tensions in cable AC and BC Problem 2.44 / page 41**Equilibrium of Particle – Example-2**Draw “Free Body” Diagram C**Equilibrium of Particle – Example-2**For simplicity C**Equilibrium of Particle – Example-2**Since the system is in equilibrium The resultant force at C is zero. C**Equilibrium of Particle – Example-2**Since the system is in equilibrium The resultant force at C is zero. C**Equilibrium of Particle – Example-2**C (1) (2)**Equilibrium of Particle – Example-2**(1) (2) C**Forces in Space ( 3 D )**• The three angle define the direction of the force F • They are measured from the positive side of the axis to the force F • They are always between 0 and 180º**Forces in Space ( 3 D )**• The vector is the unit vector along the line of action of F**Forces in Space ( 3 D )**• The vector is the unit vector along the line of action of F**Direction of the force is defined by the location of two**points, Forces in Space ( 3 D )**Sample Problem 2.7**The tension in the guy wire is 2500 N. Determine: a) components Fx, Fy, Fz of the force acting on the bolt at A, b) the angles qx, qy, qzdefining the direction of the force**Determine the components of the force.**Sample Problem 2.7**Sample Problem 2.7**• Noting that the components of the unit vector are the direction cosines for the vector, calculate the corresponding angles. or**Addition of Concurrent Forces in Space**• The resultant R of two or more vectors in space**Sample Problem 2.8**A concrete wall is temporarily held by the cables shown. m m The tension is 840 N in cable AB and 1200 N in cable AC. Determine the magnitude and direction of the resultant vector on stake A m m**Equilibrium of a Particle in Space**When the resultant of all the forces acting on a particle is zero, the particle is in equilibrium