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Chapter 6

Chapter 6. Concurrent and Parallel Forces. Introduction. Forces do not always cause motion Static = not moving: may be in equilibrium Example: Bridge Forces acting nonconcurrently May produce rotational motion Torque. Objectives. Vector sum of concurrent forces

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Chapter 6

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  1. Chapter 6 Concurrent and Parallel Forces

  2. Introduction • Forces do not always cause motion • Static = not moving: may be in equilibrium • Example: Bridge • Forces acting nonconcurrently • May produce rotational motion • Torque

  3. Objectives • Vector sum of concurrent forces • Equilibrium in one dimension • Force diagrams • Compression and tension • Torque & rotational problems • Parallel force problems • Conditions for equilibrium • Center of gravity

  4. 6.1 Forces in Two Dimensions • Concurrent forces: forces applied to or act at the same point • Resultant force: sum of forces applied at same point • Single force that has same effect as the two or more forces acting together • When acting in one dimension, add and subtract based on direction • In 2 dimensions, use vectors

  5. Finding Resultant Vectors • Use x and y-component method • Use Vector Triangle Method • Use Parallelogram Method

  6. F2 = 60 N @ 70° F1 = 50 N @ 35° x and y-component method • Forces F1 and F2 act concurrently (at same point) • Find resultant force

  7. F2 = 60 N @ 70° F2x = 60 cos 70° F2y = 60 sin 70° F1= 50 N @ 35° F1x = 50 cos 35° F1y = 50 sin 35° x and y-component method • Find x and y-components using right angle trigonometry • Add x and y-components to get resultant force

  8. R =F1+F2 Vector Triangle Method • Put vectors to be added end to end • Resultant vector is side of triangle

  9. R = F1+F2 Parallelogram Method

  10. See examples in textbook on pages 153 to 155

  11. 6.2 Concurrent Forces in Equilibrium • Equilibrium is the state of a body in which there is no change in motion • Net force acting on body is zero • No acceleration: at rest or moving at constant velocity • Study of objects in equilibrium is called statics

  12. Equation for Equilibrium (one dimension) • F+ = F- • F+ = sum of forces acting in one direction (positive) • F- = sum of forces acting in opposite (negative) direction • +/- can be up & down or left & right, etc. • See examples on page 158

  13. Conditions for Equilibrium (2 dimensions) • Equilibrant force: when two or more forces act at one point, this is the force that when applied at the same point produces equilibrium • Is equal in magnitude to resultant force, but opposite in direction

  14. Equilibrium (2-D) continued • If object is in equilibrium in two dimensions, the net force acting on it must be zero • Sum of x-components = 0 • Sum of y-components = 0 • Both must be true for equilibrium • See examples on pp. 160-163

  15. Solving Equilibrium Problems • Draw force diagram from point at which unknown forces act • Find x and y-components of each force • Substitute components into equations • Solve for unknowns

  16. Tension • Stretching force produced by forces pulling outward on the ends of an object • Example: rubber band

  17. Compression • Force produced by pushing inward on the ends of and object • Example: valve spring

  18. 6.3 Torque • Torque is the tendency to produce change in rotational motion • Torque is produced when a force is applied to produce rotational motion (ex: using wrench to turn a bolt)

  19. Torque: Equation • Depends on two factors • Amount of force applied • Distance from point of rotation that force is applied • τ = Fst • τ = torque (N∙m or lb∙ft) • F = applied force (N or lb) • st = length of torque arm (m or ft)

  20. Be sure to use perpendicular distance! • See bicycle example on pg 167 • Measure distance that is perpendicular to applied force

  21. Right-hand Rule • Torque is vector quantity that acts along axis of rotation • Use right hand rule to determine direction • Grasp axis of rotation with right hand so that fingers circle in direction of rotation • Thumb points in direction of torque vector

  22. 6.4 Parallel Force Problems • Solve using conditions of equilibrium • First condition of equilibrium: the sum of all parallel forces on a body in equilibrium must be zero (ΣF = 0) • Second condition of equilibrium: the sum of the clockwise torques on a body in equilibrium must equal the sum of the counterclockwise torques about any point (Στcw = Στccw)

  23. To solve parallel force problems (pp 169-173) • Sketch the problem • Write equation setting sums of opposite forces equal to each other • Choose point of rotation (eliminate variable if possible) • Write sum of clockwise torques • Write sum of counterclockwise torques • Set Στcw = Στccw (solve for unknown) • Substitute into force equation to solve for unknown

  24. 6.5 Center of Gravity • The center of gravity of any object is the point at which all of its weight can be considered to be concentrated • In uniform material, will be geometric center of object • Many objects, weight is not evenly distributed (ex: car, person)

  25. Irregular Object: Center of Gravity • Point at which object will balance • Weight represented as vector through center of gravity of the object • See examples pp 175-176 • Try activity on page 176

  26. Problems • 6.1 (pp 155-157) #4, 6, 12 • 6.2 (pp 164-166) #2, 4, 10, 12, 20, 24 • 6.3 (pp 168-169) #2, 8, 16 • 6.4 (pp 173-174) #4, 8, 10, 14 • 6.5 (pp 177-178) #4, 8, 14

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