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# Mechanical Equilibrium

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### Mechanical Equilibrium

1. 1. Chapter 2<br />Mechanical Equilibrium<br />
2. 2. Objectives<br />Distinguish between force and net force<br />Describe the equilibrium rule and give examples<br />Distinguish between support force and weight<br />Compare and contrast static and dynamic equilibrium<br />Distinguish between vector and scalar quantities<br />Construct force diagrams<br />Determine the resultant of a pair of parallel vectors<br />Use the parallelogram rule to determine the resultant of a pair of nonparallel vectors<br />
3. 3. Force<br />A forceis a push or a pull<br />The scientific unit of force is the newton, abbreviated N<br />
4. 4. Force<br />The combination of all forces acting on an object is called net force<br />A net force is required to change the state of motion of an object<br />
5. 5. Force<br />Net force depends on the magnitudes and directions of the applied forces<br />
6. 6. Force<br />When the girl holds the rock with as much force upward as gravity pulls downward, the net force on the rock is zero<br />
7. 7. Tension and Weight<br />A stretched spring is under a “stretching force” called tension<br />
8. 8. Tension and Weight<br />Pounds and newtons are units of weight, which are units of force<br />
9. 9. Tension and Weight<br />The upward tension in the string has the same magnitude as the weight of the bag, so the net force on the bag is zero<br />
10. 10. Tension and Weight<br />The bag of sugar is attracted to Earth with a gravitational force of 2 pounds, or 9 newtons<br />
11. 11. Tension and Weight<br />There are two forces acting on the bag of sugar:<br />Tension force acting upward <br />Weight acting downward<br />
12. 12. Tension and Weight<br />The two forces on the bag are equal and opposite<br />The net force on the bag is zero, so it remains at rest<br />
13. 13. Force Vectors<br />A vectoris an arrow that represents the magnitude and direction of a quantity<br />A vector quantityneeds both magnitude and direction for a complete description<br />Force is an example of a vector quantity<br />
14. 14. Force Vectors<br />This vector represents a velocity of 60 km/h to the right<br />
15. 15. Force Vectors<br />A scalar quantity can be described by magnitude only and has no direction<br />Time, area, and volume are scalar quantities<br />
16. 16. Mechanical Equilibrium<br />Mechanical equilibrium is a state wherein no physical changes occur<br />Whenever the net force on an object is zero, the object is in mechanical equilibrium<br />This is known as the equilibrium rule<br />
17. 17. Mechanical Equilibrium<br />The equilibrium rule:<br />The  symbol stands for “the sum of” <br />F stands for “force” <br />
18. 18. Mechanical Equilibrium<br />The sum of the upward vectors equals the sum of the downward vectors<br />
19. 19. Mechanical Equilibrium<br />F = 0, and the scaffold is in equilibrium<br />
20. 20. Support Force<br />What forces act on a book lying at rest on a table? <br />One is the force due to gravity—the weight of the book<br />There must be another force acting on it to produce a net force of zero—an upward force opposite to the force of gravity<br />
21. 21. Support Force<br />The upward force that balances the weight of an object on a surface is called the support force<br />A support force is often called the normal force<br />
22. 22. Support Force<br />The table pushes up on the book with as much force as the downward weight of the book<br />The table supports the book with a support force—the upward force that balances the weight of an object on a surface<br />
23. 23. Support Force<br />The upward support force is positive and the downward weight is negative<br />The two forces add mathematically to zero<br />F = 0<br />
24. 24. Equilibrium for Moving Objects<br />An object at rest is only one form of equilibrium (static equilibrium)<br />An object moving at constant speed in a straight-line path is also in a state of equilibrium (dynamic equilibrium)<br />
25. 25. Equilibrium for Moving Objects<br />Once in motion, if there is no net force to change the state of motion, it is in equilibrium<br />
26. 26. Equilibrium for Moving Objects<br />When the push on the desk is the same as the force of friction between the desk and the floor, the net force is zero and the desk slides at an unchanging speed<br />
27. 27. Equilibrium for Moving Objects<br />If the desk moves steadily at constant speed, without change in its motion, it is in equilibrium<br />
28. 28. Equilibrium for Moving Objects<br />Friction is a contact force between objects that slide or tend to slide against each other<br />In this case, F = 0 means that the force of friction is equal in magnitude and opposite in direction to the pushing force<br />
29. 29. Vector Operations<br />The sum of two or more vectors is called their resultant<br />
30. 30. Vector Operations<br />Combining vectors is quite simple when they are parallel:<br />If they are in the same direction, they add<br />If they are in opposite directions, they subtract<br />
31. 31. Vector Operations<br />
32. 32. Vector Operations<br />To find the resultant of nonparallel vectors, we use the parallelogram rule<br />
33. 33. Vector Operations<br />Consider two vectors at right angles to each other, as shown below<br />
34. 34. Vector Operations<br />The constructed parallelogram in this special case is a rectangle<br />The diagonal is the resultant R<br />
35. 35. Vector Operations<br />We can calculate the magnitude of the resultant, R, using the Pythagorean Theorem<br />
36. 36. Applying the Parallelogram Rule<br />When the girl is suspended at rest from the two non-vertical ropes, is the rope tension greater or less than the tension in two vertical ropes? <br />
37. 37. Applying the Parallelogram Rule<br />Notice how the tension vectors form a parallelogram in which the resultant, R, is vertical<br />
38. 38. Applying the Parallelogram Rule<br />The girl’s weight is shown by the downward vertical vector<br />
39. 39. Applying the Parallelogram Rule<br />An equal and opposite vector is needed for equilibrium, shown by the dashed vector<br />
40. 40. Applying the Parallelogram Rule<br />Using the parallelogram rule, we find that the tension in each rope is more than half her weight<br />
41. 41. Applying the Parallelogram Rule<br />As the angle between the ropes increases, tension increases so that the resultant remains at 300 N upward, which is required to support the 300-N girl<br />
42. 42. Applying the Parallelogram Rule<br />When the ropes supporting the girl are at different angles to the vertical, the tensions in the two ropes are unequal<br />