1. Mechanical Equilibrium
Conceptual Physics
UNIT 1: LINEAR MOTION
Chapter 2
Mechanical Equilibrium

2. I. Force (2.1)
A. force– is a push or pull
1. A force is needed to change an object’s state of motion
2. State of motion may be one of two things
At rest
b. Moving uniformly
along a straight-line path.

3. B. Net force
1. Usually more than one force is acting on an object
2. combination of all forces acting on object is called net force.
3. The net force on an object changes its motion

4. 2.1 Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

5. 2.1 Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

6. 2.1 Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

7. 2.1 Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

8. 2.1 Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

9. 2.1 Force
Net Force
The net force depends on the magnitudes and directions of the applied forces.

10. 4. Can add or subtract to get resultant net force
5. If forces acting on object equal zero then we say the net force acting on the object = 0
6. Scientific units for force are Newtons (N)

11. C. Tension and Weight
1. Tension is a “stretching force”

12. 2. When you hang an object from a spring scale the there are two forces acting on object.
a. Force of gravity pulling down (also called weight)
b. Tension force pulling upward
c. Two forces are equal and opposite in direction and add to zero (net force = 0)

13. 2.1 Force Tension and Weight
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.
The bag of sugar is attracted to Earth with a gravitational force of 2 pounds or 9 newtons.

14. 2.1 Force Tension and Weight
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.
The bag of sugar is attracted to Earth with a gravitational force of 2 pounds or 9 newtons.

15. D. Force Vectors
1. Forces can be represented by arrows
a. length of arrow represents amount (magnitude) of force
b. Direction of arrow represents direction of force
c. Refer to arrow as a vector (represents both magnitude and direction of force

16. 2. Vector quantity- needs both magnitude and direction to complete description (i.e. force, velocity, momentum)

17. 3. Scalar quantity- can be described by magnitude only and has no direction (i.e. temperature, speed, distance)

18. Scaler or Vector quantity?
Time interval?
scaler
Mass?
Speed?
Velocity?
vector
Temperature?
Displacement?
Acceleration?

19. Arrow-tipped line segment
Length represents magnitude
Arrow points in specified direction of vector

20. Vectors are equal if: magnitude and directions are the same
Vectors are not equal if: have different magnitude or direction or

21. Are these vectors equal or not?
YES
YES NO NO

22. II. Mechanical Equilibrium (2.2)
A. Mechanical equilibrium- a state wherein no physical changes occur (state of steadiness)
1. When net force equals zero, object is said to be in mechanical equilibrium
a. Known as equilibrium rule

23. b. Can express rule mathematically as
1). ∑ symbol stands for “the sum of”
2). F stands for “forces”
2 N
-2 N

24. 2.2 Mechanical Equilibrium
The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in equilibrium.

25. 2.2 Mechanical Equilibrium
The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in equilibrium.

26. 2.2 Mechanical Equilibrium
The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in equilibrium.

27. 2.2 Mechanical Equilibrium
The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in equilibrium.

28. 2.2 Mechanical Equilibrium
think!
If the gymnast hangs with her weight evenly divided between the two rings, how would scale readings in both supporting ropes compare with her weight? Suppose she hangs with slightly more of her weight supported by the left ring. How would a scale on the right read?

29. 2.2 Mechanical Equilibrium
think!
If the gymnast hangs with her weight evenly divided between the two rings, how would scale readings in both supporting ropes compare with her weight? Suppose she hangs with slightly more of her weight supported by the left ring. How would a scale on the right read?
Answer: In the first case, the reading on each scale will be half her weight. In the second case, when more of her weight is supported by the left ring, the reading on the right reduces to less than half her weight. The sum of the scale readings always equals her weight.

30. III. Support Force (2.3)
A. support force- the upward force that balances the weight of an object on a surface
1. The upward force balances the weight of an object
2. Support force often called normal force
Support force
weight

31. Directions of support force provided by ten bra components: (A) rigid gore, (B) elastic cup, (C) semi-elastic neckline, (D) semi-elastic underarm, (E) rigid wire, (F) rigid cradle, (G) elastic wing, (H) elastic shoulder strap, (I) elastic underband and (J) rigid fastener. 

32. 2. Two forces add mathematically to zero
B. For an object at rest on a horizontal surface, the support force must equal the objects weight.
1. Upward force is positive (+) and the downward force is negative (-).
2. Two forces add mathematically to zero
2 N
-2 N

33. IV. Equilibrium of Moving Objects (2.4)
A. Equilibrium can exist in both objects at rest and objects moving at constant speed in a straight-line path.
1. Equilibrium means state of no change
2. Sum of forces equal zero

34. B. Objects at rest are said to be in static equilibrium
C. Objects moving at constant speed in a straight-line path are said to be in dynamic equilibrium
Static equilibrium dynamic equilibrium
Static equilibrium dynamic equilibrium

35. V. Vectors (2.5)
A. Parallel vectors
1. Add vectors if in same direction
2. Subtract vectors if in opposite direction
3. The sum of two or more vectors is called the resultant vector. = =

36. 2.5 Vectors
The tension in the rope is 300 N, equal to Nellie’s weight.

37. 2.5 Vectors
The tension in the rope is 300 N, equal to Nellie’s weight.
The tension in each rope is now 150 N, half of Nellie’s weight. In each case, F = 0.

38. B. Parallel vectors– simple to add or subtract

39. B. Non-parallel vectors
1. Construct a parallelogram to determine resultant vector
2. The diagonal of the parallelogram shows the resultant
a. Perpendicular vectors R

40. At one point the lunar lander was traveling 15ft/sec forward while traveling down at 4ft/sec. What was the direction they were actually moving?

41. Combining vectors that are NOT parallel
Result of adding two vectors called the resultant
Resultant of two perpendicular vectors is the diagonal of the rectangle with the two vectors as sides
Resultant vector

42. Use simple three step technique to find resultant of a pair of vectors that are at right angles to each other.
  First– draw two vectors with their tails touching.

43. Second-draw a parallel projection of each vector with dashed lines to form a rectangle

44. Third-draw the diagonal from the point
Third-draw the diagonal from the point where the two tails are touching
resultant

45. b. Perpendicular vectors with equal sides (special case)
1). For a square the length of diagonal is or 1.414
2). Resultant = x one of sides 1
Resultant = 1

46. c. Parallelogram (not perpendicular)
Construct parallelogram
Construct with two vectors as sides
Resultant is the diagonal
resultant

47. C. Applying the Parallelogram Rule- as angle increases,
 C. Applying the Parallelogram Rule- as angle increases, tension increases.

49. 2.5 Vectors
think!
Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break?

50. 2.5 Vectors
think!
Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break?
Answer: The tension is greater in the ropes hanging at an angle. The angled ropes are more likely to break than the vertical ropes.

51. Pythagorean Theorem- can be used if vectors added are at right angles
90° B

52. SOHCAHTOA
sin, cos, and tan are functions of the angle of a triangle compared to the lengths of the sides of a triangle
If you know the distances of the triangle sides, you can determine the inside angles.
If you know the angle and one side, you can calculate the length of the other side of the triangle.
Remember the following acronym: SOHCAHTOA
These will give you the formula depending on which side or angle you need to calculate

53. Components calculated using following formulas
When angles larger than 90°, sign of one or more components may be negative

54. Remember what the sides of a triangle are called
Hypotenuse
Opposite θ
Adjacent

55. Example:
Length of Opposite side
sin 25° =
Length of Hypotenuse
Length of Opposite side
sin 25° =
100 meters
length of Opposite side = 38.3 meters
100 meters
Opposite = ? θ
Adjacent

56. Graphical Addition of Vectors
Simple method for combining vectors to get resultant vector
Use ruler to measure length of vector
Use protractor to measure angle
55°