1. Warm-Up: February 17, 2015
Write down a definition for equilibrium.

2. OpenStax Chapter 9 AP Physics 1
Statics and Torque
OpenStax Chapter 9
AP Physics 1

3. Equilibrium
When all forces acting on an object are balanced, the object is at equilibrium.
At equilibrium, there is no acceleration.

4. Statics
Statics is the study of forces in equilibrium.

5. The First Condition for Equilibrium
OpenStax Section 9.1
AP Physics 1

6. First Condition for Equilibrium
Net external force must be zero.
Net external force in any direction must be zero.

7. Static vs. Dynamic In static equilibrium, there is no motion.
In dynamic equilibrium, there is motion at constant velocity.

8. Static Equilibrium Example

9. Dynamic Equilibrium Example

10. Think-Pair-Share
Is it possible for an object to have constant zero net force, yet not be in equilibrium?
If so, give an example.
If not, explain why not.

11. Zero Net Force Insufficient

12. The Second Condition for Equilibrium
OpenStax Section 9.2
AP Physics 1

13. Torque Torque is the rotational analogue of force.
Torque is a measure of the effectiveness of changing or accelerating a rotation.
Changing the angular velocity.

14. Perpendicular Lever Arm
The perpendicular lever arm, r⊥, is the shortest distance from the pivot point to the line along which the force acts.

15. Perpendicular Lever Arm

16. Torque SI units are Newtons times meters, N·m
You must choose a “pivot point” to calculate any torque values.
Does not have to be the actual point around which the object rotates.
Torques are either clockwise (negative) or counterclockwise (positive).

17. Second Condition for Equilibrium
The net torque on a system must equal zero.

18. You-Try 9.1
The two children shown are balanced on a seesaw of negligible mass. The first child has a mass of 26.0 kg and sits 1.60 m from the pivot.
If the second child has a mass of 32.0 kg, how far is she from the pivot?
What is Fp, the supporting force exerted by the pivot?

19. What is Fp, the supporting force exerted by the pivot?
The two children shown are balanced on a seesaw of negligible mass. The first child has a mass of 26.0 kg and sits 1.60 m from the pivot.
If the second child has a mass of 32.0 kg, how far is she from the pivot?
What is Fp, the supporting force exerted by the pivot?
1.30 m
568 N

20. Assignment Read OpenStax Chapter 9 (through 9.2)
OpenStax page 314 #1-5
OpenStax page 316 #1-5 odd
Final Chapter Assignment:
Read OpenStax Chapter 9
OpenStax page 314 #1-12
OpenStax page 316 #1-25 odd

22. Warm-Up 2: February 18, 2015
When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of m from the center of the bolt.
How much torque are you exerting in newton x meters (relative to the center of the bolt)?
Convert this torque to footpounds.

23. When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of m from the center of the bolt.
How much torque are you exerting in newton x meters (relative to the center of the bolt)?
Convert this torque to footpounds.

24. OpenStax Section 9.3 AP Physics 1
Stability
OpenStax Section 9.3
AP Physics 1

25. Three Types of Equilibrium
Stable: when the system is displaced from equilibrium, it experiences a net force or torque in a direction opposite the displacement.
Unstable: when the system is displaced from equilibrium, it experiences a net force or torque in a same direction as the displacement.
Neutral: when the system is displaced from equilibrium, it remains at equilibrium.

26. Think-Pair-Share
Write down an example of a system that is in each type of equilibrium:
Stable equilibrium
Unstable equilibrium
Neutral equilibrium

27. Think-Pair-Share
Identify the type of equilibrium represented by each picture:

30. Stability
Many systems in equilibrium are only stable for small displacements.
A system remains stable as long as its center of gravity (cg) remains above the base.
A standing human can increase stability by:
Spreading apart your feet (larger base)
Bending knees (lowering center of gravity)
Using a cane or similar device (larger base)

31. Warm-Up 10: February 19, 2015
A 17.0 m high and 11.0 m long wall under construction and its bracing are shown. The wall is in stable equilibrium without the bracing but can pivot at its base. Calculate the force exerted by each of the 10 braces if a strong wind exerts a horizontal force of 650. N on each square meter of the wall.
Assume the net force from the wind acts at a height halfway up the wall and that all braces exert equal forces parallel to their lengths. Neglect the thickness of the wall.

32. A 17.0 m high and 11.0 m long wall under construction and its bracing are shown. The wall is in stable equilibrium without the bracing but can pivot at its base. Calculate the force exerted by each of the 10 braces if a strong wind exerts a horizontal force of 650. N on each square meter of the wall.
Assume the net force from the wind acts at a height halfway up the wall and that all braces exert equal forces parallel to their lengths. Neglect the thickness of the wall.

33. Stability
Many systems in equilibrium are only stable for small displacements.
A system remains stable as long as its center of gravity (cg) remains above the base.
A standing human can increase stability by:
Spreading apart your feet (larger base)
Bending knees (lowering center of gravity)
Using a cane or similar device (larger base)

34. Applications of Statics, Including Problem-Solving Strategies
OpenStax Section 9.4
AP Physics 1

35. Static Equilibrium Problem Solving
Determine whether the system is in static equilibrium. It is if a=0 and accelerated rotation does not occur.
Draw a free body diagram and/or force diagram for the system of interest. Carefully label all forces.
Solve the problem using Fnet=0 and/or τnet=0. Choose a pivot point that causes torques of unknown forces to be zero.
Check if the solution is reasonable.

36. Example 9.2 For the situation shown, calculate the following:
FR, the force exerted by the right hand
FL, the force exerted by the left hand
The hands are m apart, and the cg of the pole is m from the left hand. The mass of the pole is 5.00 kg.

37. You-Try 18
In the figure shown, the cg of the pole held by the pole vaulter is 2.00 m from the left hand, and the hands are m apart. The mass of the pole is 5.00 kg.
Calculate the force exerted by his right hand.
Calculate the force exerted by his left hand.

38. In the figure shown, the cg of the pole held by the pole vaulter is 2
In the figure shown, the cg of the pole held by the pole vaulter is 2.00 m from the left hand, and the hands are m apart. The mass of the pole is kg.
Calculate the force exerted by his right hand.
Calculate the force exerted by his left hand.

39. Assignment Read OpenStax Chapter 9 (through 9.4)
OpenStax page 314 #1-8
OpenStax page 316 #1-17 odd
Final Chapter Assignment:
Read OpenStax Chapter 9
OpenStax page 314 #1-12
OpenStax page 316 #1-25 odd

41. Warm-Up 14: February 23, 2015
A sandwich board advertising sign is constructed as shown. The sign’s mass is kg.
Calculate the tension in the chain, assuming no friction between the legs and the sidewalk.
What force is exerted by each side of the hinge?

42. What force is exerted by each side of the hinge?
A sandwich board advertising sign is constructed as shown. The sign’s mass is 8.00 kg.
Calculate the tension in the chain, assuming no friction between the legs and the sidewalk.
What force is exerted by each side of the hinge?
21.6 N

43. PhET Simulation Using a netbook computer, google “PhET balancing act”
Run the simulation, have fun, and learn.

45. Warm-Up 16: February 24, 2015
A cheerleader is attempting to perform splits. Calculate the magnitude and direction of the force exerted on each foot by the floor.

46. A cheerleader is attempting to perform splits
A cheerleader is attempting to perform splits. Calculate the magnitude and direction of the force exerted on each foot by the floor.
1110

47. Homework Questions?

48. OpenStax Section 9.5 AP Physics 1
Simple Machines
OpenStax Section 9.5
AP Physics 1

49. Simple Machines
Devices that can be used to multiply or augment an applied force, often at the expense of a greater distance.
Include levers, pulleys, wedges, and screws.
The ratio of output force to input force for any simple machine is called mechanical advantage (MA).

50. Lever
A rigid bar pivoted at a fixed point called the fulcrum.

51. You-Try 9.3
In the wheelbarrow shown, the load has a perpendicular lever arm of 7.50 cm, while the hands have a perpendicular lever arm of 1.02 m.
What upward force must you exert to support the wheelbarrow and its load if their combined mass is 45.0 kg?
What force does the wheelbarrow exert on the ground?

52. What force does the wheelbarrow exert on the ground?
In the wheelbarrow shown, the load has a perpendicular lever arm of 7.50 cm, while the hands have a perpendicular lever arm of 1.02 m.
What upward force must you exert to support the wheelbarrow and its load if their combined mass is kg?
What force does the wheelbarrow exert on the ground?
32.4 N
409 N

54. Warm-Up #20: February 26, 2015
Suppose you needed to raise a 250 kg mower a distance of 6.0 cm above the ground to change a tire. If you had a 2.0 m long lever, where would you place the fulcrum if your force was limited to 300. N?

55. Homework Questions?

56. Crank
A crank is a lever that can be rotated 360° about its pivot.

57. You-Try #22
A typical car has an axle with 1.10 cm radius driving a tire with radius of 27.5 cm. What is the mechanical advantage assuming the simplified model shown?
0.0400

58. Pulleys
A single pulley has MA=1; it only changes the direction of the force.
Combinations of pulleys are used to create mechanical advantage.
The number of cables pulling directly upward is approximately the MA.

59. Pulleys

60. You-Try #24
If you used the ideal pulley shown to support a car engine of mass 115 kg,
What would be the tension in the rope?
What force must the ceiling supply, assuming you pull straight down on the rope? Neglect the pulley system’s mass.

61. What would be the tension in the rope?
If you used the ideal pulley shown to support a car engine of mass 115 kg,
What would be the tension in the rope?
What force must the ceiling supply, assuming you pull straight down on the rope? Neglect the pulley system’s mass.
564 N
1690 N

62. Assignment Read OpenStax Chapter 9 OpenStax page 314 #1-12
OpenStax page 316 #1-25 odd