1. Introduction to Dynamics
Chapter 6 Forces

2. Sec 6.1 Force and Motion Objectives
Define a force and differentiate between contact forces and long-range forces
Recognize the significance of Newton’s second law of motion and use it to solve motion problems
Explain the meaning of Newton’s first law and describe an object in equilibrium

3. Force
Force
= a push or a pull

4. FORCE 1 N = 1 kg·m/s2 Metric Units for Force = Newtons (N)
= a push or a pull
Metric Units for Force = Newtons (N)
1 N = 1 kg·m/s2
= the force needed to give a 1 kg mass an acceleration of 1 m/s2
Note: The English unit for force is the pound: 1 lb equals 4.48 Newtons

5. Force & Mass are Different
Force is a push or pull that can change motion.
Measured in newtons (N) or pounds (lbs)
Weight is a force caused by gravity.
Measured in newtons or pounds, because it is a force.
Mass is the amount of matter in an object.
Measured in grams and kilograms
Your mass is the same everywhere in the universe, but your weight can be different.

6. Four Fundamental Forces of Nature

7. An attractive force between two bodies The weakest of all forces
GRAVITATIONAL FORCE
An attractive force between two bodies
The weakest of all forces

8. ELECTROMAGNETIC FORCE
Charged particles at rest exert electric forces on each other
Charged particles in motion exert magnetic forces on each other

9. Holds particles of the nucleus together The strongest of all forces
STRONG NUCLEAR FORCE
Holds particles of the nucleus together
The strongest of all forces

10. Form of an electromagnetic force
WEAK NUCLEAR FORCE
Form of an electromagnetic force
Happens when some nuclei radioactively decay

11. The Forces of Nature I. Gravitational: III. Weak Nuclear:
attraction b/tw masses
Ex: tides, weight
III. Weak Nuclear:
helps to explain atomic collisions
II. Electromagnetic:
attraction or repulsion b/tw charges
Ex: friction, tension, adhesion, lift, electrostatic , drag, buoyant, magnetic
•The roman numerals are in order from weakest to strongest (Demo:
Rub a balloon and stick it to the wall. Why doesn’t it fall? Gravity is not as strong as electrostatic attraction--locally).
•friction is sometimes dubbed the “total resistive force” and can be considered Coulomb attraction and meshing of surfaces. Very smooth things can have great frictional forces (Demo: rub two overhead sheets on fur and stick them together, then try to slide past each other.)
IV. Strong Nuclear:
binds atomic nuclei

12. Two Categories of Forces…
Contact Force
Acts on an object only by touching it
Long-Range Force (aka “Field Force”)
Exerted without contact
Magnets
Gravity
Agent: a specific, identifiable, immediate cause of a force

13. Examples of Forces Ff - - Friction (opposes sliding)
FA Applied Force (an external push or pull)
FN Normal (perpendicular to a surface)
Fsp Spring (push or pull of a spring)
FT Tension (spring, rope, cable)
Fthrust Thrust (rockets, planes, cars)
Fg Weight (force due to gravity)
Which of the four types of force are each of these?
….all of them but one is electromagnetic!

14. Weight Force, Fg aka gravitational force
ON EARTH:…
The weight force acts on all objects
The direction of the weight force is always towards the center of the earth
The magnitude of the weight force is always equal to the mass of the object (kg) multiplied by acceleration due to gravity
Checking understanding...
DEMO: Have a student rool across the floor on a rolling cart or skate board. Have the other students wrie a paragraph describing the motion, listing all forces involved, and drawing a free body diagram.
object
Fg = mg
Fg (or FW )

15. W = mg or Fg = mg
The magnitude of an object’s weight force is always equal its mass times the acceleration it would have if it were in free-fall.
Fg = mg

16. All Forces have an Agent and an Object
Agent: the cause of a force
(what does the pushing or pulling)
Object: the ‘victim’ of a force
(what gets pushed or pulled)
•Point out that since forces are vectors you can add them using the head to tail method or the component method. You can also resolve forces into components--and sometimes you have to in order to solve a problem.

17. Weight Force, Fg Fg (or FW ) Fg = mg ON EARTH:…
The agent of the weight force is always the earth.
Fg = mg
Checking understanding...
DEMO: Have a student rool across the floor on a rolling cart or skate board. Have the other students wrie a paragraph describing the motion, listing all forces involved, and drawing a free body diagram.
object
Fg (or FW )

18. Agents and Objects of Forces
Example: A car is towed by a tow truck:
AGENT: The tow truck
OBJECT: The car
Conventional Notation:
FTYPE (AGENT, OBJECT) FA (T,C)
•Point out that since forces are vectors you can add them using the head to tail method or the component method. You can also resolve forces into components--and sometimes you have to in order to solve a problem.

19. Forces are Vectors Forces have magnitude and direction.
We can represent forces by drawing arrows
Example:
This diagram shows all of the forces acting on an object:
•Point out that since forces are vectors you can add them using the head to tail method or the component method. You can also resolve forces into components--and sometimes you have to in order to solve a problem.

20. Drawing Force Vectors
The direction of the arrow represents the direction of the force.
The length of the arrow represents the magnitude of the force.
We always draw force vectors as ‘pulls’ on objects, not pushes (arrow starts at object)

21. Free Body Diagrams FREE BODY DIAGRAM
A picture of a ‘body’ with all the force vectors acting upon it represented graphically is called a
FREE BODY DIAGRAM
Checking understanding...
DEMO: Have a student rool across the floor on a rolling cart or skate board. Have the other students wrie a paragraph describing the motion, listing all forces involved, and drawing a free body diagram.

22. Free Body Diagrams Rules for drawing free body diagrams:
Draw the object as a dot
Only draw forces acting on that object
Draw all forces as ‘pulls’
(arrow point away from the dot)
Draw and label every force acting on the object.
Length of each arrow must reflect magnitude
(stronger forces  longer arrows!)
(equal forces  same arrow length.)
Checking understanding...
DEMO: Have a student rool across the floor on a rolling cart or skate board. Have the other students wrie a paragraph describing the motion, listing all forces involved, and drawing a free body diagram.

23. Try it...
Draw a picture of your book sitting on the desk. Identify all the forces acting on it.

24. Free Body Diagrams... FN (normal force) Fg or FW (weight force)
Book
Checking understanding...
DEMO: Have a student rool across the floor on a rolling cart or skate board. Have the other students wrie a paragraph describing the motion, listing all forces involved, and drawing a free body diagram.
Fg or FW (weight force)
Normal means perpendicular;
not ordinary or regular!

25. The “Normal” Force FN (normal force) Fg or FW (weight force)
Book
Checking understanding...
DEMO: Have a student rool across the floor on a rolling cart or skate board. Have the other students wrie a paragraph describing the motion, listing all forces involved, and drawing a free body diagram.
Fg or FW (weight force)
Normal means perpendicular;
not ordinary or regular!

26. Normal Force, FN
The direction of the normal force is always perpendicular to a surface (normal)
The magnitude of the normal force varies depending on the situation.
The agent of the normal force is always the SURFACE.
Checking understanding...
DEMO: Have a student rool across the floor on a rolling cart or skate board. Have the other students wrie a paragraph describing the motion, listing all forces involved, and drawing a free body diagram.

27. Draw free body diagrams for the following
An egg is free-falling from a nest in a tree. Neglect air resistance.
A skydiver is descending with a constant velocity. Consider air resistance.
Your physics book is sliding across the desk at constant speed (no acceleration)

28. Direction Matters! FN Ff FA Physics W or Fw Fw or W = Weight Force
surface
W or Fw
Fw or W = Weight Force
FN = Normal Force
FA = Applied Force
Ff = Friction Force
Direction Matters!

29. Net Force, Fnet or ΣF Fnet = F1 + F2 + F3 … etc.
The net force on an object is the
SUM OF ALL FORCES acting on an object
This is NOT just another force like FN or Fg !
It must be determined by analysis.
Checking understanding...
DEMO: Have a student rool across the floor on a rolling cart or skate board. Have the other students wrie a paragraph describing the motion, listing all forces involved, and drawing a free body diagram.
Fnet = F1 + F2 + F3 … etc.

30. Net Force, Fnet or ΣF If Fnet = 0 , then a = 0
When the net force on an object is zero, then the object is said to be in equilibrium, and the acceleration of the object must be zero.
If Fnet = 0 , then a = 0
Checking understanding...
DEMO: Have a student rool across the floor on a rolling cart or skate board. Have the other students wrie a paragraph describing the motion, listing all forces involved, and drawing a free body diagram.

31. Fnet (Net Force) = ΣF = the sum of all forces acting on an objectFf FA
Physics
surface
W or Fw
Fw or W = Weight Force
FN = Normal Force
FA = Applied Force
Ff = Friction Force
Direction Matters!

32. What is SF again? (aka Fnet)
SF is called:
the sum of the forces
the net force
the total force
SF = F1 + F2
Remember though that
“Left” is probably negative
“Down” is probably negative or or F1 F2
You assign the coordinate system!

33. Sample Problems What is the total force? SF = F1 + F2
(Let’s make left be the negative direction, so the 12N force to the left is really -12N.)
SF = -12N + 8N
SF = -4N m
12N 8N

34. Sample Problems What is the total force? SF = F1 + F2
(Let’s make down be the negative direction; so the 115N force is really -115N.)
SF = 158N + (-115N)
SF = 43N m
F2 = N
F1 = N

35. F1 3 Possible Situations F1 > F2 SF = F1 - F2 F2 m
mass accelerates left

36. F2 3 Possible Situations F1 < F2 SF = F2 - F1 F1 m
mass accelerates right

37. 3 Possible Situations
Balanced Forces = Equilibrium = Constant Velocity
No!
The block was already moving.
So, if the force left is equal to the force right then the block has no way to speed up or slow down.
Does this block have a larger F2 because its moving to the right? m F1 F2
F1 = F2
SF = 0
mass stays at a constant velocity

38. Balanced Forces
Produce NO
Acceleration

39. Unbalanced Forces
Produce
Acceleration

40. Free Body Diagrams... What forces are acting on a
skier as she races down a hill?

41. The Answer... FN
Ff (an)d Fd Fg

42. The Answer... FN
Ff (and FAIR)
Hmmm…
What is Fnet ? Fg

43. The Answer... FN
Ff and Fd W
Vector Resolution!

44. When does Fnet = 0 ?

45. Sir Isaac Newton (1642-1727) English physicist and mathematician
                               
English physicist and mathematician
Before the age of 30:
Formulated basic laws of mechanics
Discovered the universal law of gravitation
Invented Calculus
In 1687, published the Principia.
possibly the single most important book in the history of science!

46. Aristotle and Newton had different ideas about forces and motion.
Aristotle's idea: For an
object to move at a constant
speed, a constant force
must be applied.
Newton's idea: An object
moving at a constant speed
will continue at that speed
without additional force
being applied.

47. Newton’s Second Law F = ma
An unbalanced force will cause acceleration, but mass will resist acceleration.

48. Example
A race car has a mass of 710 kg. It starts from rest and travels 40.0 m in 3.0 s. The car is uniformly accelerated during the entire time. What net force is exerted on it?

49. Newton’s Second Law
SF = ma or
Fnet = ma

50. First let’s clarify the variables and units
Newton’s Second Law
SF = ma
First let’s clarify the variables and units
SF or Fnet = Net Force (sum of forces) measured in N
a = acceleration measured in m/s2
m = mass measured in kg

51. So to find the acceleration of a mass, m, you need to know the forces.
Newton’s Second Law
SF creates the acceleration on a mass.
SF = ma
So to find the acceleration of a mass, m, you need to know the forces. SF m a

52. Newton’s Second Law Sample #1:
How much net force does it take to make a 1.0kg block accelerate at 1.0m/s2?
m = 1.0kg
a = 1.0m/s2
SF = ?
SF = ma
SF = (1.0kg)(1.0m/s2)
SF = 1.0 kg·m/s2
1 N = 1 kg·m/s2
SF = 1.0N

53. Newton’s Second Law
A monkey pulls on a banana on a tree with a force of 25N and the tree resists with a force of 25N. What is the total force on the banana?

54. Newton’s Second Law
Two kids pull on a toy. The bigger girl pulls with 24.0N to the right. The smaller boy pulls 12.0N to the left. If neither lets go of the toy, then what will their acceleration be if the total mass of the boy, girl, and toy is 60.0kg?

55. Pick equations and Solve
Two kids pull on a toy. The bigger girl pulls with 24.0N to the right. The smaller boy pulls 12.0N to the left. If neither lets go of the toy, then what will their acceleration be if the total mass of the boy, girl, and toy is 60.0kg?
Draw a diagram
12.0N
24.0N
60.0kg
Write out variables
Pick equations and Solve
SF=F1 + F2
SF=24.0N + (-12.0N)
SF=12.0N
a = ?
SF= ma
a = SF m
a = 12.0N
60.0kg
a = .200m/s2
F1 = 24.0N
F2 = 12.0N
m = 60.0kg
a = ?

56. Example Problems What is the weight of a 75 kg person on earth?
What is their weight in an elevator?
What is their weight in a falling elevator?
What is the mass of a person that weighs 865 N on earth?
What is the weight of a 75 kg person on the moon where g = 1.6 m/s2 ?

57. Sec. 6.2 Using Newton’s Laws
Objectives
Describe how the weight and the mass of an object are related
Differentiate between the gravitational force weight and what is experienced as apparent weight
Define the friction force and distinguish between static and kinetic friction

58. Mass and Weight Weight Force = Fg = mg
The weight force, Fg , is used to find the downward force of an object.
Both the weight force and acceleration due to gravity are downward. (but the net force on an object is not always equal to its weight force!)
Weight Force = Fg = mg

59. Fg = mg
The magnitude of an object’s weight force of is always equal its mass times the acceleration it would have if it were in free-fall.

60. Example Problems What is the weight of a 75 kg person on earth?
What is their weight in an elevator?
What is their weight in a falling elevator?
What is the mass of a person that weighs 865 N on earth?
What is the weight of a 75 kg person on the moon where g = 1.6 m/s2 ?

61. Scale Problems FN (Scale , Me)
The reading on a scale is the magnitude of the force of the scale on the person or object standing on the scale!

62. Scale Problems
When a problems asks you “what is the reading on the scale”, it is asking you to determine the force of the scale on the object.
F (S , O)
Hmmm… will that ever differ from the weight force of the object ? (Yes, it can differ!)

63. Example Problems F(S,P) = ? Fnet = ma m = 75 kg a = + 2.0 m/s2
FN (S,P)
Example Problems
A 75 kg person stands on a scale which is in an elevator, accelerating upwards at 2.0 m/s2. What is the reading on the scale?
Fg (E, P)
F(S,P) = ?
m = 75 kg
a = m/s2
g = m/s2
Fg (E,P) = N
Fnet = ma
Fnet = ΣF (“the sum of all forces”)
Fnet = F(S,P) + Fg(E,P)
F(S,P) = Fnet - Fg(E,P)
= ma – (- 735 N)
= N
Fnet = 150 N

64. Example Problems
A 50.0 kg bucket is pulled by a rope. The rope is guaranteed not to break if the tension force is less than N. The bucket is lifted from rest, and after being lifted 3.0 meters, it is travelling at 3.0 m/s. Is the rope in danger of breaking?

65. Example Problem # 2 v2 = V02 + 2a(d-d0)
F (R , B)
A 50.0 kg bucket is pulled by a rope. The rope is guaranteed not to break if the tension force is less than N. The bucket is lifted from rest, and after being lifted 3.0 meters, it is travelling at 3.0 m/s. Is the rope in danger of breaking?
Fg (E, B)
FT (R,B) = ?
m = 50.0 kg
a = ?
v0 = 0
v = 3.0 m/s
d0 = 0 m
d = 3.0 m
v2 = V02 + 2a(d-d0)
Fnet = ma = (50.0kg) (1.5 m/s2) = 75 N
Fnet = ΣF (“the sum of all forces”)
Fnet = FT (R,B) + Fg(E,B)
FT (R,B) = Fnet - Fg (E,B)
= 75 – (- 490 N)
= N
g = m/s2
Fg (E,P) = N

66. Newton’s First Law: The Law of Inertia
Unless acted upon by an unbalanced force, objects at rest will stay at rest and objects in motion will stay in motion.

67. Newton’s First Law
Unless acted upon by an unbalanced force, objects at rest will stay at rest and objects in motion will stay in motion.
Lisa
Review of 1st Law
Visual example of the law of motion
Link to info on the web for reteaching

68. Newton’s First Law
Unless acted upon by an unbalanced force, objects at rest will stay at rest and objects in motion will stay in motion.

69. Newton’s First Law
Unless acted upon by an outside force, objects at rest will stay at rest and objects in motion will stay in motion.

70. Newton’s First Law of Motion
“An object that is at rest will remain at rest or an object that is moving will continue to move in a straight line with constant speed, if and only if the net force acting on that object is zero.”

71. Newton’s First Con’t
Inertia—the tendency of an object to resist change.
Equilibrium—object at rest or moving at a constant velocity

72. Finally…Misconceptions about forces
When a ball has been throw, the force of your hand remains on it. NO!
A force is needed to keep an object moving. NO!
Inertia is a force. NO!
The quantity ma is a force. NO!

73. Friction is a Force Friction is a force that resists motion.
…it is due to microscopic roughness on all surfaces.
… it slows down all moving objects.

74. Friction Static friction force Kinetic Friction Force
The force that opposes the start of relative motion between the two surfaces in contact
Friction force when object isn’t in motion
Kinetic Friction Force
The force that opposes relative motion between surfaces in contact
Friction force when object is in motion

75. Calculating Friction Kinetic Friction Force (Ff ,kinetic) = (µkFN)
Static Friction Force
(Ff ,static) < or = (µsFN)

76. Typical Coefficients of Friction
Surface µs µk
Rubber on concrete
Rubber on wet concrete
Wood on wood
Steel on steel (dry)
Steel on steel (with oil)
Teflon on steel

77. Example Problems Balanced Forces:
You push a 25 kg wooden box across a wood floor at constant speed. How much force do you exert on the box? (μk = 0.20)

78. Example Problems Unbalanced Forces:
If you push the same 25 kg wooden box across a wood floor with double the force, what is the acceleration of the box?

79. Terminal Velocity
The constant velocity that is reached when the drag force equals the force of gravity
Objects can only fall so fast due to their size and shape and density of the air/fluid
Ping-pong ball – 9 m/s
Basketball – 20 m/s
Baseball – 42 m/s
Skydiver: >62 m/s w/o chute
5 m/s w/ chute

80. THE END

81. Demo Time Demo: Hanging Weights
Question: Where will the string break if I pull on the bottom string very quickly?

82. Demo Time Demo: Hanging Weights
Analysis: Why did the string break where it did?
The string does not stretch here, because the large mass does not move. A large mass has lots of inertia. The tension force in the bottom of the string does not accelerate the large mass.

83. Demo Time Demo: Paper cup and Marble
Question: What will happen when the card is flicked hard?

84. Demo Questions Explain why the bottom string broke in the demo
Explain why the ball fell down in the cup demo.

85. Demo Questions Continued
Why do groceries slide to the side when you turn your car?
Why is it a bad idea to cut off a Hummer and then slow down in your Mini Cooper?
If you have fuzzy dice hanging from your rearview mirror, why does it swing when you stop and start moving?

86. Periodic Motion Pendulums, springs, strings Simple Harmonic Motion
Motion that returns an object to its equilibrium position as a result of a restoring force that is directly proportional to the object’s displacement
Period (T)
Time needed to repeat one complete cycle of motion
Amplitude
Maximum distance the object moves from equilibrium

87. Amplitude, Frequency, Period
The Amplitude is the displacement.
The Frequency is the number of cycles/sec.
The Period is the time for one cycle T = 1/f

88. Period of a Pendulum

89. Problems
Pg. 136
17-19

90. Sec. 6.3 Interaction Forces
Objectives
Explain the meaning of interaction pairs of forces and how they are related by Newton’s third law
List the four fundamental forces and illustrate the environment in which each can be observed.
Explain the tension in ropes and strings in terms of Newton’s third law

91. Interaction forces
Two forces that are in opposite directions and have equal magnitude
Newton’s Third Law—all forces come in pairs
FA on B = -FB on A