1. Dynamics:
The Laws of Motion

2. Intuitive Physics We all have an intuition about how objects move.
It's part of our brains, developed over millions of
years. It's how we see the world.
Our beliefs are much like those written down by
Aristotle 2400 years ago, in his book titled
"Physics".
Our beliefs are hard to change since they work well
in our day to day lives. But they limit us in developing an understanding of how the world works. We must build on our intuition and move beyond it.
That is just what Galileo did 400 years ago.

3. Galileo vs. Aristotle
In our experience, objects must be pushed in order to keep moving. So force would be needed to have a constant velocity. This is what Aristotle claimed.
But Galileo proposed the following thought
experiment which revealed another perspective..

4. Galileo vs. Aristotle
Imagine two perfectly smooth ramps connected
together by a perfectly smooth surface. If a ball rolls down one ramp, it keeps rolling up the other side until it reaches the same height.

5. Galileo vs. Aristotle
Now repeat that experiment, but make the second ramp less steep.
It will still keep rolling until it reaches the same height, but it has to roll farther.

6. Galileo vs. Aristotle
Finally, make the second ramp flat.
Now what will happen?
It will keep rolling forever, no external force is necessary.

7. Galileo vs. Aristotle
It's not that Aristotle was wrong.
In everyday life, objects do need to keep being pushed in order to keep moving. Push a book across the table. When you stop pushing, it stops moving. Aristotle is right in terms of
what we see around us every day.

8. Sir Issac Newton
( )
One of the most influential people in history
English physicist, mathematician, astronomer, natural philosopher and theologian.
Published “Principia” in It is probably the most important scientific book ever written. It lays the groundwork for most of classical mechanics
Developed calculus (along with Gottfried Leibniz)

9. Newton’s 1st Law of Motion
Galileo's principle was to become Newton's First Law of Motion:
Newton’s 1st Law of Motion
Every object continues in its state of rest or in its state of uniform velocity (constant speed and direction) unless acted on by a nonzero net force.
also called The Law of Inertia
Inertia is the tendency of an object to maintain its state of uniform motion. Mass is a measure of inertia

10. Inertia…

12. Newton’s First Law
If the net force on an object is zero, then the object is in equilibrium.
An object is in equilibrium if it is at rest (static equilibrium) or if it is moving at a constant velocity (dynamic equilibrium) .
Newton’s first law identifies a net force as something that disturbs the state of equilibrium.
Thus, if there is no net force acting on the object, then the object does not experience a change in speed or direction and is in equilibrium.

14. FORCE
Generic name for a push or a pull on an object. It results from an interaction between 2 objects.
Force is a VECTOR. It has magnitude and direction.
Unit of Force (SI) – Newton (N)

15. Inertia, Mass and Weight
Inertia – an object’s resistance to changes in motion
Mass – measure of the amount of material in an object (measure of inertia). Mass is a scalar. SI unit-kg
Weight – force of gravity. It is a measure of the gravitational force acting on an object.

16. Newton’s 1st Law of Motion states what happens if there is no net force.
What happens when a net force is exerted on an object?
A net force causes an acceleration.
What precisely is the relationship between force and acceleration?

17. Newton’s 2nd Law of Motion
The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.
Fnet = ma
Force Unit: N = kg(m/s2)

18. Example: Force of jet engine
The engine on a fighter plane can exert a force of 105,840 N (24,000 lbs). The take-off mass of the fighter plane is 16,875 kg (an F-16 weighs 37,500 lbs). If you mounted the airplane engine on your car (which has a mass of about 1500 kg), what acceleration would you get

19. Example: Force to stop a car
What net force is required to bring a 1500 kg car to rest from a speed of 100 km/h within a distance of 55 m?

20. When you throw or kick a ball, what are the forces on the ball
when you are in contact with the ball?
after the ball is free?
Once in the air, the only force on the ball is gravity (projectile motion). There is no force in the horizontal direction.
FFoot
FNet a FG FG

21. Free Body Diagram
Free Body Diagram: a physical model that shows all the forces acting on the system. FG FG
Fcar
Ffriction
FTable
Froad
Each force is drawn as a vector leading away from the object.

22. Where do forces come from?
We see that a force on an object is always applied by another object. Force arises from the interaction between objects and that interaction is not one-sided.
Ball
Wall
FWB
FBW on by

23. Newton’s 3rd Law of Motion
Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.  These two forces are called an action-reaction pair and are never applied on the same object.
Sometimes stated as –
To every action, there is an equal and opposite reaction.
(its very important to remember that the “action” force and the “reaction” are on different objects so they never cancel each other out)

24. Newton’s 3rd Law
For every action there is an equal and opposite reaction.

25. m1=5 m2=15 System F = 20N 1 2 Isolate m2 F21 2 Isolate m1 F = 20N 1
F12 and F21 are equal and opposite.
They are action-reaction pairs internal to the system.

26. When the man exerts a force to move the crate, the crate exerts an equal and opposite force back, so no matter how hard he pulls, the backward reaction force always equals the forward pulling force. So is the net force zero ? and if so, how can he ever move the crate?
Action-reaction pair
FCM
Consider ALL forces acting on the crate
FMC
Fnet
FgM
FMg
FCg
FgC

27. Two different size students, initially at rest on ice skates, push off one another.
a) Which student experiences the greater force during the push off? Explain how you know.
b) Which student experiences the greater acceleration during the push off? Explain how you know.

28. Types of FORCES Field Forces Contact Gravitational Electromagnetic
Strong Nuclear
Weak Nuclear
Contact
Normal
(perpendicular)
Friction
Tension
Elastic
Air resistance

29. Field Forces (Non-Contact)
Types of FORCES
Field Forces (Non-Contact)
Rel. Strength
Range (m)
Strong 1
10-15
(diameter of nucleus)
Electro-magnetic
1/137
Infinite
Weak
10-6
10-18
(0.1% proton diameter)
Gravitational
6x10-39

30. Contact Forces
A contact force exists when an object from the external world touches a system and thereby exerts a force on it.
Tension
Friction
Applied
Normal

31. Gravitational Force
Galileo: all objects fall to the earth with the same acceleration, g. The force that causes this is called the force of gravity, FG.
Slope = grav. field strength
(lb-force)

32. Gravitational Force Box resting on a table v = 0 FN,Table,Book
Newton’s 1st law:
Fnet = 0 for the box
v = 0
FG,Earth,Book
Newton’s 3rd law:
Forces come in action-reaction pairs

33. Perpendicular support force
Normal Force
Perpendicular support force
Normal
Normal Force, FN
Push
Normal

34. Example: weight and normal force
A friend gives you a gift box with mass 10 kg
A) Determine the weight of the box and the normal force acting on it.
Newton’s 1st law: Fnet = 0 for the box
v = 0

35. Example: weight and normal force
A friend gives you a gift box with mass 10 kg
B) Now your friend pushes down on the box with a force of 40N. What is the normal force on the box?
Newton’s 1st law:
Fnet = 0 for the box
Fpush
v = 0
Table pushes back with more force

36. Example: weight and normal force
A friend gives you a gift box with mass10 kg
C) Now your friend pulls up on the box with a force of 40N. What is the normal force on the box?
Newton’s 1st law:
Fnet = 0 for the box
Fpull
v = 0
Table does not push back with full weight of box

37. Example: weight and normal force Table cannot pull box down. FN >0
A friend gives you a gift box with mass 10 kg
D. What happens when friend pulls upward with a force equal to or greater than the box’s weight (say Fpull = 100N)? X
Fpull
Table cannot pull box down. FN >0

38. Example: pulling a box Fp 30o
A friend gives you a gift box with mass 10 kg. You pull it towards you with a force of FP=40 N, 300 to the horizontal.
Find the acceleration of the box
Find the upward normal force on the box
1. Make sketch
2. Free Body Diagram of object(s)
3. Choose axes parallel and perpendicular to direction of motion
4. Break vectors into components y
5. Apply Newton’s 2nd Law to each dimension Fp
30o x

39. Example: pulling a box Fp Fpy 30o Fpx
A friend gives you a gift box with mass 10 kg. You pull it towards you with a force of FP=40 N, 300 to the horizontal.
Find the acceleration of the box
Find the upward normal force on the box
How to Apply Newton’s 2nd Law to each dimension y Fp
Fpy
30o x
Fpx

40. Example: pulling a box Fp ax = 3.46 m/s2 ay = 0 FN = 78 N 30o
A friend gives you a gift box with mass 10 kg. You pull it towards you with a force of FP=40 N, 300 to the horizontal.
Find the acceleration of the box
Find the upward normal force on the box
How to Apply Newton’s 2nd Law to each dimension y Fp
30o x
ax = 3.46 m/s2
ay = 0
FN = 78 N

41. fk Friction Force FN FG fs Static Friction At rest
Friction is the force that opposes a sliding motion. It is highly useful, enables us to walk and drive a car FN fs
Static Friction
Keeps an object from moving
Would slide down
At rest
Fnet FG
Kinetic Friction
Opposes the sliding motion of an object
moving
Fpull fk

42. What causes friction?
Friction may or may not exist between two surfaces. If it exists, it opposes the direction object “wants” to slide. It is parallel to the surface.

43. What does friction depend on?
Frictional force depends on the materials that the surfaces are made of.
The normal force between the two objects also matters. The harder one object is pushed against the other, the greater the force of friction that results.

44. Friction and the Normal Force
The friction dependence on the normal force has several implications, such as…
Friction on a sloping surface is less than friction on a flat surface (since the normal force is less on a slope).
Increasing the weight of an object increases the friction between the object and the surface it is resting on.

45. Mathematical Model for Friction?
Fpull fk FG FN
FN = mg
If move with constant velocity
Newton’s 1st and 2nd laws
You can pull a known masses over different surfaces and measure Fpull (which equals Ff) with spring scale/force sensor.

46. Kinetic Friction
Kinetic friction (sliding friction) is generally less than static friction (motionless friction) for most surfaces.
Coefficient of kinetic friction
(empirical property of the surfaces in contact)

47. Static Friction
Static friction is tricky. It can range from zero to some maximum value for 2 surfaces
Coefficient of static friction
Static friction is zero unless there is a force trying to make the surfaces slide
It increases as the force pushing the object increases until it reaches a maximum value defined by μs.
Once the maximum value of static friction has been
exceeded by an applied force, the surfaces begin to slide
and the friction is no longer static friction.

50. Example: Friction (static and kinetic)
A 10 kg box rests on a horizontal floor. The coefficient of static friction is ms = 0.40 and the coefficient of kinetic friction is mk = Determine the force of friction, f, acting on the box if a horizontal, force, FP, is applied having a magnitude of
0 N
10 N
38 N
40 N Fp
Since no force applied in a, box doesn’t move and f=0 f

51. Example: Friction (static and kinetic)
No movement, f s= 0
No movement, f s= 10 N
No movement, fs=38 N
acceleration, f k= mkFN = 0.3(98) = 29.4 N Fp f
Since no force applied in a, box doesn’t move and f=0
Force of static friction will oppose any applied force up to max of 39.2 N.
For forces > 39, kinetic friction opposes the motion with a constant friction force

52. FN FN FN F F FG FG FG Question
A hockey puck is sliding at a constant velocity across a flat, horizontal ice surface that is assumed to be frictionless. Which of the sketches below is the correct force diagram? Which one would be correct if the puck slowed down?
Middle
Right
Motion
Motion
Motion FN FN FN
Even smooth ice exerts a tiny friction force (C) in the direction opposite the motion of the puck and the pucks velocity decreases very slowly
Tug of war demo possibility for friction. Tie rear ends of ID motorized car. Place on table. Bring attention to fact that cars are identical and joined together. Ask what will happen if cars are turned on. Short discussion. Turn on. Both barely move in tug of war.
What will happen if one car placed on sandpaper. Show effect of surface on motion
What will happen if one were heavier than other? Show by putting masses (effect of mass on friction) F F FG FG FG

53. Question
A hockey puck is given an initial speed of 7.35m/s on a frozen pond. The puck slides on the ice for 5.0 s before coming to rest. Determine the coefficient of friction between the puck and the ice.
mk = 0.15
Motion FN FG fk

54. Tension Force The use of ropes or cables to transmit a force
When a flexible cord pulls on an object, the cord is under tension and it exerts a force T on the object.
Tension is a pulling force that arises when a rope, string, cable or other long thin material resists being pulled apart.
Tension always pulls away from a body attached to a rope or string and toward the center of the rope or string.

55. T T T T

56. Tension EXAMPLE: Nellie Newton hangs at rest from the ends of the rope as shown. How does the reading on the scale compare to her weight? T T

57. Tension EXAMPLE:One day Harry is painting near a flagpole, and, for a change, he ties the free end of the rope to the flagpole instead of to his chair, as shown here. Why did Harry end up taking his vacation early?
Tension EXAMPLE: Harry the painter swings year after year from his bosun's chair. His weight is 500 N and the rope, unknown to him, has a breaking point of 300 N. Why doesn't the rope break when he is supported as shown here with both ends of the rope attached to his bosun's chair?

58. Tension EXAMPLE: Two 100 N weights are attached to a spring scale as shown. Does the scale read 0, 100, or 200 N, or give some other reading? T

59. FN F FG What do the motion graphs look like for each? Motion x vx ax x59

60. If the graphs below are velocity-time graphs of an object, which one(s) show(s) that there is no net force on the object? D
If the graphs below are position-time graphs of an object, which one(s) show(s) that there is no net force on the object?
C, D, E A B C D E 60

61. For each of the velocity-time graphs shown below, sketch the Force-time graph61

62. Perpendicular component
EXAMPLE: Draw a free body diagram for the skier who slides with negligible friction (that means ignore force of friction). Label the force vectors, break into components, and use hatch marks on the vectors to indicate equality. What is the skier’s acceleration?
x (//)
y ()
= Fnet
= mgsin30
Perpendicular component
FG
30o \
60o
a= gsin30
FG//
Parallel component
30o

63. If the tension in the rope is 61.4N, what is the mass of the climber?
EXAMPLE: Draw a free body diagram for the climber who has stopped to rest. Label the force vectors, break into components, and use hatch marks on the vectors to indicate equality.
If the tension in the rope is 61.4N, what is the mass of the climber?
x (//)
y ()
FG
55o
FG//
m = 7.65 kg
55o

64. Approach for Analyzing the Dynamics of Motion
Identify the system to be analyzed and draw a picture to represent the system if necessary.
2. Select a coordinate system to analyze your system with one axis parallel to the direction of motion and the other perpendicular to the direction of motion.
3. Identify all forces acting on the system by drawing a free body diagram. Your FBD should be large and clear
4. Resolve (break up) force vectors into horizontal (parallel) and vertical (perpendicular) components
5. Apply Newton’s 2nd law to each axis or direction: SFx = max and SFy = may
6. Solve for relevant unknowns. Keep in mind that you may sometimes have more than one unknown and therefore need the same number of equations as unknowns.

65. Example: Boxes connected by a cord
2 Boxes are connected by a lightweight cord and are resting on a table. The boxes have masses 12.0 and 10.0 kg. A horizontal force, FP =40 N, is applied to the 10 kg box.
Find the acceleration of each box
Find the tension in the cord Fp
No friction
m1 =
10kg
m2 = 12kg

66. Example: Boxes connected by a cord
2 Boxes are connected by a lightweight cord and are resting on a table. The boxes have masses 12.0 and 10.0 kg. A horizontal force, FP =40 N, is applied to the 10 kg box.
Find the acceleration of each box
Part a), can treat the 2 blocks as a SYSTEM since they move together.
FTs are internal forces, forces between the parts of the system. Internal forces always cancel out. Fp
No friction FT FT
m1 =
10kg
m2 = 12kg

67. Example: Boxes connected by a cord
2 Boxes are connected by a lightweight cord and are resting on a table. The boxes have masses 12.0 and 10.0 kg. A horizontal force, FP =40 N, is applied to the 10 kg box.
b) Find the tension in the cord
ax = 1.82 m/s2
FT = 21.8 N
Partb ): Make a Free Body Diagram for each mass
Free Body Diagram
for m2
Free Body Diagram
for m1 FT Fp
No friction. Consider each box by itself. Cord is light so neglect its mass. Fp exerts force on m1 which exerts a force on connecting cord. Cord exerts reaction force back.
CORD IS massless therefore F=ma – no net force on cord and forces pulling at cord on its 2 ends must add to zero.
If the cord remains taut and doesn’t stretch, then both boxes have same acceleration
Discuss system and internal forces FT

68. Example: Inclined Plane
A skier has just begun descending a 300 slope. Assuming the coefficient of kinetic friction is 0.10
Draw the free body diagram
Find the skier’s acceleration
Find the speed the skier will reach after 4 s. FN fk Fg
300

69. Example: Inclined Plane
300 fk FN
600
300
Fgy Fg
Fgx

70. The advantage of a pulley
Muscleman is trying to lift a piano up to a second story apartment. He is using a rope over 2 pulleys. How much of the piano’s 2000N weight does he have to pull on the rope? FT FT FT

71. Example: to push or pull a sled
Your little sister wants a ride on her sled. If you are on flat ground, will you exert less force if you push her or pull her (assume the same angle )
PULL
Fpush fk
Pushing y-component adds force to the weight so that the normal force must be greater than the weight of the sled to balance it. Since friction prop to N, more friction with push
Fpull fk

72. ATWOOD MACHINE
Two masses, m1 and m2, hang from the ends of a rope that passes over a small frictionless pulley. The system is released from rest and m2 > m1.
a. Draw a free-body diagram for each object showing all applied forces. Next to each diagram show the direction of the acceleration of that object.
b. Find the acceleration of each mass.
c. What is the tension force in the rope? . m2 m1 72

73. .
Free Body Diagrams T a a m1 m2
Fg=m2g T
Fg=m1g 73

74. Measure g in S17 a kg
g = 157a a
Measure experimentally with meter stick and timer kg 74

75. ATWOOD MACHINE
A 12 kg load hangs from one end of an Atwood machine and a 15 kg counterweight is suspended from the other end. The system is released from rest.
a. What distance does the 12 kg load move in the first 3 s?
What is the velocity of 15 kg mass at the end of 5 s? .
15 kg
12 kg 75

76. DO NOW
A 0.5 kg block lies on a horizontal tabletop. The coefficient of kinetic friction between the block and the surface is The block is connected by a massless string to a second, 0.3 kg block. The string passes over a light frictionless pulley as shown above. The system is released from rest.
a. Draw clearly labeled free-body diagrams for each of the masses. Include all forces. Draw the expected direction of acceleration next to each free-body diagram.
b. Find the acceleration of the blocks
c. What is the tension force in the string?
d. If the yellow, 0.3 kg block is 2 m above the floor, how long will it take to hit the floor?
0.5 kg
0.3 kg

77. To Solve by treating each block independently
(+)
Free Body Diagrams a
0.5 kg fk a
(+)
To Solve by treating each block independently
0.3 kg
0.5 kg
0.3 kg
Ignore mass of pulley and cord and friction in the pulley which means we can assume that a force applied to one end of the cord is the same magnitude at other end. Acceleration in both boxes same since cord doesn’t stretch
a = 2.14 m/s2
T = 2.3 N

78. fk a a a = 2.14 m/s2 T = 2.3 N To Solve as a SYSTEM For the SYSTEM
T is an internal force (for the entire system, T’s cancel out) a
0.5 kg fk a
0.3 kg
a = 2.14 m/s2
T = 2.3 N

79. Apparent weight
If you were standing on a scale in an elevator, at what times in the motion of the elevator do you feel the scale would show your expected weight, Fg?
at what times in the motion of the elevator do you feel the scale would show a value greater than your expected weight so that your apparent weight is greater than your expected weight when you are at rest?
at what times in the motion of the elevator do you feel the scale would show a value less than your expected weight so that your apparent weight is less than your expected weight when you are at rest?

80. DO NOW a v Apparent weight has increased by ma
A person stands on a bathroom scale in a motionless elevator. When the elevator begins to accelerate upwards, draw the FBD of the person in the elevator. If the person weighs 500N at rest, what does the scale read when the elevator accelerates up at 2.5 m/s2? Did the person’s weight really change? If the person drops an apple in the accelerating elevator, would it take the same amount of time to reach the floor as an apple dropped outside the elevator? a v
Apparent weight
has increased by ma

81. a v Apparent weight has decreased by ma
Now the ascending elevator slows down at a rate of 1.5m/s2 as it reaches its destination. If the person weighs 500N at rest, what does the scale read (what is the apparent weight) as the ascending elevator slows down? Did the person’s weight really change? a v
Apparent weight
has decreased by ma
In general, apparent weight , FN is
FN = mg ± ma

82. What would happen if the elevator cable were cut and the elevator went into free fall? If you were standing on a scale, what would your weight as read by the scale be?
In general, apparent weight , FN is
FN = mg ± ma a
Apparent weight Is 0!!!!! v

83. DO NOW A 51 kg person stands on a bathroom scale in an elevator descending at constant velocity. Draw the FBD of the person in the elevator. What does the scale read?
When the elevator begins to slow down with an acceleration of m/s2 as it approaches its floor, what does the scale read? Did the person’s weight really change? By what % did the person’s weight change? If the person drops an apple in the accelerating elevator, would it take the same amount of time to reach the floor as an apple dropped outside the elevator?
500 N
627.5 N (25% gain)
faster (a = 12.5m/s2) a v

84. DO NOW
A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.65 of the person’s weight. Calculate the acceleration of the elevator, and find the direction of acceleration. a v
(elevator is accelerating down)

85. Rank from greatest to least Apparent weight
ay= +2m/s2 v A
ay= +2m/s2 v B
ay= -2m/s2 v C
ay= -5m/s2 v D
ay= -9.8m/s2 v E
ay= +5m/s2 v F
F > A=B > C >D > E

86. Fp f Example - A 4.0 kg brick is sitting on a table.
The coefficient of static friction between the surfaces is If a 10 N horizontal force is applied to the brick, what will be the force of friction? Will the brick move?
When the pulling force is increased to 40 N, the block accelerates at 6 m/s2. What is the coefficient of kinetic friction?
Free Body Diagram Fp f
The brick will not move

87. Fp fk Example - A 4.0 kg brick is sitting on a table.
When the pulling force is increased to 40 N, the block accelerates at 6 m/s2. What is the coefficient of kinetic friction?
Free Body Diagram Fp fk

88. Fp fs Example - A 4.0 kg brick is sitting on a table.
The coefficient of static friction between the surfaces is 0.45 and the coefficient of kinetic friction is If a horizontal force is applied to the brick, how much force is necessary to just get the block moving?
What is the acceleration of the block? a)
Free Body Diagram Fp fs b)

89. A 1800 kg elevator moves up and down on a cable
A 1800 kg elevator moves up and down on a cable. Calculate the tension force in the cable for the following cases:
a) the elevator moves at a constant speed upward.
b) the elevator moves at a constant speed downward.
c) the elevator accelerates upward at a rate of 2.4 m/s2.
d) the elevator accelerates downward at a rate of 2.4 m/s2.