1. Equilibrium Forces and Unbalanced Forces

2. A force is a push or a pull applied to an object.
Topic Overview
A force is a push or a pull applied to an object.
A net Force (Fnet) is the sum of all the forces on an object (direction determines + or -)
Fnet = 6N to the right

3. Isaac Newton has 3 laws that describe the motion of object
1st Law: Law of inertia
An object at rest will stay at rest unless acted on by an outside force
Inertia: The amount of mass an object has
More inertia = more mass = Harder to move

4. When an object is in equilibrium, the net force equals zero
Topic Overview
When an object is in equilibrium, the net force equals zero
Equilibrium  Fnet = 0
Objects in equilibrium can either be at rest or be moving with constant velocity
Up = Down Forces
Left = Right Forces

5. 3rd Law: Equal and Opposite
For every action, there is an equal and opposite reaction.
“Things push back”

6. Topic Overview
When an object has unbalanced forces acting on it, the object will accelerate in the direction of that excess force:
Fnet = ma
This is called “Newton's Second Law”

7. Example Problem – Balanced Forces

8. Example Problem – Balanced Forces Solution

9. Example Problem – Unbalanced Forces

10. Example Problem – Unbalanced Forces - Solution

11. Make sure you know if the object is in equilibrium or not
Common Mistakes
Make sure you know if the object is in equilibrium or not

12. Circular Motion

13. Topic Overview
An object in circular motion has a changing velocity but constant speed.
This is possible because the objects speed does not change (same m/s) but the direction of its motion does change

14. The circular force (Fc ) is always directed toward the center
Topic Overview
The velocity of the object is always “tangent” to the path of the object.
The circular force (Fc ) is always directed toward the center
The acceleration is always toward the center of the circle
Velocity
Force

15. r is the radius of the circle
Equations
r is the radius of the circle

16. Example Problem

17. Example Problem - Solution

18. Be sure to square the velocity Cross multiply when solving for “r”
Common Mistakes
Be sure to square the velocity
Cross multiply when solving for “r”

19. Momentum/Impulse

20. Momentum: The product of the mass and velocity of an object
Momentum Recap
Momentum: The product of the mass and velocity of an object
Equation: p = mv
Units: p = kilograms meters per second
(kgm/s)
Momentum is a vector: When describing the momentum of an object, the direction matters.

21. Momentum Before = Momentum After
Momentum Recap
Collision: When 2 or more objects interact they can transfer momentum to each other.
Conservation of Momentum: The sum of the total momentum BEFORE a collision, is the same as the sum of the total momentum AFTER a collision
Momentum Before = Momentum After
p1i +p2i + p3i = p1f+p2f + p3f

22. To Solve Collision Problems:
Momentum Recap
To Solve Collision Problems:
Step 1: Find the total momentum of each object before they interact
Step 2: Set it equal to the total momentum after they collide
Remember momentum is a vector, so you have to consider if the momentum is (+) or(-) when finding the total!!!
Initial = Final
= (v) + (1.8)(2)
Initial = Final
(1)(6) = ( ) v

23. Fnett = p = mv Units = Ns
Impulse
An outside force will cause a change in the momentum of an object. This is called an impulse.
IMPULSE: A change in momentum
Fnett = p = mv
Units = Ns

24. Impulse
To find the impulse under a force vs. time graph, you would find the area under the line.
I = Ft

25. Example Problem - 1

26. Example Problem 1- Solution

27. Kinematics

28. Kinematics is what we use to describe the motion of an object.
Topic Overview
Kinematics is what we use to describe the motion of an object.
We use terms such as displacement, distance, velocity, speed, acceleration, and time to describe the movement of objects.

29. Distance (m): The total meters covered by an object (odometer)
Topic Overview
Distance (m): The total meters covered by an object (odometer)
Displacement (m): The difference between the start and end points.

30. How fast the car is moving is a (+) and (–) indicate direction
Topic Overview
Velocity (m/s):
How fast the car is moving is a
(+) and (–) indicate direction
Acceleration (m/s2)
Acceleration is a change in velocity
If an object is accelerating, it is either speeding up or slowing down

31. x = vt x = vavet Some objects have constant velocity
Topic Overview
Some objects have constant velocity
Again this means that acceleration = 0
The equation for constant velocity is:
x = vt
If you are given an average velocity (vave), it is the same thing as constant velocity:
x = vavet

32. a = (vf-vi) / t x = vit + ½ at2 vf2 = vi2 + 2ax
Topic Overview
Some objects have constant acceleration
This means they are speeding up or slowing down
The equations for constant acceleration:
a = (vf-vi) / t
x = vit + ½ at2
vf2 = vi2 + 2ax

33. If an object is “at rest” Velocity = 0
Topic Overview
To solve problems with constant acceleration, make a table! Vi
Initial velocity Vf
Final velocity a
Acceleration x
Distance t
time
Reminder:
If an object is “at rest” Velocity = 0

34. All falling objects accelerate at 9.8m/s2 due to gravity
Topic Overview
One example of a “constant acceleration problem” is a falling object (an object traveling through the air)
All falling objects accelerate at 9.8m/s2 due to gravity
They also start with
Zero initial velocity Vi
0m/s Vf a
9.8m/s2 x t

35. In this case, choose the equation that does not have vf
Example Problem
A stone is dropped from a bridge approximately 45 meters above the surface of a river.  Approximately how many seconds does the stone take to reach the water's surface?
Reminder:
Choose the equation that does not have the “blocked off” variable.
In this case, choose the equation that does not have vf Vi
0m/s Vf a
9.8m/s2 x 45 t ?
a = (vf-vi) / t
x = vit + ½ at2
vf2 = vi2 + 2ax

36. Example Problem - Solution

37. Graphs

38. 1) Displacement vs. Time graphs
Topic Overview
The motion of an object can be represented by three types of graphs (x, v, a)
1) Displacement vs. Time graphs
Tells you where the object is
The slope (steepness) is the velocity
In the graph above A is faster than B A X
(m)
Time (s) B

39. 1) Types of Motion for x vs. t graphs
Topic Overview
1) Types of Motion for x vs. t graphs X
(m)
Time (s) X
(m)
Time (s) X
(m)
Time (s)
Not moving because the position does not change
Constant velocity because the slope does not change (linear)
Accelerating because it is a curve

40. 2) Velocity vs Time graphs
Topic Overview
2) Velocity vs Time graphs
Tells you how fast the object is moving
Slope of the line = Acceleration
Area under curve = Displacement v
(m/s)
(s)

41. 2) Velocity vs. Time graphs
Topic Overview
2) Velocity vs. Time graphs v
(m/s)
(s) v
(m/s)
(s) v
(m/s)
(s)
Constant speed because the value for velocity does not change
Speeding up because the value of the velocity is moving away from zero
Slowing down because the value of the velocity is moving toward zero

42. Tells you the acceleration of the object Area under curve = Velocity
Topic Overview
3) Acceleration vs. time
Tells you the acceleration of the object
Area under curve = Velocity a
(m/s2)
(s)

43. 3) Acceleration vs. Time graphs
Topic Overview
3) Acceleration vs. Time graphs a
(m/s2) a
(m/s2) a
(m/s2)
(s)
(s)
(s)
No acceleration. This means the object has a constant speed
This object has positive acceleration
This object has negative acceleration

44. Example Question-2

45. Example Question-2 Solution

46. Calculation Examples:

47. Example Question-1 Displacement: Difference between y value
Average Speed: Slope between 2 time points
Instantaneous speed: Slope at 1 time point (TANGENT)

48. Example Question-1 Solution

49. What is the average speed from
Example Question-2
What is the average speed from
0-6 seconds?

50. Example Question-2 Solution
What is the average speed from
0-6 seconds?
Average is the slope between 2 points
Slope = (4 – 0) = 0.66m/s
(6 – 0)

51. What is the displacement from 1-4 seconds?
Example Question-3
What is the displacement from 1-4 seconds?

52. Example Question-3 Solution
Position increased (+) from 2m to 4m
Answer:
4 – 2 = 2m

53. Projectile Motion

54. Topic Overview
Objects that travel in both the horizontal and vertical direction are called “projectiles”. These problems involve cars rolling off cliffs, objects flying through the air, and other things like that.

55. An object traveling through the air will:
Topic Overview
An object traveling through the air will:
ACCELERATE in the VERTICAL DIRECTION
Because it is pulled down by gravity
Have CONSTANT VELOCITY in the HORIZONTAL
Because there is no gravity
Because they are different, we do calculations in the horizontal (x) and vertical (y)_ SEPARATELY.

56. Zero Launch Angle Projectile Motion
Acceleration
-9.8m/s2
VelocityHorizontal
Constant
VelocityVertical
Increasing
The time for an object to fall is determined by drop height ONLY
(horizontal velocity has no effect)

57. x = vt a = (vf-vi) / t x = vit + ½ at2 vf2 = vi2 + 2ax
Projectile Motion
The key to solving projectile motion problems is to solve the horizontal and vertical parts SEPARATELY.
Horizontal
Constant Velocity
x = vt
Vertical
Accelerating
a = (vf-vi) / t
x = vit + ½ at2
vf2 = vi2 + 2ax
Time is the only thing that is the same!
TIME = TIME

58. Example 1
A bullet is shot at 200m/s from a rifle that is 2.5m above the ground. How far downrange will the bullet reach before hitting the ground?
Step 2: Use the time to find out the distance in the other direction (in this case the horizontal direction)
Step 1: Find the time.
In this case we have to use the vertical height to find the time. (acceleration) vi vf a
-9.8 x
2.5 t ??
x = vit + ½ at2
x = vt
x = 200 (0.72)
x = 150m
t = 0.72s

59. Energy and Power

60. Kinetic Energy: VELOCITY Potential Energy: HEIGHT
Energy is the ability to CHANGE an object. These types of energy are a result of a CHANGE in…….
Work: FORCE
Kinetic Energy: VELOCITY
Potential Energy: HEIGHT
Elastic Energy: SHAPE

61. Conservation of Energy
In a system, the TOTAL
MECHANICAL ENERGY never changes
Energy can switch forms, but it cannot be created or destroyed.
WORK
POTENTIAL
KINETIC
ELASTIC

62. Conservation of Energy
Mathematically speaking that looks like this
TME Initial = TME Final
KE + PE + EE + W = KE + PE + EE + W

63. Energy: Joules (J) Work: W = Fd Kinetic Energy: KE = ½mv2 Potential Energy: PE = mgh Elastic Energy: EE = ½kx2

64. Potential Energy  Kinetic Energy
Examples
A ball is dropped from a height of 12m, what is the velocity of the ball when it hits the ground?
Potential Energy  Kinetic Energy
Since all of the energy is transferred, we cans set them equal to each other
PE = KE
m(9.8)(12) = ½(m)v  mass cancels
15.33 m/s = v

65. Potential Energy  Kinetic Energy
Examples
A ball is dropped from a height of 12m, what is the velocity of the ball when it hits the ground?
Potential Energy  Kinetic Energy
Since all of the energy is transferred, we can set them equal to each other
PE = KE
m(9.8)(12) = ½(m)v  mass cancels
15.33 m/s = v

66. Examples
A force of 50N pushes horizontally on a 5kg object for a distance of 2m. What is the final velocity of the object?
Work  Kinetic Energy
Since all of the energy is transferred, we can set them equal to each other
Work = KE
(50)(2) = ½(5)v2
6.32 m/s = v

67. TME Initial = TME Final Examples
No matter type of energy transfer, the set up is the same. Even if there is more than one type of energy present
TME Initial = TME Final
KE + PE + EE + W = KE + PE + EE + W

68. P = E/t Power = Energy/ time
On your equation sheet it lists “Energy” as Work for the top of the fraction. But you can put any type of energy on the top part of this equation.

69. Regular Physics ONLY: Electrostatics

70. Atoms have protons, neutron, and electrons.
Electrostatics:
Atoms have protons, neutron, and electrons.
Only electrons can move!
1 e- = 1.6E-19 Coulomb (C)

71. Electrostatics:
An object becomes charged when its electrons are shifted or transferred
Extra electrons = (-)
Fewer electrons = (+)

72. Electrostatics:
How many more electrons than protons are there on an object with a E-18 C charge?
What is the total charge of an object with a deficiency of 4.0 x108 electrons?
Extra electrons = (-)
Fewer electrons = (+)

73. Two charged objects will have an Electric Field between them.
Electrostatics:
Two charged objects will have an Electric Field between them.
Field Lines (+) (-)“Start Positive” 

74. Two charged objects will feel an Electric Force
Electrostatics:
Two charged objects will feel an Electric Force
Opposite charges attract (+/-)
Same charges repel (+/+) (-/-)

75. Calculating the Electric Force
Electrostatics:
Calculating the Electric Force
k = 9E9
q=charge
r= distance between the charges

76. Calculating the Electric Force
Electrostatics:
Calculating the Electric Force
k = 9E9
What is the magnitude of the electrostatic force between two electrons separated by a distance of 1.00 × 10–8 meter?

77. Regular Physics ONLY: Circuits

78. Circuits:
A circuit provides a COMPLETE path for electrons to move.
The flow of electrons is called the current (I).
Electrons flow because a voltage (V) provides an energy difference
In order to get energy out of a circuit, there has to be resistors (R).

79. Circuits:

80. Series Circuits Circuits:
A circuit in which there is only one current path

81. I = I1 = I2 = I3 = I4 V = V1 + V2 + V3 RT= R1 + R2 + R3 Series Circuit
Circuits:
Series Circuit
Current is the same in all resistors
I = I1 = I2 = I3 = I4
Voltage is distributed among the resistors
V = V1 + V2 + V3
Total Resistance is the sum of all resistors.
RT= R1 + R2 + R3

82. Parallel Circuits Circuits:
A circuit in which there are several current paths

83. Circuits:
Series or Parallel?????

84. VT = V1 = V2 = V3 IT = I1 + I2 + I3 Parallel Circuit
Circuits:
Parallel Circuit
Current is the added in all resistors
IT = I1 + I2 + I3
Voltage is equal among the resistors
VT = V1 = V2 = V3
Total Resistance is the reciprocal of all resistors.3
1/RT = 1/R1 + 1/R2 + 1/R3

85. Circuits:
RIVP TABLES!!!

86. AP ONLY: Torque

87. Units for torque: Nm (Newton-meters)
Torque Introduction
torque = distance from axis of rotation x force x sin (angle between r and F)
Units for torque: Nm (Newton-meters)

88. Torque Torque Introduction Torque is analogous to a force.
Force Torque
Linear Acceleration Angular Acceleration
Torque

89. Torque Introduction
The “distance” of the force also matters.
Lever Arm (r): The distance between the pivot point and the force.

90. The “angle (θ)” of the force also matters.
Torque Introduction
The “angle (θ)” of the force also matters.
10N
10N

91. The “angle” of the force also matters.
Torque Introduction
The “angle” of the force also matters.
Use the sin component of the force
Measure angle from the LEVER ARM  FORCE
10N
10N

92. Torque – Direction and equilibrium
Net Force = Zero  No acceleration
Net Torque = Zero  No rotation
Clockwise = (+) Counterclockwise = (-)
Is the object moving?

93. Ex 1
6kg
10kg
To weigh a fish a person hangs a tackle box of mass 6 kilograms and a cooler of mass 10 kilograms from the ends of a uniform rigid pole that is suspended by a rope attached to its center. The system balances when the fish hangs at a point 1/4 of the rod’s length from the tackle box. What is the mass of the fish?

94. Ex 2
A store sign, with a mass of 20.0kg and 3.00m long, has its center of gravity at the center of the sign. It is supported by a loose bolt attached to the wall at one end and by a wire at the other end. The wire makes an angle of 25° with the horizontal. What is the tension in the wire?

95. AP ONLY: Oscillations

96. Simple Harmonic Motion (SHM)
Oscillation:
Simple Harmonic Motion (SHM)
An object that “cycles” between having maximum kinetic and maximum potential energy.

97. Simple Harmonic Motion (SHM) - Notes
This cycle will look like a sine or cosine wave
The graph will look like this for displacement, potential energy, and kinetic energy as a function of time (It will just be shifted) 1 2 3 4

98. Simple Harmonic Motion (SHM)
Determine these for our system:
Amplitude = Maximum displacement from equilibrium
Period (T) = Time for 1 complete motion
Seconds per cycle
Units = seconds
Frequency = cycles per second
Inverse of period
Units = s-1 or Hertz (Hz)

99. Equations

100. Position Function for cosine – Class example
If the object represented in the graph experiences a maximum displacement of 0.50m and completes a cycle in 2.0s, what is an appropriate expression for displacement as a function of time?

101. Position Function for cosine - Example
A 0.50kg object on a spring (k=494) undergoes Simple Harmonic Motion. Its motion can be described by the following equation
x = (0.3 m) cos (10π t)
What is the amplitude of the vibration?
What is the period of the vibration?
What is the frequency?
What is the maximum elastic PE?
What is the maximum velocity?

102. AP ONLY: Gravitation

103. The force of gravity depends on 2 things: The mass of the two objects.
Gravitation
The force of gravity depends on 2 things:
The mass of the two objects.
The distance between them.

104. Gravitation - Example
Mars has a mass 1/10 that of Earth and a diameter 1/2 that of Earth. The acceleration of a falling body near the surface of Mars is most nearly

105. Satellites Satellites in orbit are in centripetal motion.
Fc is provided by the gravitational force.
Combining Newton’s Law of Gravitation with the formula for centripetal force, we find:
Rearrange for speed of satellite:
Note that the mass of the satellite does not matter!

106. Example
How long would it take a satellite to orbit the Mars if it were a distance of 6.79 x 106m from the center of the planet?

107. The force of gravity depends on 2 things: The mass of the two objects.
Gravitation
The force of gravity depends on 2 things:
The mass of the two objects.
The distance between them.

108. Gravitation - Example
Mars has a mass 1/10 that of Earth and a diameter 1/2 that of Earth. The acceleration of a falling body near the surface of Mars is most nearly

109. Satellites Satellites in orbit are in centripetal motion.
Fc is provided by the gravitational force.
Combining Newton’s Law of Gravitation with the formula for centripetal force, we find:
Rearrange for speed of satellite:
Note that the mass of the satellite does not matter!

110. Example
How long would it take a satellite to orbit the Mars if it were a distance of 6.79 x 106m from the center of the planet?