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Physics for Scientists and
Engineers |
Principles of Physics |
Conceptual Physics |
Virtual Physics Labs |
| (COMPETENCY
GOAL 1 is listed at the end of this document, since it does not address
physics content.) |
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| COMPETENCY
GOAL 2: The learner will build an understanding of linear motion. |
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| Objective |
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| 2.01 Analyze velocity as a rate of change of position: |
2.3 - 2.5 |
2.3 - 2.5 |
2.3 - 2.5 |
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| •
Average velocity. |
2.4 |
2.4 |
2.4 |
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| •
Instantaneous velocity. |
2.5 |
2.5 |
2.5 |
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| Content
Description |
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| Identify
a frame of reference for measurement of position and identify the initial
position of the object. |
2.1 |
2.1 |
2.1 |
·Skee-Ball |
| Develop the definition of velocity as the rate of change of
position conceptually, mathematically and graphically (see 2.04). |
2.3 - 2.8,
2.13 - 2.14 |
2.3 - 2.8
|
2.3 - 2.7
|
·Skee-Ball |
Apply the equation developed to several applications where
objects are moving with constant velocity:
v = Δx/Δt
xf
= xi + vt |
2.3 - 2.8 |
2.3 - 2.8 |
2.3 - 2.7 |
·Skee-Ball |
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| Objective |
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| 2.02 Compare and contrast as scalar and vector quantities: |
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Speed and velocity. |
2.3 |
2.3 |
2.3 |
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Distance and displacement. |
2.2 |
2.2 |
2.2 |
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| Content
Description |
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| Define
vector and scalar, incorporating
magnitude and direction. |
3.1 - 3.2 |
3.1 - 3.2 |
3.1 - 3.2 |
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| Apply concepts of speed and velocity to solve conceptual and
quantitative problems. |
2.37, 4.29 |
2.33, 4.27 |
2.23 |
·Skee-Ball |
| Distinguish between distance and displacement conceptually
and mathematically. |
2.2 |
2.2 |
2.2 |
·Skee-Ball |
| Clarify that a positive value for velocity indicates motion in
one direction while a negative value indicates motion in the opposite
direction. |
2.2 - 2.3 |
2.2 - 2.3 |
2.2 - 2.3 |
·Skee-Ball |
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| Objective |
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| 2.03 Analyze acceleration as rate of change in velocity. |
2.10 - 2.12 |
2.10 - 2.12 |
2.8 - 2.10 |
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| Content
Description |
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| Develop
the definition for constant (uniform) acceleration as the rate of change of
velocity conceptually, mathematically, and graphically (see 2.04). |
2.10 - 2.13,
2.16 - 2.18 |
2.10 -
2.12,
2.14 - 2.16 |
2.8 - 2.13 |
·Skee-Ball |
| Analyze visual representations of constant and changing
velocity. (see 2.04) |
2.9, 2.18 |
2.9, 2.16 |
2.13 |
·Skee-Ball |
Use kinematics equations for acceleration:
xf = xi + vt + (1/2)at2
a = Δv/Δt
vf2 = vi2 + 2aΔx |
2.16 - 2.18,
2.20 - 2.25 |
2.14 - 2.16,
2.18 - 2.22 |
2.11 - 2.13,
2.15 - 2.17 |
·Skee-Ball |
| Apply concepts of constant (uniform) acceleration to objects in
free fall. |
2.26 - 2.29 |
2.23 - 2.26 |
2.18 - 2.19 |
·Firing a cannon
·Juggling objects |
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| Objective |
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| 2.04 Using graphical and mathematical tools, design and
conduct investigations of linear motion and the relationships among: |
Chapter 2 |
Chapter 2 |
Chapter 2 |
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Position. |
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Average velocity. |
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Instantaneous velocity |
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Acceleration. |
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Time. |
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| Content
Description |
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| Constant
velocity: |
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| Measure position versus time of an object moving with constant
velocity. |
2.6 - 2.8, 2.15 |
2.6 - 2.8, 2.13 |
2.6 - 2.7 |
·Skee-Ball |
| Plot a position versus time graph of the measurements. |
2.6 - 2.8 |
2.6 - 2.8 |
2.6 - 2.7 |
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| Recognize that the relationship is linear and construct a
best-fit line. |
2.6 - 2.8 |
2.6 - 2.8 |
2.6 - 2.7 |
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| Identify the slope of the line as the change in position over
time (velocity) and the y-intercept as the initial position for the given
time interval. |
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| Using the slope y-intercept equation (y = mx + b) from the
graphs above, derive the mathematical relationships: |
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| final position=average velocity*time + initial position |
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| final position
- initial position=average velocity*time |
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| v = Δx/Δt |
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| Define change in position as displacement and show the average velocity equation (v =
Δx/Δt) |
2.2 - 2.4 |
2.2 - 2.4 |
2.2 - 2.4 |
·Skee-Ball |
| Constant acceleration: |
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| Measure position and time of an object moving with constant
acceleration. |
2.28 |
2.25 |
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·Skee-Ball |
| Plot a position vs. time graph of the measurements. |
2.28 |
2.25 |
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| Recognize that the relationship is not linear but fits the shape
of a parabola indicating that position is proportional to time squared. |
2.28 |
2.25 |
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| At various points on the curve, draw lines tangent to the
curve and develop the concept of instantaneous velocity (represented by the
slope of the tangent line at that time instant). |
2.6 |
2.6 |
2.6 |
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| Give several examples of and compare position vs. time,
velocity vs. time and acceleration vs. time graphs. |
2.6 - 2.9,
2.12 - 2.14 |
2.6 - 2.9,
2.12 |
2.6 - 2.7,
2.10 |
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| Recognize that the slope of the line on an instantaneous
velocity vs. time graph is the acceleration. |
2.12 |
2.12 |
2.10 |
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Develop the equations for objects that are experiencing
constant acceleration (rolling down an inclined plane or objects falling
toward the earth):
xf = xi + vt + (1/2)at2
a = Δv/Δt
vf2 = vi2 + 2aΔx |
2.19 - 2.20,
2.24 |
2.17 - 2.18 |
2.14 - 2.15 |
·Skee-Ball
·Firing a cannon
·Juggling objects |
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| COMPETENCY
GOAL 3: The learner will build an understanding of two-dimensional motion
including circular motion. |
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| Objective |
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| 3.01 Analyze and evaluate projectile motion in a defined frame
of reference. |
4.8 - 4.22 |
4.7 - 4.21 |
4.3 - 4.14 |
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| Content
Description |
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| Resolve
vectors into vertical and horizontal components. |
3.4, 4.1 - 4.6 |
3.4, 4.1 - 4.6 |
3.4, 4.1 - 4.2 |
·Firing a
cannon
·Juggling objects |
| Evaluate the motion of a projectile both horizontally and
vertically. |
4.8 |
4.7 |
4.3 |
·Firing a cannon
·Juggling objects |
| Recognize that the horizontal component of velocity does
not change (neglecting air resistance). |
4.8 |
4.7 |
4.3 |
·Firing a cannon
·Juggling objects |
| Recognize that the vertical component of velocity does
change due to gravity at the rate of 9.8m/s2 downward. |
4.8 |
4.7 |
4.3 |
·Firing a cannon
·Juggling objects |
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| Objective |
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| 3.02
Design and conduct investigations of two-dimensional
motion of objects. |
Chapter 4 |
Chapter 4 |
Chapter 4 |
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| Content
Description |
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| Select
appropriate measurements for an investigation of projectile motion. |
4.15 |
4.14 |
4.10 |
·Firing a
cannon
·Juggling objects |
| Identify factors that may affect results. |
4.15, 4.21 |
4.14, 4.20 |
4.10 |
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| Predict and measure the path of the projectile including
horizontal range, maximum height, and time in flight (such as a projectile
launched horizontally or from the ground at a given angle). |
4.8 - 4.21 |
4.7 - 4.20 |
4.3 - 4.13 |
·Firing a cannon
·Juggling objects |
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| Objective |
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| 3.03 Analyze and evaluate independence of the vector
components of projectile motion. |
4.8 - 4.21 |
4.7 - 4.20 |
4.3 - 4.13 |
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| Content
Description |
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| Recognize
that vector components are independent of each other. |
4.8 |
4.7 |
4.3 |
·Firing a
cannon
·Juggling objects |
| Apply the equations of uniform velocity to the horizontal
component. |
4.8 - 4.21 |
4.7 - 4.20 |
4.3 - 4.13 |
·Firing a cannon
·Juggling objects |
| Apply the equations of accelerated motion to the vertical
component of velocity. |
4.8 - 4.21 |
4.7 - 4.20 |
4.3 - 4.13 |
·Firing a cannon
·Juggling objects |
| Relate height, time in air and initial vertical velocity (such
as a projectile launched horizontally or from the ground at a given angle). |
4.8 - 4.21 |
4.7 - 4.20 |
4.3 - 4.13 |
·Firing a cannon
·Juggling objects |
| Relate range of projectile, time and initial horizontal velocity
(such as a projectile launched horizontally or from the ground at a given
angle). |
4.8 - 4.21 |
4.7 - 4.20 |
4.3 - 4.13 |
·Firing a cannon
·Juggling objects |
| Relate height and time in the air to the initial vertical
velocity |
4.8 - 4.21 |
4.7 - 4.20 |
4.3 - 4.13 |
·Firing a cannon
·Juggling objects |
| Relate range of projectile to time in flight and initial
horizontal velocity |
4.8 - 4.21 |
4.7 - 4.20 |
4.3 - 4.13 |
·Firing a cannon
·Juggling objects |
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| Objective |
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| 3.04 Evaluate, measure, and analyze circular motion. |
Chapter 9 |
Chapter 9 |
Chapter 8 |
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| Content
Description |
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| Recognize
that an object may move with constant speed but changing velocity. |
9.1 |
9.1 |
8.1 |
·Navigating race tracks |
| Recognize that the directions of the velocity and
acceleration vectors are perpendicular to each other. |
9.4 |
9.4 |
8.3 |
·Navigating race tracks |
| Understand that centripetal acceleration is a consequence
of the changing velocity due to change in direction. |
9.4 |
9.4 |
8.3 |
·Navigating race tracks |
| Design
and conduct investigations of circular motion. |
9.0 |
9.0 |
8.0 |
·Navigating race tracks |
| Experimentally verify the proportional relationships described
in 3.06. |
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·Navigating race tracks |
| Combine proportional relationships into a single equation. |
9.4 - 9.5, 9.7 |
9.4, 9.6 |
8.3, 8.5 |
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| Calculate velocity using radius or circumference of the
circle and time to complete one or more circuits. |
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| Calculate centripetal acceleration as the velocity squared
divided by the radius. |
9.4 |
9.4 |
8.3 |
·Navigating race tracks |
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| Objective |
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| 3.05 Analyze and evaluate the nature of centripetal forces. |
9.7 - 9.14 |
9.6 - 9.13 |
8.5 - 8.7 |
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| Content
Description |
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| Evaluate
and understand that a net force is required to change the direction of a
velocity vector. |
9.7 |
9.6 |
8.5 |
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| Understand that for uniform circular motion the net force is
called the centripetal force. |
9.7 |
9.6 |
8.5 |
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| Understand that the centripetal force is not the result of
circular motion but must be provided by an interaction with an external
source. |
9.7 |
9.6 |
8.5 |
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| Evaluate the direction of the force and acceleration vectors as
pointing to the center of the circle in the case of constant speed but not
constant acceleration. |
9.7, 10.17 |
9.6, 10.14 |
8.5 |
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| Objective |
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| 3.06 Investigate, evaluate and analyze the relationship among: |
Chapter 9 |
Chapter 9 |
Chapter 8 |
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Centripetal force. |
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Centripetal acceleration. |
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Mass. |
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Velocity. |
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Radius. |
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| Content
Description |
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| Design
and conduct an investigation of circular motion. |
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·Navigating race tracks |
| Apply the proportional relationship between force and speed
squared when radius is constant. |
9.7 - 9.14 |
9.6 - 9.13 |
8.5 - 8.7 |
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| Apply the inverse relationship between force and radius when
speed is constant. |
9.7 - 9.14 |
9.6 - 9.13 |
8.5 - 8.7 |
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Apply the formula for centripetal force as mass times
centripetal acceleration using the following equations:
ac = v2/r
Fc = mv2/r |
9.7 - 9.14 |
9.6 - 9.13 |
8.5 - 8.7 |
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| COMPETENCY
GOAL 4: The learner will develop an understanding of forces and Newton’s Laws
of Motion. |
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| Objective |
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| 4.01 Determine that an object will continue in its state of
motion unless acted upon by a net outside force (Newton's First Law of
Motion, The Law of Inertia). |
5.2 |
5.2 |
5.2 |
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| Content
Description |
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| Observe
motion and draw force diagrams for objects moving at constant velocity with
very little friction (examples: air
track, air puck, balloon puck, dry ice) |
5.2 |
5.2 |
5.2 |
·Helicopters in flight |
| Identify that the state of motion must be a constant
velocity, including zero velocity, unless acted upon by a net force. |
5.2 |
5.2 |
5.2 |
·Helicopters in flight |
| Define inertia. |
5.2 - 5.3 |
5.2 - 5.3 |
5.2 - 5.3 |
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| Objective |
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| 4.02 Assess, measure and calculate the conditions required to
maintain a body in a state of static equilibrium. |
Chapters 5, 6 and 12 |
Chapters 5, 6 and 12 |
Chapters 5, 6 and 11 |
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| Content
Description |
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| Describe
forces as interactions between two objects, including contact and forces at a
distance. |
5.1 |
5.1 |
5.1 |
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| Recognize that force is a vector quantity. |
5.1 |
5.1 |
5.1 |
·Helicopters in flight |
| Define normal force. |
5.11 |
5.11 |
5.11 |
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| Represent the forces acting on an object using a force diagram. |
5.14 |
5.14 |
5.14 |
·Helicopters in flight |
| Analyze force diagrams to calculate the net force on an object. |
5.14 - 5.17,
Chapters 5 & 6 |
5.14 - 5.17,
Chapters 5 & 6 |
5.14 - 5.15,
Chapter 5 |
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| Determine that the net force acting on an object in static
equilibrium is zero. |
12.1 |
12.1 |
11.1 |
·Helicopters in flight |
| Design and conduct investigations of objects in static
equilibrium. (Torque and rotational equilibrium are
enrichment topics.) |
Chapters 6 & 12 |
Chapters 6 & 12 |
Chapter 11 |
·Helicopters in flight |
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| Objective |
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| 4.03 Assess, measure, and calculate the relationship among the
force acting on a body, the mass of the body, and the nature of the
acceleration produced (Newton's Second Law of Motion). |
5.5 - 5.9 |
5.5 - 5.9 |
5.5 - 5.9 |
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| Content
Description |
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| Design
and conduct investigations of force and acceleration. |
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·Helicopters in flight |
| Experimentally verify the proportional relationships among
acceleration, force and mass. |
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·Helicopters in flight |
| Apply proportional reasoning to the relationship between
force and acceleration when mass is constant. |
Chapters 5 & 6 |
Chapters 5 & 6 |
Chapter 5 |
·Helicopters in flight |
| Apply proportional reasoning to the inverse relationship
between mass and acceleration when force is constant. |
Chapters 5 & 6 |
Chapters 5 & 6 |
Chapter 5 |
·Helicopters in flight |
| Analyze force diagrams for accelerating objects. (solve for
mass, acceleration, various forces) |
Chapters 5 & 6 |
Chapters 5 & 6 |
Chapter 5 |
·Helicopters in flight |
| Calculate the net force on an object: Fnet = ma |
Chapters 5 & 6 |
Chapters 5 & 6 |
Chapter 5 |
·Helicopters in flight |
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| Objective |
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| 4.04 Analyze and mathematically describe forces as
interactions between bodies (Newton's Third Law of Motion). |
5.10 |
5.10 |
5.10 |
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| Content
Description |
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| Identify
interaction pairs of forces for contact forces and forces at a distance. |
5.10 - 5.13 |
5.10 - 5.13 |
5.10 - 5.13 |
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Analyze Newton’s Third Law as the relationship evidenced
by
Force of Object A on Object B = –Force of Object B
on Object A |
5.10 |
5.10 |
5.10 |
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| Observe and experimentally measure equal and opposite
forces using pairs of spring scales or force sensors. |
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| Objective |
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| 4.05 Assess the independence of the vector components of
forces. |
Chapters 5 & 6 |
Chapters 5 & 6 |
Chapter 5 |
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| Content
Description |
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| Resolve
forces into components. |
5.23 -
5.27,
Chapter 6 |
5.23 -
5.27,
Chapter 6 |
5.21 - 5.22 |
·Helicopters in flight |
| Apply Newton’s Laws of Motion to the perpendicular
components of force in the following examples: |
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| a. objects pulled or pushed along a horizontal surface by a
force at an angle to the surface; |
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| b. objects sliding down an inclined plane; |
5.25, 5.27, 6.7 |
5.25, 5.27, 6.7 |
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| c. three concurrent forces acting on an object in static
equilibrium. |
6.1, 6.2 |
6.1, 6.2 |
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| Objective |
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| 4.06 Investigate, measure, and analyze the nature and
magnitude of frictional forces. |
5.18 - 5.20 |
5.18 - 5.20 |
5.16 - 5.18 |
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| Content
Description |
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| Describe
friction as a contact force. |
5.18 |
5.18 |
5.16 |
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| Distinguish between static friction and kinetic friction. |
5.18 - 5.20 |
5.18 - 5.20 |
5.16 - 5.18 |
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| Solve quantitative problems with frictional forces. (coefficient of friction is an enrichment topic) |
5.18 - 5.22,
5.24, 6.7 |
5.18 - 5.22,
5.24, 6.7 |
5.16 - 5.18,
5.22 |
·Navigating race tracks
·Electric golf |
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| Objective |
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| 4.07 Assess and calculate the nature and magnitude of
gravitational forces (Newton's Law of Universal Gravitation). |
13.1 |
13.1 |
12.1 |
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| Content
Description |
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Calculate
gravitational force between any two masses:
F = Gm1m2/d2 |
13.1 |
13.1 |
12.1 |
·Orbiting
satellites |
| Apply proportional reasoning to the inverse square relationship
between gravitational force and the distance between the centers of two known
masses. |
13.1 |
13.1 |
12.1 |
·Orbiting satellites |
| Apply proportional reasoning to the direct relationship
between gravitational force and the product of masses. |
13.1 |
13.1 |
12.1 |
·Orbiting satellites |
Determine the force of gravity (weight) of an object:
F = mg |
5.4 |
5.4 |
5.4 |
·Helicopters in flight |
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| COMPETENCY
GOAL 5: The learner will build an understanding of impulse and momentum. |
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| Objective |
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| 5.01 Assess the vector nature of momentum and its relation to
the mass and velocity of an object. |
8.1 |
8.1 |
7.1 |
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| Content
Description |
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| Define
momentum. |
8.1 |
8.1 |
7.1 |
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| Identify that momentum is a vector quantity because velocity is
a vector quantity. |
8.1 |
8.1 |
7.1 |
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| Recognize that momentum is proportional to mass and proportional
to velocity. |
8.1 |
8.1 |
7.1 |
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| Apply the momentum equation: p = mv |
8.1 |
8.1 |
7.1 |
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| Objective |
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| 5.02 Compare and contrast impulse and momentum. |
8.1 - 8.6 |
8.1 - 8.5 |
7.1 - 7.4 |
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| Content
Description |
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| Define
impulse. |
8.3 - 8.4 |
8.3 |
7.3 |
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| State that impulse is equal to change in momentum: FΔt = Δp = mΔv |
8.3 - 8.4 |
8.3 |
7.3 |
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| Recognize that the change in momentum of an object is
proportional to the force applied to the object and to the time the force is
applied to the object. |
8.3 - 8.4 |
8.3 |
7.3 |
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| Objective |
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| 5.03 Analyze the factors required to produce a change in
momentum. |
8.1 - 8.6 |
8.1 - 8.5 |
7.1 - 7.4 |
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| Content
Description |
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| Distinguish between impulse
and force. |
8.3 |
8.3 |
7.3 |
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| Determine the change in momentum of an object by finding
the area under the “curve” on a force vs. time graph. |
8.3 - 8.6 |
8.3 - 8.5 |
7.3 - 7.4 |
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| Show that the larger the mass of an object, the smaller the
change in velocity of an object for a given impulse. |
8.3 |
8.3 |
7.3 |
|
Apply the impulse equation in various situations:
FΔt = Δp = mΔv |
8.3 - 8.6 |
8.3 - 8.5 |
7.3 - 7.4 |
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| Objective |
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| 5.04 Analyze one-dimensional interactions between objects and
recognize that the total momentum is conserved in both collision and recoil
situations. |
Chapter 8 |
Chapter 8 |
Chapter 7 |
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| Content
Description |
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| Verify
that the total momentum before an interaction is equal to the total momentum
after an interaction as long as there are no outside forces. |
8.0 |
8.0 |
7.0 |
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| Solve problems using conservation of momentum in the following
instances: |
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| two objects initially at rest push each other apart; |
8.9 |
8.8 |
7.7 |
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| a moving object collides with a stationary object and the
two objects stick together; |
8.20 - 8.21 |
8.18 - 8.19 |
7.13 |
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| a moving object collides with a stationary object and the
two objects move off separately; |
8.12 - 8.19 |
8.11 - 8.17 |
7.9 - 7.12 |
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| two moving objects collide and either stick together or move off
separately. |
8.12 - 8.21,
8.29 |
8.11 - 8.19,
8.24 |
7.9 - 7.13,
7.16 |
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| Design and conduct investigations verifying the
conservation of momentum in the four situations listed above. |
8.29 |
8.24 |
7.16 |
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| Identify the special case of an elastic collision (recoil) where
the objects do not stick together and both momentum and kinetic energy are conserved. |
8.11 - 8.19, 8.29 |
8.10 - 8.17,
8.24 |
7.8 - 7.12,
7.16 |
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| Objective |
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| 5.05 Assess real world applications of the impulse and
momentum, including but not limited to, sports and transportation. |
Chapter 8 |
Chapter 8 |
Chapter 7 |
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| Content
Description |
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| Use
examples, such as baseball and golf, to explain that “follow through” is a
strategy for increasing the impulse on the ball. |
8.3 |
8.3 |
7.3 |
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| Solve collision problems. (Momentum is conserved - assume the
system is limited to the colliding objects. Example: car crash.) |
8.9 - 8.21 |
8.8 - 8.19 |
7.7 - 7.13 |
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| Recognize elastic collisions: |
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