Download Unit 6 Curvilinear Motion Particle Models

Physics
Curvilinear Motion Models
Unit 6
What are the descriptive models of curvilinear motion and how are they used?
What are the causal models of curvilinear motion and how are they used?
Unit Essential Questions
What are the graphical models and the mathematical models that are used to represent
and analyze the behavior of an object moving along a curvilinear path?
What is the motion of a projectile?
What is the relationship between an object’s velocity and the central net force needed to
keep the object’s path curved?
What is the relationship between an object’s mass and the central net force needed to
keep the object’s path curved?
What is the relationship between the curve radius and the central net force needed to keep
an object’s path curved?
New Enduring Understandings
A. The translational motion of an object following a curved path can be mathematically
separated into an x-motion and a y-motion that occur simultaneously.
B. The vertical motion of a freefalling projectile object is identical to the vertical motion
of a freefalling object moving only in the vertical direction.
C. The x-motion of a projectile object is independent of the y-motion of that projectile
object.
D. Following a curved path requires a net force on the object that is not directed along
the path.
E. Following a circular path requires a net force on the object that is directed toward the
path’s center of curvature.
F. Noncircular curved paths can be approximated as circular paths.
G. The net force needed to keep a constant speed object’s path circular is directly
proportional to the object’s mass.
H. The net force needed to keep a constant speed object’s path circular is directly
proportional to the object’s velocity squared.
I. The net force needed to keep a constant speed object’s path circular is inversely
proportional to the path radius.
J. The net force needed to keep a constant speed object’s path circular is exactly equal
to the product of the object’s mass and squared speed divided by the path radius.
K. The centripetal net force is just a special case of a net force.
L. An accurate analysis of motion and forces requires a careful consideration of
reference frames.
M. Human sensations and perceptions of the net force are often opposite in direction
from reality.
Edington 5/31/05 Unit 6 Curvilinear Objectives v5.doc
Physics
Curvilinear Motion Models
Unit 6
N. Isaac Newton recognized that the same force that causes objects to fall toward Earth
cause astronomical objects to orbit.
O. An orbiting object is a special case of a freefalling projectile.
P. Graphical models and mathematical models are used to represent, analyze, and
communicate structure and relationships in physical systems and physical
interactions.
Q. A relatively small number of models can be used with great versatility for a wide
variety of physical systems and physical interactions.
Performance Objectives
1. You should be able to use video analysis techniques to produce position vs. time
graphs and velocity vs. time graphs for an object moving in two dimensions.
2. Given an object undergoing parabolic motion, you should be able to draw a twodimensional motion map.
3. Given an object undergoing parabolic motion, you should be able to draw a force
diagram for the object.
4. You should be able to determine which model (zero net force or constant net force) is
appropriate to describe the object’s horizontal motion and to describe the object’s
vertical motion.
5. Given information about the initial velocity and height of a projectile, you should be
able to determine the object’s time of flight, the object’s landing position, and the
object’s impact velocity.
6. You should be able to explain the effect of object mass on the path of a projectile, and
the effect of air resistance on the path of a projectile.
7. For a given location on a curved path, you should be able to approximate the path
with a circular path.
8. Given an object traveling on a circular path, you should be able to draw a motion map
and a force diagram.
9. You should be able to state the relationships between linear path velocity, path radius,
object mass, and centripetal net force for an object following a circular path. Given
three, you should be able to calculate the fourth.
10. You should be able to state the relationships between linear path velocity, path radius,
and centripetal acceleration for an object following a circular path. Given two, you
should be able to calculate the third.
11. You should be able to use all of these and your prior knowledge, skills, and
understandings to represent, analyze, and communicate structure and relationships in
physical systems and physical interactions
Edington 5/31/05 Unit 6 Curvilinear Objectives v5.doc
Physics
Curvilinear Motion Models
Unit 6
New Math Concepts
Parametric equations, vector resultants, inverse square relationship, hat variables, unit
vectors, inflection points, linear velocity, rotational velocity
New Technology Skills
Digital video analysis, constructing a physics simulation using a physics simulation
software toolkit
New Terms and Symbols
r̂
ay
centrifuge
circular motion
critical velocity
Fc
horizontal circular motion
modeling software
parabolic motion
path velocity
r
simulation software
velocity components
vy
ac
central net force
centripetal acceleration
computational algorithms
curvilinear motion
Fcnet
inflection point
muzzle velocity
parametric equations
projectile
range
trajectory
vertical circular motion
Edington 5/31/05 Unit 6 Curvilinear Objectives v5.doc
ax
centrifugal force
centripetal force
coreolis force
digital video analysis
frame of reference
linear velocity
orbits
path radius
projectile motion
rotational velocity
unit vector
vx