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Content Area: Physics (11-12)
Topic: Two-Dimensional Motion
Sub-Topic: Projectiles
Computer requirements: Vensim, STELLA, Interactive
Physics or Excel
Prior content covered: Linear velocity and
acceleration, free fall
Estimated time for computer portion of lesson:
30 - 45 min
Essential Questions or Ideas to address:
- Independent nature of the x and y components of projectile
motion
- How do the horizontal and vertical velocity vectors change
as the object moves through its path?
- In the case of no horizontal forces, what is the direction
of the acceleration acting on the projectile?
The lesson (90-min block): Students build or
use a Vensim or STELLATM model, Excel spreadsheet or an Interactive Physics
simulation to investigate projectile motion. The structure of the Projectile Motion systems model
illustrates the
independent nature of the vector quantities. On the other
hand, Interactive Physics allows the students to see the vectors as the
object progresses through its trajectory. Students can use any of
the models to determine the best angle for maximum distance.
For an example of a Vensim/STELLATM model and companion activities see the
Projectile Motion Activity Packet.
Common misconceptions addressed:
- The acceleration follows the flight path.
- The vertical motion "affects" the horizontal motion and
vice versa.
Evaluation of lesson effectiveness: While
building a projectile model can be time consuming, having the students
use a pre-built model is valuable. Student understanding of the
nature of the vectors involved and their chance to manipulate the
variables in meaningful ways leads to deeper conceptual understanding
of projectile motion.
Alternate presentation:
There are many applets available on the web. For web applets which show the vectors, look under
two-dimensional motion at The Physics Classroom.
Other web applets can be found at Projectile Motion WebSim or
http://www.walter-fendt.de/ph11e/projectile.htm
Math topics: Linear and quadratic equations,
graph interpretation for those equations, vectors and vector addition
Standards:
MSDE (from the website as of 9/05):
| Physics/Core Learning Goals |
| Science Indicator 5.1.2 |
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The student will use algebraic and geometric concepts to
describe an object's motion.
Assessment Limits
direction, position, distance/displacement,
speed/velocity, motion with a constant acceleration, one and two
dimensional motion, frames of reference
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Goal 5 Concepts Of Physics
The student will demonstrate the ability to use scientific skills and
processes (Core Learning Goal 1) to explain and predict the outcome of
certain interactions which occur between matter and energy.
Expectation 5.1
The student will know and apply the laws of mechanics to explain the
behavior of the physical world.
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The
standards do not directly address kinematics, but an understanding of
motion is necessary before students can address the standards as they
appear here.
National Science Standards:
Physical Science: Motion and Forces:
Objects change their motion only when a net force is applied. Laws of
motion are used to calculate precisely the effects of forces on the
motion of objects. The magnitude of the change in motion can be
calculated using the relationship F = ma, which is independent of the
nature of the force. Whenever one object exerts a force on
another, a force equal in magnitude and opposite in direction is
exerted on the first object.
AAAS Benchmarks:
The Physical Setting: Forces of
Nature:
- The change in motion of an object is is proportional to
the applied force and inversely proportional to the mass.
- All motion is relative to whatever frame of reference is
chosen, for there is no motionless frame from which to judge all motion.
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