Math Sci 9 Unit: Physics/Kinematics
Rationale for order of topics
· Students must fully understand acceleration before studying Newton’s Laws
· Center of gravity is a useful concept in understanding the forces on and motion of irregularly shaped objects
· Students must have time and opportunity to explore the normal force before understanding Newton’s Laws
Center of Gravity
Monday April 7th: 90 minutes
Vocabulary:
Center of Gravity, Plumb bob, Center of Mass
Skills:
· Find COG by hanging
· Find COG with coordinates and mathematical formula
· Find COG from rotation point when object is a projectile
Materials: Scissors, cardboard, graph paper, paper clips, push pins, string, masses
Activity: see Center of Gravity Lab sheet
Motion: Velocity and Acceleration
Tuesday April 8th: 90 minutes
Vocabulary
Definition of velocity: xf-xi/t or change in position over change in time
Definition of acceleration: vf-vi/t or change in velocity over change in time
Average velocity x = ½(vi+vf)t
Instantaneous velocity
Skills
· Identify objects which are accelerating and which are not (through examples)
· Understand the importance of correctly identifying the difference
· Use equations to solve basic problems
· Graph distance vs. time for a moving object/Understand time as an “invisible” dimension
· Interpret distance vs. time graph for a moving object
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Materials: Tape to make number lines, objects to move along number lines, CBL’s/Motion Detectors
Homework – Assignment 1
Wednesday April 9th: 100 minutes
Vocabulary
Definition of velocity: xf-xi/t or change in position over change in time
Definition of average velocity
Definition of acceleration: vf-vi/t or change in velocity over change in time
Skills
· Use equations to solve basic problems (given xi, t and v, find xf)
· Graph velocity vs. time for a moving object
· Interpret velocity vs. time graph for a moving object
· Translate between v vs. t and d vs t graph
Homework Assignment 2 ( practice problems: calculations and graphing problems)
Thursday April 10th: 100 minutes
Skills
· Use new equation x = 1/2at2 to solve more complex problems (given a, t, solve for x)
Lab: Estimate the acceleration of gravity
Materials: tennis balls, stopwatches, tape measure
1. Students stand on chairs or tables.
2. Students drop ball, time how long it take to hit the ground.
3. From x and t, students calculate average velocity
4. Assuming vi=0, students calculate acceleration
5. Collect data from each student, and take class average. Should be approximately 10 m/s2
6. Discuss sources of error
7. Discuss why all objects fall at same rate. Gravity pulls more on a heavy object, but it takes more force to make a heavy object move. Consequently, all objects experience the same acceleration. Demonstrate with a penny and a heavy ball.
Lecture: Combining equations used in the activity to create a quadratic.
For situations where vi = 0 (falling objects), show how to algebraically combine x = ½(vi + vf)t and a = (vf - vi)/t to make x = 1/2at2.
Homework – Assignment 3 use new equation and a = 9.81 m/s2 to solve problems about falling objects.
Friday April 11: 100 minutes
Whiteboard answers to Assignment 3
Reaction Time Lab
Materials: meter sticks
One person drops meterstick without warning. Second person tries to catch it. From distance stick falls, determine reaction time (student must know a = 10 m/s2 in order to solve. They must have already derived x= 1/2at2).
Students write up Reaction Time Lab independently. Required components:
Name:
Title: Reaction Time Lab
Purpose: to determine my reaction time without using a stopwatch
Hypothesis: My reaction time will be:
Materials: Meterstick
Procedure: One person drops meterstick without warning. Second person tries to catch it.
Data: xi = __________ xf = ___________ Δx = ____________
Calculation: Calculate Δt
Conclusion: Compute Percent error
Give reason for percent error
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Monday April 21
Falling Objects Lab
Skills
· Students will learn to set up and use photogate and CBL equipment
· Students will accurately collect data and compute the acceleration of gravity using x = 1/2at2
See Power point presentations for Warm-up activities and lab information
Tuesday April 22:
Split Block Schedule
First half: wrap up lab
Second half: review for quiz – see quiz review
Wednesday April 23
Questions on Quiz Review (about 20 minutes)
Kinematics Quiz (about 30 minutes)
Begin Forces Unit
Whiteboarding Part I
Question posed to students:
What are the forces on a book sitting on a table?
What are the forces on a book hanging from a spring scale (stationary)
What are the forces on a book being held up by someone’s hands?
How are these situations alike? How are they different?
Students whiteboard diagrams in groups and share answers with whole class.
Introduction of rules about force diagrams – relative lengths of arrows represent relative strength of forces.
Thursday April 24
Lecture:
mass vs. weight
Newtons as the SI unit of weight
Converting mass to weight
The NORMAL force
Whiteboarding Part II
Question posed to students:
What are the forces on an object being lifted by a spring scale at a constant velocity
Students whiteboard diagrams in groups and share answers with whole class.
Question posed to students:
What are the forces on an object being lifted by a spring scale at that is accelerating
Students whiteboard diagrams in groups and share answers with whole class.
Question posed to students:
Here I have a book on a table. Is the book moving?
How do I know that something is moving? Can I tell if I am moving at a constant velocity?
Discuss the concept of relative velocity.
Summary Lecture:
Newton understood that the critical difference is not between moving and not moving but between accelerating and not accelerating.
This idea is expressed in his three laws.
1. For objects at rest or moving at constant velocity, every force has an equal an opposite force
2. Objects that experience an unbalanced force will accelerate according to F = ma
3. Objects at rest will remain at rest. Objects in motion will remain in motion at a constant velocity unless acted upon by an unbalanced force.
Homework: Practice Problems