Motion and Design: an STC kitBruce Palmquist, CWU, palmquis@cwu.edu

M&D-related National StandardsAbilities necessary to do scientific inquiry

◦Plan and conduct investigationsPosition and motion of objects

◦Describe changes in positions of objects using the concepts of displacement, velocity, and acceleration

◦Represent motion on a graph Motion and forces

◦Define forces◦Apply the concept of forces to motion and changes

in motionIf you have a question, write it on a post-it

note and stick it to the question wall.

Workshop outlinePart 1: Describing Motion

◦Constant motion activity◦Speeding up motion activity◦Graph analysis computer simulation (if time)

Part 2: Forces and Motion◦ Introduction to forces◦“Deriving” Newton’s 2nd Law of Motion◦Ramp: Forces and Motion (computer)

Part 3: Energy◦Types of mechanical energy◦Mini-hovercraft activity◦Conservation of mechanical energy

Material at http://cwuphys106.pbworks.com/◦Click ESD 105 folder in the Navigator box on the right

Learning Objectives◦Describe the motion of a fan cart using words,

graphs, and “oil drop” diagrams. ◦Translate between a verbal description, a

graph, or an “oil drop” diagram of motion.Engage: Page Keeley Assessment ProbeExplore: Describing constant motionExplain: Fan cart lab activityElaborate: Name that motion (if time)Evaluate: Translating motion descriptions

Part 1: Describing Motion

From Uncovering Student Ideas in Physical Science by Page Keeley and Rand Harrington, page 23-30

Engage: What do you think?

From Uncovering Student Ideas in Physical Science by Page Keeley and Rand Harrington, page 23-30

Engage: What do you think?• Take 1

minute to answer on your own.

• Compare answers with partners for about 1 minute. Come up with a group answer to the graphing question.

• Share your group’s answer with the class.

Given whatever tools you have or can find around you, determine the velocity of your car.

Is the velocity constant? How do you know? Devise a method to test if the velocity is constant.

Summarize your method and results in a short paragraph on the provided note card.

We know the velocity is constant if equally sized displacements are travelled in equal time intervals.

The smaller the duration measured, the more accurate our proclamation that the velocity is constant.

Explore: Describing Constant Motion

Explore: Constant velocity GraphThe car moves equal

intervals in equal amounts of time.

Car is not speeding up or slowing down (or changing direction).

Graph is a straight line. See example.

How do we know the car is not speeding up or slowing down between data points?

Now you will get a car that speeds up. Please be careful of the propeller. It can pinch your finger.

You will also get a tape timer, a device that puts a mark on a paper every 0.1 s or 0.025 s.

Attach about 2 meters of tape to the back of your cart.

Make a data table with about 10 position and corresponding time values.

Use Excel to make a position vs. time graph for your car. Excel worksheet template at http://goo.gl/1SvRV

When you are done with your spreadsheet and graph, give the file a creative name and email it to me at dbp1920@yahoo.com.

Explain: Fan Cart Activity

Explain: Graphing motionTime (s) Position

(cm)Velocity (cm/s)

0 0 00.1 1.5

(compared to the zero point)

15

0.2 3.5(compared to the zero point)

20

0.3 6.0 25

To make a position vs time graph, plot time along the x-axis and position along the y-axis.

Determine the best fit curve using Excel (either linear or polynomial)

Email to dbp1920@yahoo.com

Excel template:http://goo.gl/1SvRV

Sample data

Explain: Increasing velocity

The car moves increasing distances in equal amounts of time.

Graph is a upward curve.

How do we know the car is not constant or slowing down between data points?

Compare different cars.

Sample Position vs. time graph

What does each parameter represent here?

Here y is position, x is time, 8.1279 is 1/2a, 22.288 is initial velocity and 0.8107 is initial position.

0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140

160

f(x) = 8.1279072707048 x² + 22.287649155627 x + 0.8106671554252R² = 0.999929612637343

Motion of a Fan Cart

Time (s)

Posi

tion

(cm

)

The slope of a position vs. time graph is the velocity.

If the velocity is changing, the slope at each point represents the velocity at that point.

The slope of a velocity vs. time graph is the acceleration.

Definition of acceleration:Acceleration = change in velocity/change in time

a=∆v/ ∆tThe more the velocity changes for a set time

interval, the greater the acceleration.Acceleration can be positive or negative

Explain: Acceleration

Explain: Ticker Tape diagramsDescribe the motion of the object that made each of these tapes. Justify your answer.

Explain: Ticker Tape diagramsLet’s practice this more.

Constant velocity

High acceleration Low acceleration

(If time and technology permits)Open the Name that Motion

simulationWork in your groups. Just enter one

name on the screen but fill out your own answer sheet.

View each motion. Type the number of the description on the worksheet that matches the motion.

Elaborate: Describing complex 1-D motion

Screen shot of Name that Motion simulation

From Uncovering Student Ideas in Physical Science by Page Keeley and Rand Harrington, page 31-34

Evaluate: Analyzing a graphTake one minute to

answer on your own.Talk to your partners

for about two minutes and compare answers. On the back of your sheet, write your group answer and explanation.

Share your group’s answer with the class.

Bill has confused the position vs. time graph with a picture of the path of motion. He needs help understanding what a position vs. time graph tells him.

Patti seems to understand that a steeper line means faster and less steep line means slower. But she does not adequately describe the meaning of the flat line.

Kari has the best answer. She seems to understand that a flat line on a position vs. time graph means no change in position, an object that is not moving.

Mort has confused the position vs. time graph with a picture of the path of motion. He needs help understanding what a position vs. time graph tells him.

Evaluate: What understanding does each answer indicate

Part 2: Forces and MotionIntroduction to forces“Deriving” Newton’s 2nd Law of

MotionForces in 1-Dimension activity

(computer)

Learning ObjectivesSketch the main forces acting on an

object.Name the main forces acting on an

object using the official naming rules.Sketch and name the major forces

acting on a rolling ball.Use Newton's second law of motion

to solve for an unknown.

Naming forcesDevelop a definition of a force.A force is a push or pull that changes

the motion of an object.Bruce’s rule for naming forces: “The

(blank) push/pull of the (blank) on the (blank)”

Typical forces in k-12 science: gravitational, contact, elastic, friction, tension, electric and magnetic

A force is a vector meaning it has magnitude and direction

ForcesThe contact push of the table on the book.

The gravitational pull of the Earth on the book.

ForcesNow I’ll give a

book a push. Sketch a diagram of all of the forces acting on the book well after the push but before the book stops.

Go over Net Force Help Sheet

The frictional push of the table on the book

Rolling ball motionSketch and name the forces for

the ball◦Rolling uphill◦Rolling on a flat surface◦Rolling downhill

In which of these situations are the forces balanced? Unbalanced?

Rolling ball motionUphill

Flat

Downhill

What do you notice about the uphill and downhill diagrams?

Newton’s Laws of MotionFrom his study of the work of Galileo

and Kepler, Newton extracted three laws that relate the motion of a body to the forces acting on it.

Deriving Newton’s 2nd LawMaterials: low friction cart, kitchen

scale, long hall, 1 “pusher”, 3 “riders”The pusher will push each rider

individually down the hall with the same force (same reading on the scale).

The rest of the class will note how the motion of each rider differs.

The rest of the class will also make sure the pusher keeps the same force reading on the scale the entire time.

Results of Newton’s 2nd Law demoForce Size of rider Rate of speeding

up

•Another word for “rate of speeding up” is acceleration.•Conclusions?•For a constant force, as the size of the rider (m) decreased, the acceleration (a) increased.•m α 1/a (mass is inversely related to acceleration) •A more familiar way to write this is FNet = ma•Practice using newton’s 2nd Law

Newton’s 2nd law of MotionWork on Forces in 1-Dimension at

http://phet.colorado.edu/en/simulation/forces-1d or http://goo.gl/ijN0Q

What happened as the person pushed harder on the cabinet before it moved?

The friction force grew as the applied force grew.What happened to the friction force once the cabinet

started to move?It got smaller.What happened to the cabinet as the applied force was

continually exerted on the cabinet?It accelerated.Review homework

1. If the total force acts in the same direction as the crate is sliding, the crate

A. slows downB. speeds up C. remains at same speed D. slows down, changes direction and

then speeds up going the other way

E. remains at same speed, but changes direction

Crate was moving to the right

Then, the guy pushed the crate

2. If the total force acts in the opposite direction as the cabinet is sliding, the cabinet would A. slow downB. speed up C. remain at same speed D. slow down, change direction and

then speed up going the other way

E. remain at same speed, but change direction

Cabinet was moving to the left

Then, the guy pushed the cabinet

3. If there is zero total force acting on on the refrigerator, the refrigerator would A. slow downB. speed up C. remain at same speed D. slow down, change direction and

then speed up going the other way E. remain at same speed, but change

direction

Refrigerator was moving to the right

Then, the guy pushed the refrigerator

FrictionPair up. You’ll need

a pusher and a sitter.

Push the sitter’s chair lightly. What do you notice?

Push harder but not hard enough to move? What do you notice?

Once sitter starts to move, what did you notice about the “feel” of your push?

Part 3: EnergyTypes of mechanical energyMini-hovercraft activityConservation of mechanical

energy

Learning objectivesUse the definitions of Work, KE,

PE, and TME to solve for an unknown

Given a scenario, determine whether KE, PE or TME increases, decreases or stays the same.

Work = F*d*cosqScenario 1: Maximum

positive work done, typically means an increase in kinetic (motion) energy

Scenario 2: Maximum negative work done, typically means an decrease in kinetic (motion) energy

Scenario 3: No work done, no change in kinetic (motion) energy

WorkWhich path requires the least energy to get

to the top of the hill?A D, the straight steep path (2)B D, the winding path (5)C D, the straight non-steep path (15)All equal (7)Pick an answer and justify using the

concept of workWatch

Mechanical energyThere are two main types of mechanical energyMotion energy, also called kinetic energyKE = ½ mv2

◦m=mass of the object, v = velocityGravitational potential energyPE = mgh where h = height of the object above

the “ground”

Work and energyAs the skier goes down the hill, how do

KE, PE, work, and TME (total mechanical energy) change? Is there a relationship?

Work and energyAs the skier goes downhill, KE + PE = TME.On the packed snow, PE = 0 and KE = TME.TME is a constant when no work is being

done by friction.On the unpacked snow, KE goes down as

friction due to snow does negative work on the skier.

Let’s practice mechanical energy concepts

Energy and frictionless pucksUse the wooden ramp, plastic puck, rubber stopper

and balloon for the following.Determine the speed of each mass puck at the

bottom of the ramp without using a stop watch. Use formulas for PE and KE. Assume no frictional force.

Determine the relationship between the angle of a ramp and the speed of a frictionless puck near the bottom of the ramp. Before starting the activity, write a hypothesis and share it with the instructor. Sketch a speed vs. angle graph in your notebook. Extra challenge: derive a formula that shows the relationship.

Discuss.

Challenge solutionPE at top = KE

at bottommgh = ½ mv2

gh = ½ v2

gLsinq = ½ v2

2gLsinq = v2

(2gLsinq)½ = v

hL

q

Sinq = h/Lh=L sinq

Teacher applicationHow can you use what you learned today

to enhance your own instruction of the Motion and Design unit?◦Pick a specific activity you did or concept you

heard about today◦Decide where it would support your teaching of

the Motion and Design unit or some other topic◦Briefly describe how you will use this activity

or concept.◦Think about this by yourself or with your school

team for about five minutes. Then share with another group.

Online Resources used todayOnline physics resource including tutorials,

simulations, and worksheets.◦ I took my worksheets and notes from here.◦http://www.physicsclassroom.com/

Detailed simulations for teaching physics and other science concepts◦My force “lab” activity is found here. Many other

simulations for upper elementary through college students.

◦http://phet.colorado.edu/Website for my CWU Physics by Inquiry course

◦My CWU physics course for pre-service elementary and middle school teachers. Today’s notes found here.

◦http://cwuphys106.pbworks.com/