Kinematics and Dynamics Activities For Eighth Grade Science

Summary:

Students will use STELLA software to build simple kinematics and dynamics models which then use to answer problems. This activity assumes no prior knowledge of STELLA.

Acknowledgements:

The eighth grade science department at Colville Junior High School (CJHS) would like to thank Susan Ragan* from the Maryland Virtual High School (MVHS) for her support and generous supply of curriculum materials. Susan and other MVHS staff developed the high school physics curriculum materials to be used with STELLA. These materials were then modified by CJHS staff for the activities in this document.

Kent Roberts

Colville Junior High School

990 South Cedar Street

Colville, WA 99114

TEL: 509-684-7820, ext 5004

e-mail: kroberts@colsd.org

*Susan Regan can be reached at the following address:

Maryland Virtual High School

51 University Blvd. East

Silver Spring, MD 20901

TEL: 301-649-2880

e-mail: sragan@mvhs1.mbhs.edu

Table of Contents

Topic Page No.

Kinematics and Dynamics: Overview, Skills Required, & EALRs 3

Stella Model: Constant Velocity 4

Stella Model: Acceleration 8

Stella Model: Free Fall 12

Stella Model: Newton’s Laws of Motion 16

Appendix 20

Stella Model: Constant Velocity Answers 21

Stella Model: Acceleration Answers 23

Stella Model: Free Fall Answers 25

Stella Model: Newton’s Laws of Motion 26

Assessment for Stella Modeling of Kinematics & Dynamics 30

Assessment Answers 35

Scoring Rubric for Assessments 37

Links to Sites for STELLA Modeling 39
Kinematics and Dynamics: Overview, Skills Required, & EALRs

Overview:

Students will translate their experience with simple kinematics (linear motion & free fall) into a computer model. Students will change variables and analyze how these changes affect an object’s motion.

In dynamics students perform experiments to discover Newton’s first and second laws of motion. Using previously constructed models students examine graphs to determine relationships between force, mass, and acceleration.

Prior Knowledge/Skills Required:

Prior to engaging in the modeling activities, students should have performed one or more simple linear motion activities. This is an introduction to STELLA, so they do not require any prior knowledge of this software. They should have been introduced to the basic motion equations (velocity and acceleration). In addition, they should be aware of the graphs that result from constant velocity and constant acceleration of motion. Students should also understand the physical relevance of the slope and y-intercept and what it means if the slope is negative on a distance-time or velocity-time graph.

Applicable State of Washington Essential Academic Learning Requirements (EALRS) for Science:

1. Describe the positions, relative speeds, and changes in speed of objects.

2. Know the factors that determine the strength of various forces.

3. Identify questions that can be answered through scientific investigations.

4. Design, conduct, and evaluate scientific investigations, using appropriate equipment,

mathematics, and safety procedures.

5. Use evidence from scientific investigations to think critically and logically to develop

descriptions, explanations, and predictions.

6. Correlate models of the behavior of objects, events, or processes to the behavior of the

actual things under investigation; test models by predicting and observing actual

behaviors or processes.

Name________________________

Period_____

Stella Model: Constant Velocity

Double click on the STELLA icon. When the full screen appears, click on the icon of the world once. It should change to an . The top bar looks like this:

This is the source of the icons we will use to build our model. First click on the icon that looks like this : . This is known as a stock. Now slide your pointer out into the open field and click again. A large stock should appear with the word Noname 1 highlighted. Before doing anything else, type the word Distance.

Now click on the icon which looks like this: . This is a flow. Slide your pointer to a position some distance to the left of the stock, click and drag until the arrow just touches the stock and the stock becomes shaded. Let go of the mouse button. Type the word Rate of Change of Distance. Your diagram should look like this:

To get rid of the question marks, double-click on the Distance stock. When that window opens, enter 0 (that’s a zero) and click on OK. Next double-click on the Rate of Change of Distance flow. When that window opens, enter 7 and click on OK.

What about units? In physics, all values should be accompanied by units. STELLA can work with any system of units, so the 0 above could be zero feet or zero meters. Likewise, the 7 could be 7 feet per sec, or 7 meters per sec or 7 miles per hour. Unfortunately, STELLA cannot do the math if the numbers have units behind them. There are two ways we can deal with this. We can remember what units we are using or we can put the units in brackets (like this {}), for example 7 {m/s}. Add units to your numbers.

Now go back to the menu bar and click on the graph icon, which looks like this: . Slide your mouse pointer to a clear spot in the window and click again. A small graph icon should appear and immediately be replaced by a large gray graph. Double-click anywhere in this graph and a new window will open. In the top center of this window, you will see two boxes which look like the two on the next page:

Click on the word Distance, then click on the >> symbol. Repeat for Rate_of_Change_of_Distance. The boxes would now look like this:

Click on OK.

You should be back at Graph 1, with the word Distance in red at the top and Rate of Change of Distance in blue. From the top menu, Click and hold on the word Run, then without letting go of the mouse button, slide down to Run on the menu and click on it. Two lines should form on the graph.

1. Sketch the graph on the axes below. Identify which line is Distance and Rate of

Change of Distance.

Note that there are two scales on the y-axis, one for Distance and one for Rate_of_Change_of_Distance. Lock the graph by clicking on the padlock in the lower left-hand corner of the graph window.

2. Explain why the graph appears as it does.

_____________________________________________________________________

Close the graph window by clicking in the square in the upper left-hand corner. Bring a second graph icon to a clear spot in the window and double-click to open it. Select Distance and Rate_of_Change_of_Distance as the items to graph. To set the scale on Graph 2 to be the same as the scale on Graph 1, highlight Distance, click on the double-headed arrow to the right of the Selected box, and set Min to 0 and Max to 90 and press Set. Highlight Rate_of_Change_of_Distance, click on the double-headed arrow to the right, set Min to 0 and Max to 14 and press Set. Click OK.

3. In the Distance stock, change the initial distance to 5. Run the model and

double-click on Graph 2.

a. Sketch the graph on the axes below.

b. Describe the appearance of the graph and explain what is happening to Distance

and Rate_of_Change_of_Distance.

_____________________________________________________________________

4. In the Distance stock, change the initial velocity to 0 and change the

Rate_of_Change_of_Distance flow value to 3. Run the model and double-click on

Graph 2.

a. Sketch the graph on the axes below.

b. Describe the appearance of each graph and explain what is happening to

Distance and Rate_of_Change_of_Distance.

_____________________________________________________________________

Experiment with changing the Distance value in the stock and the Rate of Change of Distance value in the flow. Change one or both values in each experiment.

Name______________________________

Period_______

Stella Model: Acceleration

Part I.

Open the file Constant Acceleration Model. The model should look like this:

Double-click on the Rate of Change of Distance icon, and when the window opens, Velocity should have been selected from the Required Inputs box. Click OK. Double-click on the Velocity stock and type the number 0 and OK. Double-click on the Rate of Change of Velocity icon and Acceleration should have been selected from the Required Inputs box. Click OK. The circular icon, Acceleration, is known as a converter. Double-click on the Acceleration converter and the number 3 should be typed in the Required Inputs box.

1. In the Constant Velocity STELLA Model, the Rate of Change of Distance was

equal to a constant (7). Why can we now equate Rate of Change of Distance with Velocity?

_____________________________________________________________________

Double-click on the Graph 1 icon. Distance, Velocity, and Acceleration have been

selected and the scales have been set. Run the model.

2. a. Sketch the graph and identify which line is Distance, Velocity, and Acceleration.

b. Describe the appearance of the lines for Distance, Velocity, and Acceleration.

_____________________________________________________________________

3. In the Velocity stock, change the initial velocity to 5. Run the model and

double-click on Graph 1. Describe the appearance of the graph and explain what is

happening to Distance and Velocity.

_____________________________________________________________________

4. In the Velocity stock, change the initial velocity to 0 and change the Acceleration

converter value to 5. Run the model and double-click on Graph 1. Describe the

appearance of each graph and explain what is happening to Distance, Velocity, and

Acceleration.

_____________________________________________________________________

Part II: Extensions

Experiment with changing the acceleration values (Acceleration converter), initial velocity (Velocity stock) and the initial distance (Distance stock). Remember to use appropriate testing procedures: change one variable at a time. For the moment, keep all values positive.

5. What were the effects on the graphs when you changed each of these variables?

_____________________________________________________________________

6. Predict the effect of having a negative acceleration. What will all the graphs look like

if the initial distance and velocity start at zero? Sketch your answer on the graph

below.

To check your prediction, make the following changes in the model. Double-click on the Distance stock and in the upper left corner of the dialog box, click in the Non-negative box so that it is blank (no X). Click OK. Repeat this for the Velocity stock. This allows both of these variables to go negative. Now double-click on the Rate of Change of Distance flow and in the upper left corner of that dialog box, click in the BIFLOW bullet. Click OK. Repeat for the Rate of Change of Velocity flow. This allows the flows to add or subtract amounts from the stock. Now change the value in the Acceleration converter to a negative number (try -3).

Click on Graph 2 and the dialogue box should open. In the Selected box, highlight Distance and in the Scale box change Min to -250 and Max to 50 and click on Set. Highlight Velocity and set Min to -40 and Max to 0. Finally, highlight Acceleration and set Min to -4 and Max to -2.

Run the model. Click on Graph 2 and observe.

7. Sketch and explain the appearance of the graph.

_____________________________________________________________________

STELLA can be used to model a car accelerating, traveling at constant velocity and then decelerating. Double-click on the Acceleration converter. Type the following in place of the negative value you just used above:

If (Time < 3) then 5 else if (time > 9) then -5 else 0

This statement says, that if time is less than 3 seconds, the car will accelerate at 5, it will stop accelerating at all between 3 and 9 seconds and then at 9 seconds, it will decelerate at the rate of -5.

Run the model. Click on Graph 3 and observe the results.

8. Describe the graph created by the model.

_____________________________________________________________________

Name______________________________

Period_______

Stella Model: Free Fall

Part I.

Open the file Free Fall Model. The model should look like this:

1. Sketch what you think the graphs of Height and Velocity will look like when an object

is dropped from a height of 100 m.

Run the model and sketch the graphs below.

3. a. Close Graph 1, open Table 1 and examine the data. At about what time does the

object hit the ground?

Answer_________seconds

b. Using the equation d = 0.5at2 where d is distance, a is acceleration due to

gravity, and t is the time, find the time it takes for the object to fall 100 meters

on Earth. How does your calculated answer compare to the answer in a?

Answer_________seconds

__________________________________________________________________

c. What happens to the height after the object passes the zero mark (i.e., hits the

ground)?

____________________________________________________________________

4. Close the Free Fall Model and open Free Fall Model.Hits Ground. You should see

a model that looks like this:

This model has been modified so the object’s fall will stop at ground level. Notice in the previous model that it kept gathering data even after the object hit the ground. To fix this problem, STELLA uses the pause feature. Pause is a command that tells the model to stop running. You are going to tell the program to stop running when the object hits the ground.

A new converter, called “Hits Ground”, has been added near the Height stock. The Height stock is connected (using a connector) to the Hits Ground converter. Double-click on Hits Ground and you will see the following statement:

If (Height < 0.5) then pause else 0

This statement means that the model will stop running when the height becomes smaller than 0.5 (or close to zero). This will make the model stop when the object has almost touched the ground. We say ‘almost’ because computer models can only approximate the real world. The height will never be exactly equal to zero because of the way that computers make calculations.

5. Run the model and examine the graphs. Close Graph 1 and open Table 1. When

does the object hit the ground?

Answer____________seconds

From the very top menu, click and hold at the word Run, slide down to the word

Stop and then click on it.

6. The acceleration due to gravity on the Moon is 1/6th that of Earth, 1.6 m/s2. We can

compare the effects of gravity on a falling object on the Moon and Earth using this

model.

Double-click on the converter Acceleration due to gravity and change the

-9.8 {m/s^2} to -1.6 {m/s^2}. Close the converter. From the very top menu, click

and hold on the word Run, slide down to the word Time Specs on the menu and then

click on it. In Length of simulation change the 5 to 12 and click OK.

Run the model and examine the graphs. Close Graph 1 and open Table 1. When

does the object hit the ground?

Answer____________seconds

From the very top menu, click and hold at the word Run, slide down to the word

Stop and then click on it. Reset the acceleration for Earth (-9.8 {m/s^2}) in the

converter Acceleration due to gravity and save it.

7. Compare how gravity affects the fall of an object on the Earth and the Moon

_____________________________________________________________________

Name______________________________

Period_______

Stella Model: Newton’s Laws of Motion

Part I.

Open the file Newton’s Laws of Motion. The model should look like this:

Open the Distance stock and make sure the initial distance is set to 0 {m}; and, then open the Velocity stock and make sure the initial velocity is set to 0 {m/s}. Double-click on the Acceleration converter. The following formula should be in the converter:

Net_Force/Mass.

1. Double-click on the Net Force converter and set a value of 10 {N}; set Mass to

2 {kg}. Make sure you have a graph which shows Distance, Velocity, and

Acceleration. Then run the model and observe the graph. Sketch the graphs below

and explain why they appear the way they do.