Content Teaching Academy 2014James Madison UniversityIntermediate Physics-Graduate Credit

Lesson Plan 2

Lesson Plan

Teacher Name: Ms. Kristen RoscoeUnit: 6-Two Dimensional MotionLesson Title: Motion Analysis with Logger Pro

Skills/Instructional Goals:A projectile moves both horizontally and vertically, and, in the absence of air resistance, traces out a parabolic path.The horizontal and vertical motions of a projectile are completely independent of one another.

a. In the absence of air resistance, there is no net horizontal force on the projectile; therefore the projectile travels with a constant horizontal velocity.

b. In the absence of air resistance, gravity is the only vertical force on the projectile; therefore the projectile travels with a uniformly accelerated vertical motion. Every second, the vertical velocity of the projectile changes by -10 m/s.The motion map for a projectile is best drawn with horizontal and vertical component vectors of the velocity. The horizontal spacing of the motion map dots is uniform and the horizontal velocity vectors are equal in length. The vertical spacing of the motion map dots and the length of the vertical velocity vectors will increase or decrease as the object's vertical speed increases or decreases due to gravitational acceleration.

Virginia Standards of Learning:

PH.5 The student will investigate and understand the interrelationships among mass, distance, force, and time through mathematical and experimental processes. Key concepts includea) linear motion;b) uniform circular motion;c) projectile motion;d) Newton’s laws of motion;e) gravitation;f) planetary motion; andg) work, power, and energy.

Objectives: SWBATUse motion analysis software to depict the motion of an object moving in a parabola. Define projectileDefine projectile motionAnalyze the effects of gravity on a projectile

Evaluation: Lab, Whiteboards, and Worksheet 1

Materials:COW’s (Matilda)LoggerPro SoftwareVideo

WhiteboardsMarkersErasersWorksheet 1SMART Board

Procedures:Video Analysis with LoggerPro: The students will be performing an introductory lab exercise analyzing projectile motion of a basketball. The students will use a pre-made video of a person shooting a basketball into the air. Lab Performance Notes:

o Have students launch Logger Pro; from the command bar choose Insert ► Movie which will enable them to navigate to the Sample Movies folder where they can choose the Basketball shot movie.

o Have students follow the instructions in "Motion Analysis with Logger Pro" to set the scale, choose the origin and mark the location of the ball every few frames during its motion. Each time they mark the position of the ball, the x and y positions are plotted on the accompanying graph.

o When they reach the end of the movie, they can select the graph window and chose to observe the x-position, y-position, x-velocity or y-velocity vs time graphs for the motion. They can perform linear or curve fits as appropriate to describe the motion. Students should select the range of data for which they wish to fit a best-fit line or quadratic, as the motion changes somewhat after the ball bounces.

Post Lab Notes:

o Students should mathematically model the motion of the object in the both the x and y directions. The straight-line position-time graph should indicate to students that the object is moving at constant velocity in the horizontal direction. Students should be asked to discuss the meaning of the slope of the x-position vs time graph.

o The parabolic y-position vs. time graph should be a clue that the object is accelerating vertically. When students fit a quadratic to the curve, they should recognize the a parameter of the quadratic fit as one-half of the acceleration of a freely falling object. The b parameter represents the initial vertical component of the object's velocity.

o Students should analyze the graph of y-velocity vs. time to make sure that the object is undergoing uniform acceleration. The endpoints of a linear segment of the graph should not be used when performing a linear fit to the graph, as Logger Pro uses a number of points on either side of a particular data point to determine the velocity at that point. See http://www.vernier.com/til/1011/ for further detail.

Whiteboarding: Students will whiteboard the results of their graphs from the video analysisClass Discussion: Students will have a class discussion about their whiteboards and we will talk about the vectors and the graphs. We will look at the results and have a discussion about what makes a projectile, the angles of the vectors, and how to use vector resolution to find the horizontal and vertical components of a projectile. Worksheet 1: Students will complete worksheet 1, which is a review of free fall kinematics from Unit 3. This worksheet will prepare them for the projectile motion word problems.

Assessments: Lab and worksheet 1

Motion Analysis with Logger Pro

1. Obtain a pre-recorded video clip or create your own with a standard digital camera. Make sure that you have a reference standard in the video. Using a meter stick or marking the wall with white tape often works well.

2. Open up Logger Pro. Click Insert Movie… Navigate to the location of the desired movie on your computer's hard drive.

3. Resize the movie clip (by clicking and dragging one of the corners) so that you can still see the graphs and data table in Logger Pro.

4. Play the video.

5. Enable Video Analysis by clicking on the button in the lower-right corner. This brings up a toolbar with a number of buttons (see Figure 1).

6. Click the Set Origin button (third from top), then click in the movie frame to set the location of the origin. If needed, this coordinate system can be rotated by dragging the yellow dot on the horizontal axis.

7. Click the Set Scale button (fourth from top), then drag across an object of known length in the movie. In this movie, the object of known length is the 2 m stick on the floor. When you release the mouse button, enter the length of the object; be sure the units are correct.

8. Use the frame advance to advance the movie clip until the object is released. Click the Add Point button (second from the top). Decide where on the object you will mark its location (center, top, other) and then click the object in the movie. Important: Be consistent in your marking. Each time you mark the object’s location, the movie advances one frame. Depending on the frame rate, you may choose to mark the position every 2nd or 3rd frame. Notice that data are being plotted on the graph.

9. Continue this process as long as is desired. Should you wish to edit a point, click the Select Point button (top). This allows you to move or delete a mismarked point.

10. Select the graph window. Logger Pro defaults to display both the x and y positions of the object as a function of time. You should analyze the position-time behavior of each of these components separately. Perform either linear or curve fits as appropriate.

11. Similar analysis can be done of the x-velocity and y-velocity graphs.

Animated Displays

Use of the Animated Display tool in Logger Pro allows you to display vectors representing the velocity of the projectile at various points in its flight. If you have not used Animated Displays before, you might wish to study the example given in the file: Exploring Animated Displays.cmbl following the path: Experiments ► Sample Data ► Physics ► Animated Display Vectors.

To use an Animated Display for your projectile movie, choose Meter ►Animated Display from the Insert menu into your Logger Pro experiment file, then double-click the window to bring up the Animated Display Options window. Some sample settings are provided below.

After configuring the coordinate system, click on the [Animate Point] button and change the settings to those displayed at right.

Next, click on the [Vector 1] button and change the settings to

the ones shown below.

Choosing Replay from the Analyze menu brings up the Replay control window. When the movie is played at reduced speed, one can see the points and vectors appear on the movie window during the projectile’s flight.

Name

Date Pd

Particle Models in Two Dimensions Worksheet 1:Free-Fall Kinematics

1. A ball is thrown downward with an initial speed of 20 m/s on Earth.a. Make a well-labeled diagram of the situation.

b. Make a list of given quantities and quantities to find, labeled with units and appropriate algebraic signs (+, -).

c. What is the acceleration of the ball?

d. Calculate the displacement during the first 4 s.

e. Calculate the time required to reach a speed of 50 m/s.

f. Calculate the time required to fall 300 m (Hint: factor the quadratic or use the quadratic formula).

g. Calculate the speed after falling 100 m.

2. A rock is thrown upward with an initial speed of 15 m/s on Earth.a. Make a well-labeled diagram of the situation.

b. Make a list of given quantities and quantities to find, labeled with units and appropriate algebraic signs (+, -).

c. What is the acceleration of the rock?

d. Calculate the rock's height after 1 sec.

e. Calculate the time required to reach an upward speed of 3 m/s.

f. Calculate the time required to reach a downward speed of 5 m/s.

3. A ball punted vertically has a hang time of 3.8 seconds. What was its initial velocity? Make a well-labeled diagram of the situation. Make a list of given quantities and quantities to find, labeled with units and appropriate algebraic signs (+, -).

4. A rock is thrown straight up with an initial speed of 22 m/s. How long will it be in the air before it returns to the thrower? Graph the vertical position, velocity, and acceleration of the rock on the axes provided. Make a well-labeled diagram of the situation. Make a list of given quantities and quantities to find, labeled with units and appropriate algebraic signs (+, -).

5. A student throws a baseball off a 120 m high bridge with an initial downward speed of 10 m/sa. How long does it take the ball to hit the ground below?

b. How fast is the ball going at the moment of impact?

6. When a kid drops a rock off the edge of a cliff, it takes 4.0 s to reach the ground below. When she throws the rock down, it strikes the ground in 3.0 s. What initial speed did she give the rock?