The Pitch: Drag Simulation Activity

Forces and properties of air

AUTHOR: Shawn Piasecki

LESSON SOURCE: http://www.pbs4549.org/baseball/pitch1.htm

DATE LESSON TO BE TAUGHT: 6^th and 7^th days of the 4 week unit.

GRADE LEVEL: 10-12

CONCEPT(S): The purpose of this lesson is to give students a better understanding of the forces that act upon a moving body that is airborne.

OBJECTIVES:

SWBAT

· Simulate the complex processes associated with air drag.

· List the variables that contribute to the calculation of air drag.

· Predict the effect of changing variables within the simulation.

· Calculate the air drag on a moving body which is airborne.

TEKS: §112.47. Physics: (2)  Scientific processes. The student uses scientific methods during field and laboratory investigations. The student is expected to: (A)  plan and implement experimental procedures including asking questions, formulating testable hypotheses, and selecting equipment and technology; (B)  make quantitative observations and measurements with precision; (C)  organize, analyze, evaluate, make inferences, and predict trends from data; (D)  communicate valid conclusions;

(4)  Science concepts. The student knows the laws governing motion. The student is expected to: (A)  generate and interpret graphs describing motion including the use of real-time technology; (B)  analyze examples of uniform and accelerated motion including linear, projectile, and circular; (C)  demonstrate the effects of forces on the motion of objects; (D)  develop and interpret a free-body diagram for force analysis; and (E)  identify and describe motion relative to different frames of reference.

MATERIALS LIST and ADVANCED PREPARATIONS:

Per class of students

• One large room (such as a gymnasium or lawn area)

SAFETY:

Students should be warned that any activity outside of the one planned is strictly forbidden.

ENGAGEMENT

What the Teacher Will Do	Eliciting Questions Formative Assessment	Student Responses
Take the students to the gymnasium or outside.
Explain to the students that they are going to be role-players in a simulation that will give them a feel for the mechanism and variables associated with the phenomenon of air drag as it relates to the flight of a baseball. Remind the students that the purpose of this activity is not to play, but to learn, and any activity other than those planned is strictly forbidden for safety issues).		Hopefully students will be very excited that they get to participate in the activity.

EXPLORATION

What the Teacher Will Do	Eliciting Questions Formative Assessment	Student Responses
Assign two or three students to hold hands in a small circle. They will act as the "ball" in the simulation. Ask the remaining students to stand to one side and just observe for the time being. Ask the "ball" to walk from one side of the room to the other.	-This represents a baseball thrown in a vacuum with nothing to affect it along the way.
Now ask the remaining students, or a portion of them, to act as molecules of air. Have them spread out at least arms-length apart and randomly scattered around the open area of the floor. Have the "air molecules" begin milling around in a sort of slow-motion slam dance. Now have the "ball" walk from one side of the room to the other again. Let students observe and describe the fact that the "ball's" progress is now impeded by collisions with the air molecules.	-This roughly simulates the flight of a baseball pitched through the air on its way to home plate.

EXPLANATION

What the Teacher Will Do	Eliciting Questions Formative Assessment	Student Responses
Through a series of "What if?" questions posed by the teacher and/or coaxed out of the students, the simulation can be modified to investigate all of the variables that factor into the calculation of air drag.	a. What if the density of the air were to change due to a change in temperature or humidity? Simulate an increase in air density by adding more "air molecules" into the group and/or having them move closer together. b. What if the size of the ball changed, from a baseball to a softball? Simulate this by adding a few more students to the "ball," making a larger circle. They should see that this larger "ball" will interact with more "air molecules." c. What if the shape of the ball were to change? Simulate the effect of aerodynamic properties by having the "ball" flatten out or become more streamlined like the nose cone of a rocket. The overall aerodynamics of an object are expressed as its drag coefficient. d. What if the ball were thrown faster? Simulate this by having the "ball" move faster across the room. Students should see that if the ball moves faster it will collide with "air molecules" more often and more violently, slowing it down even more.	a. If the density increased, the speed of the ball would decrease. b. If the size of the ball were larger, the speed would decrease. c. The more streamlined the ball is shaped, the faster (easier) it can move between the air molecules. d. If the ball were thrown faster, the speed of the ball would make it hit air molecules harder and it would be slowed down a lot.

ELABORATION

What the Teacher Will Do	Eliciting Questions Formative Assessment	Student Responses
After the group has acted out all of the "What if?" scenarios, the teacher can then have the students go back to the classroom to derive an equation that calculates the force of the air on a moving body.
Once the students are back the teacher has the students list out factors that affect wind resistance (or air force).	-What are some things that affect a body in motion that is airborne? -Ok, now that we have the factors that need to be included in our equation, we can safely assume that the equation somewhat has the form of: Fw = V^a*A^b*ρ^c -What are the units of velocity? -How about area? -What about density? -Using your skills learned from dimensional analysis, find the values of a, b, and c. -Great! Now that we have this formula, we can calculate the force acted upon a moving body by air as a function of the body’s velocity, shape, and the density of the air.	-The velocity of the moving body, the shape of the object (or cross-sectional area), and the density of the air. - m/sec -m^2 -Kg/m^3 - a=2, b=1, and c=1 so that Fw = V^2*A*ρ

EVALUATION

What the Teacher Will Do	Eliciting Questions Summative Assessment	Student Responses
Homework question: -What is the air drag on a ball with a diameter of 10cm traveling at 15m/s? (the density of air is 1.2 kg/m^3) (hint: watch your units!)