Science/9/Physics 1.0 Newton's laws predict the motion of most objects. As a basis for understanding this concept:
a. Students know how to solve problems that involve constant speed and average speed.
b. Students know that when forces are balanced, no acceleration occurs; thus an object continues to move at a constant speed or stays at rest (Newton's first law).
c. Students know how to apply the law F=ma to solve one-dimensional motion problems that involve constant forces (Newton's second law).
d. Students know that when one object exerts a force on a second object, the second object always exerts a force of equal magnitude and in the opposite direction (Newton's third law).
e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth.
f. Students know applying a force to an object perpendicular to the direction of its motion causes the object to change direction but not speed (e.g., Earth's gravitational force causes a satellite in a circular orbit to change direction but not speed).
g. Students know circular motion requires the application of a constant force directed toward the center of the circle.
h. * Students know Newton's laws are not exact but provide very good approximations unless an object is moving close to the speed of light or is small enough that quantum effects are important.
i. * Students know how to solve two-dimensional trajectory problems.
j. * Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components.
k. * Students know how to solve two-dimensional problems involving balanced forces (statics).
l. * Students know how to solve problems in circular motion by using the formula for centripetal acceleration in the following form: a=v2/r.
m. * Students know how to solve problems involving the forces between two electric charges at a distance (Coulomb's law) or the forces between two masses at a distance (universal gravitation).
Students will learn how perpendicular velocity vectors aid in sports and in general. Through class discussion, investigations with the apparatus, and small group discussion, students will develop a kinesthetic intuition for the addition of velocity vectors . The activity will be followed up with a formal lesson on a graphical method for adding vectors. The lesson includes several extensions as well as an individual practice worksheet, a quiz, and teacher keys.
Through discussion and watching the video, students will learn how two perpendicular vectors combine into a resultant vector. Students will use the understanding developed in the activity to explain how a quarterback’s horizontal velocity and the release velocity of the ball combine to create a resultant velocity for a football. Students will learn how to add vectors using the tip-to-tail method or the parallelogram method.
Students will be able to:
Express the definitions of a vector
Express that velocity is a vector
Use either the parallelogram method or the tip to tail method to add vectors.
Use the concepts of vectors to explain why a running quarterback must sometimes release a football in a direction that is not pointing directly at the intended receiver.
Computer and internet access or downloaded videos.
Anticipatory Set (Lead-in):
Take a moment and try to think of as many different sports as you can where athletes, at times while moving, need to pass or throw an object. Share your list with your neighbor and then we will share to make a class list (football, basketball, baseball, soccer, hockey, dodge ball, cricket, rugby, pickle, monkey in the middle…) In this lesson we will learn about the physics of making a pass in one direction while moving in another direction. We will do this by watching a fun little video that simulates a quarterback, and then learning a way to graphically predict the best speed and direction to complete a pass. Along the way, we will learn about vector addition which is a skill physicists use to analyze many types of phenomena in the physical world.
Lesson Plan Procedure:
Part I: Intro Discussion/Demo (15 minutes)
Complete question 1 on the activity worksheet.
Consider question 2 on the activity worksheet. The graphic depicts a top view of a person running past a garbage can and trying to throw away his apple core. Emphasize that the apple is being tossed in a direction perpendicular to the motion of the runner (in this case, north). Ask students whether the apple should be released at point A (even with the garbage can), or point B (before the runner comes to a spot due south of the garbage can_. (If your class has covered the law of inertia, you may want to make the connection that the apple core has inertia and is going to tend to keep moving in the original direction.)
A very simple demonstration can be done to show this situation and to demonstrate that the object must be released before reaching the garbage can. The teacher or a student can demonstrate this by jogging, using a ball and a bucket. When performed in front of the class, have students notice that the ball continues to travel in the original direction of the person tossing the ball.
Part II: Video Analysis and Discussion (30 minutes.)
Watch the 5 minute YouTube video “Vectors and the Quarterback Pass” (http://www.youtube.com/watch?v=4D66N7_Ys3w). During the video, you can stop and discuss each section. Replay as needed. (The rolling ball is a bit hard to follow so you may need to point its path out to the students.)
Have students answer questions 3 and 4 on the activity worksheet.
As a class, share the results for each question. Be sure to clarify any misconceptions, and try to elicit from students' answers the fact that the path of the ball is the result of two velocities - the velocity of the apparatus and the velocity of the ball rolling down the ramp. (This will be an appropriate segue to vector addition and the concept of a Resultant Vector.)
Part III: Vector Addition (40 Minutes)
Note: This lesson assumes some familiarity with geometry and drawing. Depending upon the class, you may need to go very slowly to introduce the methods of vector addition in part III.
To begin this segment, formally define a vector as a quantity with magnitude (size) and direction. You may want to list other types of vectors often used in physics (velocity, forces, acceleration, displacement). Compare and contrast vectors with scalar quantities, which do not have a direction (temperature, mass, age).
Define the resultant vector, as the sum of two or more vectors. Refer to the previous activity and explain, with words and pictures, that the resultant velocity was the vector sum of the apparatus velocity and the perpendicular release velocity generated by the ramp.
You can very easily demonstrate the resultant displacement vector that “results” from walking a displacement of three steps in one direction and then a displacement of four steps in a perpendicular direction. The resultant displacement is an arrow that points from where you began to where you ended up.
You can demonstrate the resultant force vector by having two students simultaneously pull or push and object in perpendicular directions. (You can have them safely apply the perpendicular forces to a person on a rolling chair, or any object of your choice.)
Have students write out the instructions for a method (the tip-to-tail method is shown on the answer key.) Demonstrate the method using a few examples and give students time to complete the vector addition worksheet.
If there is time after completing the vector addition worksheet, you can have a student competition, or have students experiment with different release velocities by changing the position on the ramp where the paper clip releases the ball.
Closure (Reflect Anticipatory Set):
Ask students to explain how the class activities relate to some of the sports listed at the beginning of the activity (basketball, hockey, soccer). Ask them to think of other situations where the vector addition is important (tossing something while riding a bicycle or skateboard, taking shortcuts, using a slingshot, etc.)
Assessments & notes
Plan for Independent Practice:
You can assign the Vector Addition: Individual Practice worksheet.
Assessment Based on Objectives:
Quiz: Vector Addition and a Quarterback Pass
Possible Connections to Other Subjects:
Language Arts: Students can write a reflection about a quarterback’s ability to precisely calculate in a split second a release velocity that will produce the correct resultant velocity to complete a pass.
Students can write a short story describing how they have experienced vector addition in their lives.
Math: Students can measure the lengths of vectors and reflect upon whether or not vector lengths add up like numbers (they do not).
The angle of the resultant vector can be measured using a protractor.