# Applying Newton's Second Law Quantitatively

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## Objective

Students solve a variety of problems with free body diagrams and Newton's Second Law.

#### Big Idea

The acceleration of an object is always in the direction of the net force acting on it.

## Context and Supplies

My students have worked with free body diagrams, are able to determine the net force acting on an object and now they know Newton's 2nd Law (F=ma) from the previous lesson on Discovering Newton's 2nd Law.  In this lesson, students solve a variety of F=ma problems which combine the ideas learned so far. This lesson involves the NGSS Performance Standard HS-PS2-1, the mathematical relationship between the net force acting on an object and its acceleration. Students work to understand that the direction of an objects acceleration matches the direction of the net external force acting on it with a simple demonstration that requires a tricycle and a length of string or rope.

Students also use the concepts within Science Practice 5: Using Mathematics and Computational Thinking and Math Practice 2: Reason Abstractly and Quantitatively as they problem solving real-life situations using Newton's 2nd Law.  Also, they apply Science Practice 6Constructing Explanations (for science) for the demo in the beginning of class.

## Tricycle Demo

10 minutes

I begin class with a demonstration in which I pull a tricycle with a piece of string. This demonstration helps students develop their own conclusion that the direction of acceleration of an object is always in the same direction as the external net force acting on that object. To prepare, I tie string from the end of each handle bar to the seat. This keeps the front wheel straight during the demo. Then I tie a string to one of the pedals. No matter what position the pedal is in, when I pull the string to the right (see picture below), the tricycle moves to the right (see video).

I have fun with this demo and make it into a guessing game.  The Socrative quiz, tricycle demo questions (SOC #13867550), is displayed on the board and the questions on the Socrative bring us through the following sequence:

1. Pedal is in the up position and pull the tricycle to the right (left picture above).  Students predict the direction of motion of the tricycle and I display their guesses. Then I pull the string to the right and the tricycle moves right.
2. Pedal is in the down position and pull the tricycle to the right (right picture above). Students predict the direction of motion of the tricycle and I display their guesses. Then I pull the string to the right and the tricycle moves right.
Most students get the direction correct with the pedal in the up position, but in the down position, many students think that a pull to the right will move the tricycle left (backwards).
I am dramatic while conducting the demo, but I provide no answers or explanations.  The Socrative Tricycle Demo has students supply explanations.  I know this is an effective demonstration because most of the students supply correct explanations just by watching the demo and thinking about what they witnessed. We review the answers after all students have finished so that there is no confusion: "Acceleration is always in the direction of the net force, not matter what."

## Lecture on Newton's 2nd Law

10 minutes

Once the activity is over, I give a short 10 minute lecture on Newtons 2nd Law presented with Power Point. In the previous class, students Discovered Newton's 2nd Law experimentally, but if any students are confused by the results or their analysis, this lecture serves to clarify any misunderstandings. Students are informed that F=ma, the standard S.I. Unit for force is the newton. I model good problem solving with two real-life examples. I use lecture for this because it is a fast and effective way to make sure students have all the information they need to solve problems using Newton's 2nd Law. Students will next be using this information to work through such problems. There is a picture of Tom Brady, the NFL quarterback for the New England Patriots, that appears on the slide of F=ma.  The reason he is there is because I tell the students that F=ma is the most important of equations. It is so important that many refer to it as "The Tom Brady" of physics equations! The students enjoy this and all of the Jets fans in my classroom roll their eyes. I like to break up my lectures with humor and have fun with the students.

## Students Practice 2nd Law Problems

25 minutes

This activity helps students develop expertise in using Newton's Laws of Motion. For 25 minutes, students deepen their understanding of Newton's 2nd Law with work on the Newtons 2nd Law Practice Worksheet. This is an opportunity for students to combine all of the concepts learned so far in this unit as they solve a variety of real-life problems. I give this to them in class so that I can circulate the room and help students who need support. Each student gets his or her own sheet to work on; they are also free to help each other as long as they stay on task. Next class period, I check that students completed the worksheet and we review the answers.

## Closure - g-forces!

5 minutes

With 5 minutes left in the class, I instruct students to finish the worksheet for homework if they didn't finish during class (though over half the class has finished and most only have a few problems left).  Then I show a video of the testing that the airforce officer, Colonel John Stapp, did right after World War II. The video talks about the 'g-forces' that he subjecting himself to while undergoing testing to determine the effects of large accelerations on the human body. I show this because it ties in directly to Newton's 2nd Law and is a real-life example of its application. Also, 'g-force' is a term that most students are familiar with and this helps them to understand what it means.

Lastly, I share with the students how impressed I am with Col Stapp. His was a rank right below general, but that is not what made him a great leader. He was the person in charge of the whole testing program, yet he didn't consider himself more important that the people he led. He never asked anyone to do anything that he wouldn't do himself. In fact, he was first in line.