### Newton's 2nd Law

Intro:

You are beginning lab #2, Newton's 2nd Law.  The purpose of this page is to familiarize you with the apparatus, goals, procedural details, and data that will be collected.  Please know that the specifics of the procedure, as long as they fall within the guidelines, will be up to you.

Apparatus: Modified Atwood Machine

Please note: This image does not include the black dynamics tracks, which we will be using.  It is important that the track is level, the end is in line with the pulley, and that the string which extends from the cart over the pulley runs parallel when there is tension.

From this point on, the word "system" will be used frequently.  The "system" is whatever is accelerating, which in this case is not only the cart, but also any mass sitting on top of the cart, the string, and any mass at the end of the string.  To get the total mass of the system, find the mass of each and add them together.

The smart pulley is a motion sensor.  As the low friction pulley spins, it blocks/unblocks a small photogate, and the data is compiled in a LoggerPro program. It will present the data in the form of a velocity-time graph.  Recall that the slope of a velocity-time graph is acceleration.

This lab will be divided into two portions, with half of the lab groups doing one portion, and the other half assigned the 2nd portion.  I will call these group 1 and group 2.

Group 1: Determine the effect of net force on acceleration

You are to derive the mathematical relationship between net force and acceleration.  This will require you to vary the net force (how many Newtons are pulling on the end of the string) and measure the acceleration that results (slope of the velocity-time graph).

IT IS CRUCIAL THAT THE MASS OF THE SYSTEM IS A CONTROL IN THIS PART!!! This means that you will want to begin with a fair amount of mass on top of the cart, and then as you do trials, move the masses between the cart and end of the string.  At no point should you remove mass from the system entirely, as that creates an additional variable. The masses you use, number of trials you do, etc, is up to you, but remember, the more data, the better. Make sure you do record the total mass of the system at some point in your procedure.

The data you gather (net force & acceleration) should then be graphed, either by hand or with a graphing program.  I recommend net force on the y-axis, acceleration on the x, just because the slope will be easier to interpret.  Form an equation for the line (y = mx + b) and generalize it to create a mathematical expression of Newton's 2nd Law.

Group 2: Determine the effect of (total) mass on acceleration

To test this, keep the amount of net force (mass at the end of the string) constant, and vary the mass of the system.  Your goal is to determine the mathematical relationship between total mass and acceleration.  I would start high (whole bunch of masses on the top of the cart), figure out how much net force it takes to barely accelerate the system, then remove mass each trial.  Your last trial can be your net force accelerating an empty cart.  Again, the more data, the better.  It is important that each trial you record the TOTAL MASS OF THE SYSTEM and the acceleration that results (slope of v-t graph). Make sure you record the value of the net force (control) at some point in your procedure.

This data will also be graphed, mass on x, acceleration on y, and then (hint hint) linearized according to the methods given within the summer assignment. The mathematical relationship (equation for the line) will come from the linearized graph. Generalize the equation.

- Create well-organized data tables ahead of time. Consult with your group to determine the number of times you are going to test.
- Be aware that conversions are necessary.  Most mass sets are labeled in grams, but you will need to take that to kilograms, then frequently to Newtons.  It is up to you if you include additional columns in your data table to express these conversions, or if you just do it in the calculator as you go.
- It is necessary to calculate slope in each portion of the lab, and try to determine the physical meaning of the slope value.  Hint:1 N =1 kg x 1 m/s​2
-What does it mean to "generalize an equation"?  After you have formed an equation for the line on your graph, take it a step further and replace all x's, y's and numbers with variables or words.  For example, the toy car activity graph line may have had an equation such as y = (50 cm/s)x + 3 cm.  This could be generalized to final position = (average velocity) x time + initial position, or x = vt + x0.
-Review the types of proportions (direct, inverse, etc) listed in the summer assignment.  Note the graph shapes that they refer to.  In your conclusion, I want you to address the type of proportion that exists between the independent and dependent variable that you are testing.