NEWTON’S SECOND LAW
CHANGES IN VELOCITY WITH A CONSTANT FORCE
Knight Foundation Summer Institute
Elizabeth Chesick, Haverford College
Introduction:
This lesson is a great demonstration of Newton’s Second Law which states that force acting on an object is equal to the objects mass times its acceleration. Ask the students to take a look around them. What is moving? What is at rest? Why does it stay at rest? It seems from everyday experience, that a constant force must be added to move an object from rest or to change its velocity while it is moving.
In this experiment we are going to investigate what happens if a constant force is applied to an object free to move along a tabletop. It is possible to investigate the quantitative relation between the velocity changes and the force with a tape and a laboratory cart. The experiment is best performed on a smooth, level table. Bricks may be placed on the carts to change to mass If the bricks are uneven in mass and if they are crumbly, they may be wrapped in paper.
Objectives:
Vocabulary:
force
velocity
acceleration
mass
speed
Materials:
Per group of 45 people

Procedure:
Data and Results
After all the tapes have been made, each partner will have a tape to analyze. Divide the tape into intervals of 6 ticks, as the teacher will show. Number each interval. Make a chart in your lab record book to record the data. Measure the length of each interval and enter it in the table. The length of the interval is really the velocity, or speed, of the cart. (It is length divided by time, or speed, if the time is assumed to be one unit.)
Interval (1 band) 
1 brick 
2 bricks 
3 bricks 
4 bricks 
1 

2 

3 

4 

Etc. 
Analysis:
Make a graph of the results. Place the interval number on the x axis (each interval is a tenth of a second.) The y axis will have the length of the interval which is the velocity. After plotting one set of data for one load (brick number), plot the data for another load. Connect the dots with a best fit line. The line should be straight. Compare the two lines. (Each line should go through 0,0). Plot all four lines on the same graph paper.
Assessment:
Have the students think about the following questions with their group:
For the teacher’s reference, here are the answers to the above questions:
(The lines should be straight passing through the origin on the graph, 0.0. The slope of the lines measures the acceleration. The largest mass, 4 bricks, is the line with the smallest slope, or the most horizontal. As the mass, number of bricks decreases the slope increases until the line with 1 brick is the most vertical. Motion with constant acceleration is produced by a constant force. Or another way to way it is that motion with constantly increasing velocity is produced by a constant force. Newton’s Second Law is " F = ma" where "F" is force, "m" is mass, and "a" is acceleration. The size of the force can be changed by using more rubber bands. If the mass is constant, the more the force, the larger the acceleration or the more vertical is the line on the graph. There are other forces besides the rubber band. They are friction, gravity, air resistance, and the white paper tape. Errors are in analyzing the tape, not keeping the rubberband constant length, calculations and making the graph, friction on the table, uneven mass bricks, etc. )
Have the students complete the graphs and turn them in with a written report.
Extensions:
The experiment may be varied by using 2 or 3 rubber bands and 1, 2, 3, or 4 bricks. Recommended is 1 rubber band with 2 and 4 bricks and 3 rubber bands with 2 and 4 bricks. That way there will be enough variation in force and mass to see significant differences.
Another extension of the experiment involves putting the timer on the ring stand as in the picture below. Thread the white paper tape through the timer and hang some washers on the end of the tape. Let the washers go to fall to the floor, pulling the paper tape through the timer. Make several tapes. Analyze the tape as above to find the velocity in each interval. Make a graph of velocity on the y axis and time interval on the x axis, just as before.
Draw the best line.
What is true about the motion of the falling mass?
What is making the mass fall to the floor?
(This will show that gravity exerts a constant force, which increases velocity constantly. The acceleration is constant because the line is straight. The value of the acceleration (the slope of the line) does not give a very good value. There is too much friction in the timer. The acceleration due to gravity should be 9.8 m/sec^{2} (or about 10 m/sec ). This experiment gives values of 3 to 7 m/sec^{2}).
Philadelphia Science Content Standards:
Science Content Standard #1: Nature of Science
This experiment satisfies Benchmark #3 for grades 58: "Collect and summarize data from an experiment and interpret the results in terms of the data."
Science Content Standard #2: Physical Setting
This experiment satisfies Benchmark #4 for grades 58: "Investigate the relationship between force and motion."
Cross References
This lesson is primarily useful for a physics unit on motion, However, some added bonuses to the lesson is that it is a fun, interactive project for the students. It also reviews graphing and math skills as the students analyze data.