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:

  1. To investigate the motion of the loaded cart when pushed from rest.
  2. To investigate the motion of the loaded cart when subjected to a constant pulling force.
  3. To investigate the motion of the cart loaded with different masses but pulled by a constant force.

Vocabulary:

force

velocity

acceleration

mass

speed

Materials:

Per group of 4-5 people
  • a dynamics cart
  • three or four rubber bands
  • bricks
  • a timer,
  • white paper timer tape
  • a meter stick.
  • graph paper
  • pencil
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Procedure:

  1. Investigate the motion of the cart when it is pushed. Load the cart with one brick.
  2. Attach a strip of timer tape to the cart and run it through the timer. The timer will make a record of the motion by little dots on the paper.
  3. Give the cart a push and let it move. Examine the paper tape and look at the dots. The dots will give evidence as to how uniformly the cart is moving. Try pushing the cart so that it goes faster.
  4. Is the velocity (speed) constant when there is no force? Why? Is the velocity more nearly uniform when the cart is moving slowly or rapidly?
  5. Investigate the motion of the cart when it is pulled by a constant force.
  6. Attach one end of a rubber band to the cart. Hook the other end of the rubber band over the end of a meter stick. One partner should hold the cart while a second partner pulls on the rubber band
  7. The second partner pulls on the rubber band keeping it stretched to 70 cm.
  8. A third partner should catch the cart as it nears the end of the table.
  9. Be sure to practice a few times without using the timer.
  10. After mastering the pulling of the cart, attach the timer tape. The fourth partner should watch the timer. Make a tape. This tape will be for one rubber band and one brick.
  11. Detach the tape and keep the masking tape on the end of the paper tape so the beginning of the paper tape may be clear. Also mark the tape "one brick, one band".
  12. Make another paper tape with two bricks following the same procedure. Be sure to mark the paper tape.
  13. Use three rubber bands and one brick and three rubber bands and two bricks. Attach each of the three rubber bands to the cart.

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:

  1. What can be concluded about the lines on the graph?
  2. The slope (slant) of the graph is called "acceleration".
  3. What kind of motion is produced by a constant force?
  4. What is the effect of different masses?
  5. Could the size of the force be changed? How?
  6. What would be the effect?
  7. Is the rubber band the only force on the cart? Explain?
  8. What is Newton’s Second Law?
  9. What are some possible sources of error?

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/sec2 (or about 10 m/sec ). This experiment gives values of 3 to 7 m/sec2).

Philadelphia Science Content Standards:

Science Content Standard #1: Nature of Science

This experiment satisfies Benchmark #3 for grades 5-8: "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 5-8: "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.