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## The Parachute

### Learning Context/ Introduction

The Parachute is an activity in which students design and then conduct an experiment to investigate the effects of various factors on the rate of fall of parachutes.

This learning experience was designed as a variance for the Physics Regents examination (35% Option). In addition to supporting student progress toward meeting the Mathematics, Science, and Technology learning standards, the goal of this experience was to incorporate performance tasks into the examination to assess the skills, processes, and kinds of thinking that are essential in an investigatory science project but are not adequately evaluated in the traditional Regents examination. In this experience, the students were assessed on experimental design, observational skills, graphing and interpretation, critical thinking and synthesis, and error analysis.

A constructivist learning model is implicit in this learning experience, with students first engaged, and then involved in exploring a natural phenomenon, explaining their observations, and then applying the knowledge they have constructed to make predictions. Assessment occurs throughout the experience.

To succeed with this learning experience, students need to have an understanding of the concepts of free fall and gravity as well as skills in solving a problem by designing, conducting, and evaluating a scientific experiment using an appropriate model.

1. After engaging student interest in parachutes (by referring to Leonardo da Vinci's plans for such a device, for example, and the effect of free fall on human bodies), students are asked to write a procedure to determine the effect of different size parachutes and different masses on the time it takes the masses to fall. Students are asked to study the nature of a parachute and the factors that affect the time of fall.
2. The students are divided into groups and each group is given a stopwatch, several masses, a balance, a meter stick, and materials to construct parachutes.
3. The students work in groups to perform a mutually agreed upon procedure. They record all their data, and repeat steps as needed. From this point on, the students work as individuals consistent with the protocol for an exam. If this were a class activity, they might continue to work in groups.
4. After completing the experiment, students are asked to write three observations they made, plot a graph, interpret the graph, and evaluate the reliability of the data and sources of error. They also interpret their experimental data to determine the mathematical relationship between time of fall and the parachute mass.
5. Students are asked to perform the following experiment at home. They push a plastic cup into a sink full of water and observe the resistance to the pushing as they make a hole; and then enlarge the hole in the bottom of the cup. They are then asked to apply their results with the plastic cup to the use of an adjustable hole in the top of a parachute. They are to predict the effect of a hole in the parachute and then cut the hole and actually measure the effect.
6. Students are presented with a diagram of a parachute with an attached basket, and are asked to draw and label the forces acting on this combination, which causes its vertical motion. They also must calculate the speed with which the parachute hit the ground.
7. Students are provided with an experimental procedure for measuring the relationship between the diameter of a parachute and the time of fall. They are asked to critique the procedure, indicating if it is clear and if it is adequate to obtain the desired information. They must also compare this procedure to their own procedure.

During the experimental phase, Step 2 , the teacher coaches the groups to insure that, for example, they construct a functioning parachute, measure the drop distance, and discard the results if the parachute hits an obstacle.

### Procedure

SECTION 4

A. What are two specific sources of error in the parachute experiment, which would have caused
your data to be inaccurate? (2 points)

RUBRIC (2 points) Any two of the following errors:
a) Human timing error at the initial drop or the point of hitting the floor.
b) The basket may have been at different heights since the parachutes deformed differently.
c) A given parachute did not always fall at the same angle.
d) Some parachutes swung from side to side more than others.

Hitting the table or the parachute not opening are not errors. They are mistakes causing that trial

B. Based on your experiment, was there a linear relationship between the time to fall and the

RUBRIC (2 points) The answer depends upon the data. The answer is yes if a given multiple of
mass produces the same multiples of time. The answer is not if not. A graph sketch of the data
will be acceptable providing a “yes” or “no” answer is also given.

(1 point) Either the correct answer based on the data or the reason.

C. Actual parachutes have an adjustable hole in the top of the chute. With reference to the experiment
you performed at home with the cup, what do you think is one reason for that adjustable
hole? (2 points)

RUBRIC (2 points) The answer must show that the experiment was performed by noting any
observation (e.g., It went down straighter, the hole size changed the force necessary for a given
descent; it went down faster as hole increased in size, it was more stable.) and the relationship

(1 point) A statement as to what an adjustable hole might do without reference to the experiment
they performed at home.

SECTION 5

A. Draw and label the vector forces acting on this combination, which cause its vertical motion to
increase or decrease. Be sure to show the direction of the force and where it is acting. (3 points)

RUBRIC (3 points) The diagram shows the force acting down on the basket due to the gravitational
pull on the weight and is so labeled. The diagram shows the upward force of the air on
the parachute and is so labeled.

(2 points) The diagram shows both forces but only one is labeled or the diagram shows both
labels but only one force.

(1 point) The diagram shows only one of these forces, which is labeled.

The force of the air acting up on the basket will not be counted.

B. In speaking to various skydiving schools, one finds that many factors affect the speed with which you hit the ground. A rough estimate is that it is similar to jumping off a 5 ft. (1.5 m) table.

Note: In the items below, you must show your work to receive credit. (6 points)
1) Calculate the slowest speed obtained during your parachute experiment.
2) Calculate the speed with which one would hit the floor if jumping off the table noted in “B” above.
3) Using percent of error compare the speeds calculated in “1” and “2” above.

RUBRIC (6 points) The answer must contain the following:
a) The formula to find velocity given height and the acceleration of gravity.
b) The formula to find the velocity given displacement and time.
c) The formula for percent of error.
d) Correct substitution into these formulae.
e) The correct answer reported to the proper number of significant figures.
f) The units of the answer provided (percent of error must be stated in percent, not in decimals.)

(5 points) Any 5 of the above, etc.

SECTION 6

A) The following is an experiment to determine the relationship between the diameter of a parachute and the time it takes for a mass to fall. The equipment is the same as was available previously.
1) Attach the basket to one of the parachutes using the cord and clips provided.
2) Place one of the weights in the basket.
3) Hold the parachute by its top above the floor.
4) Let the parachute drop and time its descent to the floor.
5) Repeat steps “3” and “4” three times more.
6) Place another weight in the basket and repeat steps “3” through “5”.
7) Choose another parachute and repeat steps “1” through “6”.

Consider the above experiment in comparison to the one your group did. It has some good points as does yours, and some problems.
Critique the above procedure by stating five(5) reasons why yours is better, or five(5) reasons why this is better or as good, or five(5) reasons why this is worse, or any combination of better, the same, or worse as long as you have a total of five(5).

As you critique, say to yourself, “If I was doing a lab, would this be sufficient? Is it clear? Does it
accomplish the aim?”, etc.

RUBRIC
(5 points) Any five(5) of the following:
a) It is easier to control a given variable.
b) The variables are truly independent.
c) There is less chance of the equipment malfunctioning or causing an error.
d) There is less chance of human error.
e) This approach is less complicated.
f) The order of operations is more logical.
g) The diagram helps to explain the setup.
h) The approach gives more consistent results.
i) The approach clearly defines what to use and how to use it.
j) Other (Depends on response. Personal preference is not acceptable.)

Use below and the back for your critique. (5 points)

### Resources

The parachutes are muslin obtained from a local fabric store. The basket was obtained at a party supply house (plastic wedding basket favors). The paper clasps may be purchased at an office supply store. It may be necessary to put a dot of glue on the rope knots to prevent slipping or unraveling due to drops.

### Assessment

Students are assessed throughout the activity on the following:

1. the procedure for the experiment
2. the data obtained

### Reflection

The use of cooperative learning groups promotes meaningful student dialog, encouraging student discussion as they construct relationships, see connections, and make sense of what they are observing. With these approaches, this learning experience is likely to enable students with a wide range of learning styles to meet the targeted learning standards. This activity, as noted, was designed to be a commencement test. However, it lends itself easily to being a research project, or class enrichment activity.

### Author

Jay Emmer
North Shore High School
North Shore Central Schools

### Source

Emmer, Jay. “The Parachute.” Mathematics Science and Technology Resource Guide, Part II.2. New York State Department of Education, 12-19.

### Procedure

THE PARACHUTE

No one knows when the first person took a large piece of cloth, held it over his/her head, and jumped off a hill to experience the effect of a parachute. We do know that Leonardo da Vinci provided detailed plans for such a device. Obviously, it is important to anyone who plans to jump out of a plane that manufacturers of parachutes understand how they work.

You will be conducting a series of experiments, which will give you some insight into the behavior of a parachute. Working as a group you will have the opportunity to discuss what to do and how to do it. Before a group meeting you may be asked to describe what you think should be done or, after a group meeting, you may be asked to describe, analyze, assess, or critique what was done. Although you will, in part, be working with a group, you are free to report your own results.

THE EXPERIMENT

Each group will have been given the following materials:

a stopwatch, a meter stick, four circles of cloth of differing diameters to use as parachutes, five weights, a small basket to hold the weights, and a triple beam balance. The basket has four equal length cords tied to it with clips on the end of each cord so that the basket can be attached to the parachute material.

The aim of the experiment is to determine the effect of different size parachutes and different masses on the time it takes the mass to fall.

Based on the aim of this experiment and the equipment given, describe the procedures you would use to accomplish this aim. Your description may be in outline form, but you must use complete sentences. Be as clear as you can be about what must be done. If something is to be repeated, be clear as to how many times. You may use any or all of the equipment. Use the worksheet provided for your description.

SECTION 1

Write the description of your experiment in the space below. You may use the back if needed. (5 points)

RUBRIC (5 points)

a) Student provides a procedure, which is logically ordered, and complete.
b) Student uses at least four different weight combinations.
c) Student shows the need to repeat a given procedure at least three times to obtain an average.
d) Student shows awareness of changing only one variable (parachute or mass) at a time.
e) Student indicates the need to drop from the same height in all trials.

(4 points) Any four(4) of the above, etc.

SECTION 2

Now go to your group and perform the experiment. To provide some uniformity, please make sure of the following:
a) Attach the basket clips to the parachute so that the spacing is roughly even.
b) Drop the parachute so that its top is touching the ceiling.

Be sure to share with your group your opinions as to how you thought the experiment should be performed. If the group disagrees with you and fails to perform a part of the experiment you think is essential, feel free to perform that part on your own. Use this sheet so that you will have your own copy of the data. If you performed a part by yourself or without the whole group, the data collected need not be shared.

RUBRIC
This section is not marked. It is performed as a group. A sheet of “Lab Hints” has been provided to encourage a degree of uniformity in the actual procedures of each group. This is done because some of the following parts rely on the data gained in this section.

SECTION 3

A. What are three observations you made based on the parachute experiment you performed?
(3 points)

RUBRIC (3 points) Student describes any three(3) of the following:

a) The greater the mass the shorter the time of fall (the “faster it went” or “the greater the
acceleration” will not be accepted since they are measuring time.)
b) The larger the diameter of the parachute, the greater the time to fall.
c) The parachute swung from side to side as it fell.
d) The parachute fell at an angle.
e) Depends on response. “It fell” without descriptor will be given no credit.

(2 points) Any two of the above, etc.

B. Using the data collected for any one of your weights, plot a graph of the time to fall (dependent
variable) vs. the diameter of the parachute (independent variable). The diameter axis
should extend to 0.5 m. It should be clear as to what this graph shows. Use the graph paper provided.
Be sure to put your name on the graph paper. (3 points)

RUBRIC (3 points)
Both axes are correctly labeled w/units and scaled. The plot contains at least four(4) points. A
smooth curve representing the best average line is drawn.

(2 points) The axes are not labeled w/unit or they are not scaled correctly or less than four
points have been chosen but the best average line is drawn.

(1 point) The axes are not labeled w/units or are not scaled correctly. Four(4) points have been
chosen but the best average line is not drawn.

C. Based on the graph you have drawn, what would be the time for a diameter of .48 m? Use
the graph you have drawn to find your answer. Be sure you have made it clear how your

RUBRIC (2 points) The student has made a reasonable attempt to extend the line until it passes
the .48 m mark. The student has indicated how the point was determined (guidelines, etc.) The

(1 point) The point does not lie on the best average line or the answer does not include units.

D. Extrapolation of given data, though correctly done, can still lead to inaccurate results. What
are two possible reasons for this? Use the space below. (2 points)

RUBRIC (2 points) Any two of the following answers:
a) The line drawn is the best average line and does not represent any point specifically, just
the average.
b) When extrapolating, I assumed that the curve followed the trend shown. This may not
be true.
c) The best average line or the guidelines may have been drawn incorrectly.

(1 point) Any one of the above.