### Learning Experience/Unit

## The Parachute

### Grade Levels

Commencement, 11th Grade, 12th Grade

### 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.

- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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

to be discarded.

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

mass? Justify your answer. *(2 points)*

* 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

this had to their experiment.

* (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:

- the procedure for the experiment
- 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

Glen Head, NY

### 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

answer was found. *(2 points)*

* 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

answer includes units.

*(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.