Materials Included In Kit

Additional Materials Required

Prelab Preparation

At each lab station, place both a large 1⅓" ball and a small ⅝" ball and a foam pad. If time permits, set up the catcher’s boxes and measure and mark the drop height at each lab station. Note that two meters is a suggested height and may be adjusted to suit the needs of the classroom. Two meters was chosen to ensure enough free fall time to minimize human error in terms of reaction time.

Safety Precautions

Wear safety glasses to protect from possible flying projectiles. Remind students that horseplay is not allowed in the laboratory and to follow all laboratory safety guidelines.

Disposal

All materials may be saved and stored for future use.

Lab Hints

• Enough steel balls are provided in this kit for 30 students working in groups of 3 or for 10 groups of students. Both parts of this laboratory activity can reasonably be completed in one 50-minute class period. The prelaboratory assignment may be completed before coming to lab, and the data compilation and calculations may be completed the day after the lab.
• The error inherent in using a stopwatch to time free fall stems mostly from human reaction time, which is within 0.15 seconds. Average the class data to minimize the human error as much as possible, and show the results to the class.

Teacher Tips

• Before the lab starts, you may wish to introduce the concept of independence of mass and acceleration due to gravity with a small demonstration in front of the class. Pick a small ball and a larger ball, and point out that one is ten times the size of the other. Starting them from the same height, ask students to predict which ball will hit the ground first. Tell them to look closely, and listen to the sound of them hitting the floor. Drop them. Students should be able to hear, if not see, that they hit the ground at the same time.
• Go to http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html to view a QuickTime movie of David Scott dropping a hammer and feather on the moon (accessed February 2019).
• For greater accuracy calculating the acceleration due to gravity, consider using a Flinn PSWorks Photogate Timer (AP6998) in conjunction with a picket fence (TC1546). A picket fence is a long rectangular bar with evenly spaced black bands, that allows for highly accurate calculations of the acceleration due to gravity.

Answers to Prelab Questions

1. If a feather and a hammer are dropped at the same time on Earth, which will hit the ground first? What if they were dropped on the Moon? Mars? Justify your answer.

   On Earth and Mars, the hammer will hit first as they both have an atmosphere that will create air resistance that slows the feather more than the hammer. On the moon, they will both hit the ground at the same time since the Moon has no atmosphere.

2. If the acceleration due to gravity of the Moon is 1.6 m/s², how long will it take a feather to fall 1 m? What about the hammer?

   Using Equation 2 and solving for t,

   {12011_Answers_Equation_4}

   Both the feather and the hammer would take 1.1 s to drop one meter.

3. What are some of the possible sources of error in this experiment? What might you do to minimize these?

   Student answers will vary; examples include reaction time on the stopwatch will cause an error in the timing data—a longer drop would minimize this; giving the ball an initial velocity instead of just dropping it will throw off the results, so it will be very important to just release the ball instead of throwing it down, etc.

Sample Data

Mass of small ⅝" ball (g): ___16.31___
Mass of large 1⅓" ball (g): ___160.26___
Drop height (m): ___2.0___
Mass ratio of large ball to small ball: ___9.8___

Small Sphere Drop Data

Answers to Questions

1. Use Equation 2 to calculate the acceleration of each drop. Fill in the data table for each size ball.

   Acceleration should be calculated using a = 2d/t².

2. Use Equation 3 to calculate the percent error between the measured and accepted values for the acceleration due to gravity for each drop. Use 9.8 m/s² for the accepted value. Fill in the data tables.
   {12011_Answers_Equation_3}
3. What are some of the sources of experimental error in this experiment?

   Student answers will vary; examples include:
   
   With the Photogate Timers: The curved surface of the ball means that the photogates may not be measuring the same “leading edge” from gate to gate. Additionally, the ball had a little bit of velocity when it passed through the photogate, which means Equation 2 is an approximation, and not entirely accurate, etc.
   
   With the stopwatches: It was difficult to accurately measure the drop time as it happened so quickly. Human reaction time and error played a large part of this experiment, etc.

4. Calculate the average acceleration for each size ball and enter the results in the data table. Compare the average acceleration of the small ball to that of the large ball. What conclusion can be drawn about the relationship between gravity and mass?

   The acceleration of both the small and large ball were very close. Although the larger ball had a mass 10 times greater than the smaller ball, its acceleration was 10.5, only a little faster than the small ball with 10.9 and likely within experimental error. The acceleration due to gravity appears to be independent of mass.

Introduction

Do objects of different size or mass fall at the same rates? At first glance, the answer would appear to be “no.” Drop two steel balls of different mass and calculate the acceleration of each. The results might surprise you!

Concepts

• Free-falling objects
• Acceleration
• Gravity

Background

Galileo Galilei (1564–1642) was the first person to claim that all objects fall at the same rate, regardless of their size, shape or mass. He had difficulty convincing his contemporaries of this because everyday experience seemed to suggest otherwise. Everyone at the time thought that heavy objects, such as cannon balls, fell faster than light objects, such as small stones or feathers. Legend has it that Galileo attempted to convince his skeptics by dropping two cannon balls, one heavier than the other, from the Leaning Tower of Pisa. (This legend is likely a stretch of the truth, but he did perform similar experiments to try to prove to others that his theory was correct.)

The reason that an object such as a feather falls slower in air than a hammer is due to air resistance. Air creates friction and drag for all objects that travel through it. This drag has a tendency to slow down lighter objects (or objects with more surface area) more than heavier objects (or objects with less surface area). Hence, in air, a feather floats to the ground while a hammer falls quickly. In a vacuum, where there is no drag friction due to air, a heavy hammer will fall at exactly the same rate as a light feather. (A modern demonstration of this phenomenon occurred during the Apollo 15 moon landing when astronaut David Scott dropped a hammer and feather at the same time. As he watched the objects hit the lunar surface at the same time, Scott proudly announced that Galileo had been correct!) At the surface of the Earth, the acceleration toward the center of the Earth experienced by all objects is measured to be (on average) 9.8 m/s² (32 ft/s²).

With steel balls, however, air resistance is negligible, leaving gravity as the only force acting on the balls. When an object is dropped with no forces other than gravity acting on it, the object is said to be in free fall. Dropping two steel balls of significantly different weights will show that the acceleration due to gravity does not depend on the mass. Equation 1 shows how far an object will travel in a given amount of time with a constant acceleration.

d is the distance the object moves (in m)
a is the acceleration of the object (in m/s²)
t is the time (in s)
v_i is the initial velocity of the object

Experiment Overview

One lab partner will drop the ball from a set height of 2 m. Using a stopwatch, the other partner will time the interval between the release of the ball and the ball striking the ground. With the drop height kept constant and the time being thus measured, the acceleration can be calculated from Equation 2.

Materials

Prelab Questions

1. If a feather and a hammer are dropped at the same time on Earth, which will hit the ground first? What if they were dropped on the Moon? Mars? Justify your answer.
2. If the acceleration due to gravity of the Moon is 1.6 m/s², how long will it take a feather to fall 1 m? What about the hammer?
3. What are some of the possible sources of error in this experiment? What might you do to minimize these?

Safety Precautions

Wear safety glasses. Please follow all laboratory safety guidelines.

Procedure

1. Set up a “catcher’s box” on the floor to capture the steel balls after they have dropped on the floor. Note: This may be a small box, basket or cushion—anything that will prevent the balls from rolling across the floor.
2. Using a meter stick, measure a height of two meters against a wall (or any object) starting from the height of the capture box, and mark it with a piece of masking tape.
3. Choose one partner to drop the ball, one partner to time the drop, and one partner to retrieve the ball and record the data. Alternatively, the third partner may also time the drop, if a second stopwatch is available, in order to average the two times and reduce error.
4. Independently measure the mass of both the smaller ⅝" steel ball and the larger 1⅓" steel ball, and record these values in the Free Fall Student Worksheet.
5. Practice dropping the ball from the marked height a few times while the Dropper and Timer discuss and coordinate when to start timing. Note: Develop a system such as having the Timer call out “1, 2, 3, DROP!” and start timing. It will take practice to obtain reliable measurements.
6. When ready, begin recording the data in the Free Fall Worksheet.
7. Repeat steps 5 and 6 nine more times.
8. Obtain the second ball from and repeat steps 5 and 6.
9. Do the calculation on the worksheet.

Student Worksheet PDF

12011_Student1.pdf