Project: Calculating the Acceleration Due to Gravity

Context

Gravitational acceleration is one of the most interesting topics studied in Physics and it plays an undeniable role in defining life as we know it. It is what keeps our feet on the ground, the oceans in place and the birds flying.

This invisible force keeping us bound to Earth was first studied by Galileo Galilei in the XVII century. He was the first to propose that the acceleration of an object in freefall would be constant - a revolutionary idea at the time that contradicted the dominant Aristotelian thinking. However a century later, it was Isaac Newton who was able to really quantify the idea in his famous universal law of gravitation.

But what is the acceleration due to gravity? Technically it is the increase of velocity of an object caused by the force of gravity. On Earth, the acceleration due to gravity is approximately 9.8 m/s², meaning the velocity of an object in freefall will increase by 9.8 meters every second that passes. However, its value changes depending on your location on Earth’s surface and on the altitude.

Knowing how and why the acceleration due to gravity happens allows us to make startlingly precise predictions on how objects will move. Imagine, for example, if we wanted to calculate how a space probe would need to be launched in order to accurately reach the orbit of Mars, or how a plane needs to plan its landing, both scenarios rely on an accurate understanding of gravitational acceleration.

In our daily lives, we don’t often think about the critical role played by the acceleration due to gravity. Think of gravity when pouring yourself a cup of coffee, when throwing a ball or even walking. Understanding the acceleration due to gravity allows us to understand the world we are in, and explore beyond it.

Here are a few resources you can check out for a deeper dive into the subject:

1. Halliday, D., Resnick, R., & Walker, J. (2018). Fundamentals of Physics: Gravitational Acceleration
2. Educational video in portuguese from the portuguese YouTube channel "Ciência Todo Dia" "Why is gravity 9,8 m/s²?" (in portuguese)
3. Educational video in portuguese from the portuguese YouTube channel "Manual do Mundo" "What is acceleration due to gravity?"(in portuguese)
4. Article from the portugese Wikipedia: "Gravity" (in portuguese)

Hands-on Activity

Activity Title: "Calculating the acceleration due to Gravity"

Objectives

This project is designed to provide the students with a hands-on experience with one of the most important concepts of Physics - Gravitational Acceleration.

Students will have the chance to calculate the acceleration due to gravity for two different scenarios - on Earth and on a fictional planet created by the team.

Students are expected to develop a more informed understanding of what gravitational acceleration means and how it can vary based on specific characteristics of planets.

Detailed Description of the Project

Teams of 3 to 5 students will do two simulations:

• First they will measure the acceleration of gravity on earth using the simple experiment of a free falling object, measuring its acceleration experimentally.
• Then they will imagine a fictitious planet, with specific characteristics defined by the team (such as its mass and radius) and calculate the expected acceleration of gravity on this “new planet”.

Required Materials:

1. A ruler or measuring tape that is at least 2 meters long
2. A small, heavy object that can be dropped without causing damage (such as a tennis ball or a lump of clay)
3. A stopwatch
4. A computer with internet access to do research and calculations
5. Paper and pencils for note taking

Step-by-Step guide for the Activity

1. Measuring the acceleration due to gravity on Earth:

• Using a ruler or measuring tape, measure out a 2-meter distance in a safe location, clear of any obstacles. Mark the 2 meters height.
• A team member should hold your object at the 2m mark, and another team member will be in charge of the stopwatch.
• Drop the object and start the stopwatch at the same time. Stop the stopwatch once the object hits the ground. Note the time it took.
• Repeat the experiment a number of times to obtain an average time.
• Using the equation: g=2h/t² (where h equals the height and t is your average time), calculate the acceleration due to gravity. Compare with the accepted value for the Earth’s acceleration due to gravity 9.8 m/s².

2. Creating and measuring a fictional planet's acceleration due to gravity:

• As a team, imagine a planet. Determine a mass for the planet and determine a radius for the planet.
• Use Newton's universal law of gravitation to calculate what the fictional planet’s acceleration due to gravity would be using the equation: g=Gm/r² (Where G is the Gravitational Constant (6.674x10^-11 N(m/kg)^2) and m is the planet’s mass, while r represents the planet’s radius).
• Record all of your findings and observations, for later use when writing up your project.

Deliverables / Write up

After doing the experiment, students are required to write a complete report that includes:

1. Introduction: Theoretical contextualization on the concept of gravitational acceleration, the relevance of the topic. Description of the project’s objectives and the activities to be developed.
2. Development: Description and detailed account of the activities done, theoretical discussion of the concept of gravitational acceleration and Newton's universal law of gravitation. Presentation and analysis of results obtained in the experiments - experimental value of the acceleration due to gravity on Earth compared with the theoretical value. Description of the characteristics of the created fictional planet, including mass and radius, acceleration due to gravity calculations on this planet.
3. Conclusion: Analysis of results and reflection on the concepts learned, discussion on possible errors found in either experiment. Connection between the experiments done and real-world applications of the concept.
4. Bibliography: Citations of sources consulted during the development of the project.

The report is due one month, at most, after the beginning of the project and it will be evaluated taking into account the theoretical content and accuracy of experiments done, quality of presentation of the results and analysis made.