Falling Physics

Teacher’s Guide

Intro

If someone drops two objects from the same height, one heavy, one light, which one will hit the ground first? If you are like most people, you may instinctively pick the heavier object. And why wouldn’t you? After all, rocks fall faster than feathers. There are other factors besides weight that affect the speed of an object as it falls. This experiment will help students explore those factors, such as gravity and air. Students will use both their eyes and their ears to figure out how mass affects the speed at which something falls.

Key Terms

Mass: A measure of the amount of stuff (or matter) an object has. Not to be confused with weight or volume. Mass only says how much actual stuff there is, not how big an object is or how hard something is pulling on it.

Weight: Mass (amount of stuff) times how hard the planet is pulling on it (gravity). This means that your weight on the moon will be 1/6 of that on Earth (gravity on the moon is 0.166 times of that on Earth). However, your mass will still be the same.

Force: The push or pull an object feels because of interactions with other objects. If the interaction stops, then there is no force. It is formally defined as mass times acceleration. For example, gravity is a force that represents the pull the Earth has on all objects.

Velocity: A measure of how fast something is going in some specific direction. Not to be confused with speed, which is only how fast something is moving. “The car was going 65 mph south on I-95” is a measure of velocity. “The rollercoaster was moving at 65 mph when Billy got sick” is a measure of speed.

Acceleration: How fast the velocity is changing. When something accelerates it changes how fast it is going or the direction in which it is moving. For a positive change in acceleration means that the object is moving faster, a car going from 30 mph to 40 mph. A negative change means the object is moving slower, the car is going from 40mph to 30 mph. Finally, a change in the direction of the object’s velocity without changing speed, such as if a car is moving North and turns East still moving, then the car accelerated because the direction of the car’s velocity changed. Remember that velocity is a vector with direction and magnitude, therefore changes in any (or both) of those factors will produce an acceleration.

Air resistance: The force air exerts on something moving through it. When an object with a bigger surface falls through air, it feels more air resistance. Air resistance does not depend on the mass of the object.

KEY QUESTION:

How does mass affect how fast an object falls?

Before the activity students should know:

Gravity from the Earth makes things fall by pulling objects toward the ground

  • There’s a difference between weight and mass.
  • There’s a difference between speed, velocity and acceleration.
  • That a force is mass times acceleration.
  • When something falls through air it experiences air resistance.

AFTER the activity students should know:

  • How mass affects the speed at which objects fall.
  • Why a hammer and a feather will fall at the same rate on the moon but not on Earth.


The Science Behind Falling Objects

If someone showed you two spheres of the same size but with different masses, say 1g and 10kg, and asked which would hit the ground first after being dropped from the Leaning Tower of Pisa, what would you say? If you’re like most people, you would say the 10kg sphere would hit the ground first. Aristotle said so too, and for 1,000 years everyone believed him. But doing the experiment would show you, besides a great view of Pisa, that in fact, both spheres hit the ground at the same time.

This is exactly what Galileo did, showing the world that objects of different masses fall at the same rate. (This is also a good example of why it is important to do experiments yourself and not to just take someone else’s word for it.) To start understanding why Galileo was right, we need to understand the difference between several physics words that are often jumbled together and confused: mass, weight, speed, velocity, acceleration, and force.

Let’s start with mass and weight. Mass is the amount of stuff an object has. Mass and weight are not the same thing: the mass of an object will stay the same no matter where it is in the Universe, but weight will not. If I had some amount of stuff, say an apple, and took it from the Earth to the Moon, I would still have the same amount of stuff: one apple (assuming I didn’t get hungry on the trip). No matter where I put that one apple, I will always have the same amount of apple, unless I eat it. This means that here or on the Moon, my apple has the same mass. Mass has the unit of kilograms.

Now, weight is the amount of mass times the force of gravity, or how hard a planet is pulling an object towards itself. Going back to our apple, that apple would be a lot easier to lift and put in my mouth on the Moon than on Earth, right? The Earth pulls on the apple harder than the moon would, because the pull of the Earth (gravity) is stronger than that of the Moon. Even though I have the same amount of stuff, the same mass, the weight of my apple is greater on Earth than it is on the Moon. Weight is mass times acceleration, this acceleration is from the gravity force that pulls the objects toward the ground. Weight has the unit of Newtons, which is the units of mass (kilograms) times the units of acceleration. But how do we sometimes get units of mass when we ask for the weight of things? That is because the scales we use to measure weight factor in the acceleration of the pull of the Earth on the object. This factor is a constant on the Earth, meaning that it is always the same if you are on Earth. If I were on the moon and my apple weighs .25 Newtons, I will need to know the value of the acceleration of gravity on the moon to find its mass.

Now on to velocity, speed, acceleration and force. Velocity and speed are two different things, but the difference is very small. Velocity gives more information than speed does, because it tells us how fast something is moving in a specific direction. Speed is how fast something is going, but says nothing about the direction of that motion.. Acceleration says how much the velocity is changing in a specific direction. If something has a constant velocity, say moving south at 65 mph, there is no acceleration.

Now how can you make something accelerate? To accelerate, an object needs to feel a force, that means a pull or a push. If you kick a football with some amount of force, the football is going to change its velocity, which means it’s accelerating. Force is mass times acceleration. This means that force is the amount of stuff times how hard it is being pushed or pulled. The bigger the force (the stronger the kick), the bigger change in the football’s acceleration, since its mass doesn’t change.

When something falls, it falls because of gravity. Because that object feels a force, it accelerates, which means its velocity gets bigger and bigger as it falls. The strength with which the Earth pulls on something in the form of gravity is a type of acceleration. Earth pulls on everything the exact same amount. Everything gets accelerated towards the Earth exactly the same way. The force that objects feel may be different because they have different masses, but the acceleration on Earth they experience is exactly the same. Weight is the force that acts on the mass due to gravity, because it is how much stuff there is times the acceleration at which is pulled towards the Earth, or any planet or moons. Because Earth gives everything the exact same acceleration, objects with different masses will still hit the ground at the same time if they are dropped from the same height.

The first time you say that, no one will believe you because everyone has dropped a marble and a feather at the same time and they hit the floor at different times. That is not because of differences in the acceleration - which is constant on Earth, it is because air is pushing against the object in the opposite direction the Earth is pulling. This force is caused by air resistance.

The less massive the object is, the more the force of air resistance slows the object down as it falls. If two objects were dropped on the moon, where there is no air, they would fall at the same rate no matter how much they differ in mass. The shape of the object can impact how much it is affected by air resistance. For example, if you drop a piece of paper horizontally, it has a lot of surface that is exposed to the air resistance. But if you drop the paper vertically, on the thin side, then there is less surface exposed to the air resistance. This means that, in that position, the paper will feel less push from the air and the same pull from the Earth. Two pieces of paper with the same mass dropped from the same height but with one in the horizontal position and the other in the vertical position will not hit the floor at the same time.

Astronaut Neil Armstrong did an experiment on the moon to convince everyone that Galileo was right, that two objects of different mass and shape -in this case a feather and a hammer - in the absence of air resistance will hit the ground at the same time.

Experiment 2 that you will be performing, two objects of different masses that roughly experience the same air resistance will be dropped and hopefully convince your kids that mass has nothing to do with how things fall.

Experiment 1

Materials

  • 2 equal-sized pieces of paper
  • Chair or table (or both)
  • A ruler or metric tape (optional)
  • Beam balance (optional)
  • A camera to record the experiment (optional)
  • A chronometer or something to measure the time (optional)

In the student’s guide we have asked the students to design their own experiment to test if two objects of the same mass but different shape hit the ground at the same time. The idea is to encourage them to be creative, to understand how to design experiments, and to think like scientists and engineers. They are given a set of materials that they can use to do their experiments. This is to prompt them, but they should be allowed to use other materials in their design. As the teacher, you can ask prompting questions to get them to think about the different aspects of the experiments. Below are the full instructions for one possible design.

The goal of the experiment is for students to understand that mass is not a factor that affects how objects fall, that they notice the shape matters and why it matters. Crumpling the paper or changing the direction in which the paper is dropped can support those ideas. They need to figure out which variables they should control for, for example dropping the papers at the same time or the presence of a strong air current, and consistency of the repeated experiments.

We ask the students to follow the scientific method to design the experiment.

The scientific method has five basic steps, plus one feedback step:

  • Make an observation.
  • Ask a question.
  • Form a hypothesis, or testable explanation.
  • Make a prediction based on the hypothesis.
  • Test the prediction.

Setting up

  • Take the two pieces of paper and crumple one into a ball.
  • If you have a beam balance, find the mass of each piece of paper. Write those values on your notes
  • Measure the height from which you will drop the pieces of papers. Make sure it is the same height. Write the height value on your notes
  • Get your timer and camera ready for recording
  • Come up with a hypothesis: Which piece of paper do you think would hit the ground first? The lighter one or the heavier one?
  • Drop the pieces of paper at the same time

Students should reflect on how the masses of the two pieces of paper were the same, yet the crumpled piece hit the ground first. Why?

Experiment 2

For this experiment students are asked to design a way to test if two objects of different mass but similar shapes hit the ground at the same time. They have been given a different set of materials from Experiment 1. In this case there are other variables to control for, such as how similar or different shapes affect the result and the difference in mass between the two objects.If the mass is double but the shape is the same, will the objects hit the floor at the same time? As with Experiment 1, we have given you a possible set up for the experiment. But again, students should have freedom to create their own designs.

Materials

  • 2 balls similar in size but different mass 2 aluminum tart pans
  • Chair or table (or both)
  • A ruler or metric tape (optional)
  • Beam balance (optional)
  • A chronometer or something to measure the time (optional)
  • A camera to record the experiment (optional)

In the kit there are different sets of balls, repeat the experiment with all the possible wooden and rubber balls combinations. Make sure to label the balls and measure them to make good comparisons.

If you are working at home and do not have the exact materials, you can always substitute the balls with clay or playdough (see suggested resources for a recipe of homemade playdough). If you do not have either clay or playdough, then find two objects around the house that have the same shape but different weights. For example, two identical water bottles, one full and the other one with less water or no water. The purpose of this experiment is to test if objects with different masses but the same shape fall at the same time. Instead of aluminium tart pans you can use aluminum foil or any other type of paper/foil that will produce a sound when the dropped objects hit them.

As with activity 1, we ask the students to follow the scientific method to design the experiment.

Setting up

  • Place the two tart pans on the floor, bottom up, about a foot apart.
  • Select two equal sized balls
  • If you have a beam balance, find the mass of the two balls and write those values on your notes
  • Get your timer and camera ready to record your experiment
  • Come up with a hypothesis: Which ball do you think would fall faster? The lighter one or the heavier one?
  • Drop the balls at the same time
  • How many bangs did you hear on the tart pans each time you dropped the balls

Students should pay attention to how many bangs they heard each time they dropped the balls. Did it depend on how different the masses of the balls were? Which ball hit the floor faster?


Corresponding Extension Activities

https://colab.research.google.com/drive/1zTsyJ5SZ8bFXugZMmCT0pUtRWgf0pXcg?usp=sharing

https://colab.research.google.com/drive/1rliGPMBM7Ixy97Z0xpzADKcq4_aRzqIS?usp=sharing

Suggested Resources

Videos for younger children

Gravity & Free Fall

Danger! Falling Objects

Simulations & Videos:

Was Galileo Right?: Investigate the effect of gravity on objects of various masses during free fall. Predict what the position-time and velocity-time graphs will look like. Compare graphs for light and heavy objects.

Free Fall Model: This simulation allows students to examine the motion of an object in free fall.

Free Fall Fall Air Resistance: This simulation allows students to compare the motion of free falling objects with and without the influence of air resistance.

Veritasium: Misconceptions About Falling Objects 3.5-minute video