Testing Galileo’s Ramp Hypothesis

Wall Coaster

by Janice VanCleave

www.scienceprojectideasforkids.com

Objectives

Students will:

• study the motion of freely falling objects;
• student the motion of objects on a ramp at different slopes, angles, and heights.

 

Background

The Italian scientist Galilei Galileo (1554-1642) did not have accurate timers. Thus Galileo could not with accuracy test his hypothesis about the motion of free falling objects. Galileo’s hypothesis was that free falling bodies accelerate uniformly, thus as they fall they increase in speed by an equal amount during each time interval. This means that from rest, a falling object moves twice as fast after two seconds than it did after one second and three times as fast after three seconds, and so on. With modern day timing tools this hypothesis can be relatively easy to test. But, not so for Galileo. This scientists used the beat of his heart as well as a water-clock to measure time, but things fell too fast for Galileo to measure the velocity at one second time intervals.  Galileo designed a way to slow the motion of objects due to the pull of gravity. 

Galileo Slows Down Motion
Instead of dropping an object so that it would free-fall, Galileo timed the motion of balls rolling down ramps. Galileo’s hypothesis was that balls rolling down ramps of equal height would reach the same velocity as a free-falling ball no matter the slope (steepness) of the ramps. Galileo based his hypothesis on the results of his investigations with pendulums.  See Galileo’s pendulum investigations     ( https://scienceprojectideasforkids.com/2013/galileos-pendulum-exp/  ) for information and instructions about Galileo’s experiments using a pendulum to test his hypothesis about falling objects . 

Discover for yourself how Galileo used ramps to compare the velocity of objects due to gravity.  

Materials:

two 10” Wall-Coaster tracks

tack

marble (marble or rubber marble that easily rolls down the coaster track

Engage:

1. In advance, position two coaster tracks on a vertical surface, such as a wall or chalk board. One track must be horizontal so that a marble placed on this horizontal track will not move. The second track is to be vertical.

How to Secure the Coaster Track

Use pieces of tack and roll them into pea-size balls. On the flat side of a coaster track, place two tack-balls, one at each end. With your thumb on the inside of the track, press the track so that the tack-balls are flattened against the wall.

2. Provide background information about Galileo. Then, discuss the effect of gravity on objects sitting on a flat horizontal surface. Point out that gravity is a force between two objects and that gravity is actually one of the smaller forces in nature. But, if the mass of one object is great enough it can pull objects with less mass toward toward it. The force of Earth’s gravity on objects is an example.

Note that earth’s gravity pull everything down, which is toward the center of the Earth. This can be demonstrated by placing a marble on the horizontal coaster track.

3. Place and hold a marble at one end of the horizontal track. Ask students what they think will happen when you release the marble.

4. Hold your hand at the end of the track to catch the marble. [The marble should remain in place because gravity is pulling the marble down causing it to push against the coaster track. The same thing would happen if the marble were placed on any flat horizontal surface, such as a table.]

5. Repeat step 1 with the coaster track in a vertical position. Don’t forget to be prepared to catch the marble at the end of the track. [The ball actually free-falls, meaning it moves down because of the force of gravity pulling it toward the center of the earth. 

6. Remind students that the earth is pulling on the marble and the marble is pulling on the earth. Since the mass of the marble is so small in comparison to the mass of the earth, it is the marble that moves. This motion is vertically toward the center of earth. The vertical force of gravity on an object is equal to the weight of the object. Gravity pulling free falling objects down results in the objects accelerating at a rate of 9.8m/s².

Sitting on a horizontal surface, gravity is still pulling on the marble but there is zero motion, thus there is zero acceleration. The force due to gravity on objects moving down a ramp with a slope between horizontal and vertical will have an acceleration between zero and 9.8m/s².

Explore:

Students working in groups, will discover how the height of the coaster track affects the velocity of the marble falling down the track. 

Clues:

1. Demonstrate how to secure the track to the wall.

2. Draw a diagram to to show students that the height of the track is measured from the horizontal line drawn from the bottom end of the track. Note that the height and horizontal lines form a ninety degree angle where they meet.

3. Point out that the length of the ramp (the track) remains constant.

4. The velocity is not being calculated. Instead, time is being used to make comparisons of velocity of marbles moving down the ramps at different heights. The faster the marble moves down the track the faster is its velocity. A timer can be used to measure the time of the marble’s movement on each ramp or students can determine by observation which height caused the marble to move faster.  

Adding Rigor

1. Ask each group to collect data for specific heights. Groups will share their results so that each group can crate a bar graph showing the results for each height. 

Remind students that the independent variable (the one you change) is on the horizontal (x) axis and the dependent variable (the one responding) is on the vertical (y) axis.

More Rigor

For each track height, calculate and compare their slopes. Facts Known: The rise (height) and the length of the ramp. Use the Pythagorean Theorem to calculate the run (horizontal). 

Explain

Guide students to use the data from their experiments to explain why the time differs if the height of the track is different. Remind them that at horizontal the acceleration is zero and at vertical the acceleration of free-falling objects is 9.8m/s^2.

Thus, tracks at angles between horizontal and vertical will have accelerations between 0 and 9.8m/s^2. The greater the angle the greater is the acceleration of the ball. The greater the acceleration the faster the velocity in one unit of time. Remind them that acceleration of free-falling objects has the greatest acceleration due to the force of gravity. 

Students should learn that acceleration means that the velocity of the ball increases with every second of time it falls down the ramps. 

Elaborate: 

What effect does the height of the ramp have on the final velocity of the marble if the slope of the ramp is constant?

Galileo’s hypothesis was that as long as the height of ramps were equal, the final velocity of the ball rolling down the ramps would be equal.

 

CLUES:

Students can set up one ramp using a 10 inch coaster track.  Students need to know that the slope of a ramp is determine by dividing the height (rise) by the horizontal (run). The diagram shows changes in height by placing the marble at different places on the track. Note that the angle of the ramp remains the same, thus the slope remains the same. 

1. Independent variable: height of the track

2. Dependent variable: time to move down the track Using the same ramp, the angle of the ramp doesn’t change no matter where the marble is placed on the coaster track. 

Evaluation:
Test Galileo’s Hypothesis : With a constant height, the velocity of objects moving down ramps with different slopes is the same. 

Students should be able to design an experiment to test Galileo’s hypothesis. The diagram is one way. The angle of the tracks doesn’t matter as long as the height of the marble is the same.