Gravity and the Laws of Motion: Ramp Lab¹

Introduction:  Until the time of Galileo, everyone accepted the Aristotelian concepts of physics. Aristotle taught that everything tries to seek its “proper place”.  In Aristotle's view, lighter objects fall more slowly than heavier ones, simply because lighter things contain more of the lighter elements, air and fire which tend to rise, and heavier things tend to fall faster because they contain more earth and water. Similarly, Aristotle said that the natural state of an object is to be at rest, so that an object will stop moving as soon as the force acting on it is removed. Aristotle had no concept of acceleration.

Galileo did a series of experiments to show that all bodies accelerate toward the earth and that they all accelerate in the same way. He also showed that in the absence of friction, bodies would keep moving forever. In effect, he achieved a partial understanding of gravity, and he discovered the concepts of acceleration and inertia. Galileo (and Newton after him) showed that the acceleration of gravity is a constant for all objects at the surface of the Earth, which means that the velocity of a falling object increases continuously. In Newtonian terms, Galileo found that the following relations hold:

V_f= at

d = ½ at²

     Where V_f  is the final velocity of the object after falling for time, t, the acceleration is a and d is the distance the object has fallen. The average velocity (of any object) is just  

V_a= d / t 

In this experiment, you will be able to calculate the average velocity, V_a.  The final velocity, V_f, will be twice as large.  

Available equipment:

1. Balls of different materials and sizes

2. Scale for weighing the balls

3. Ramps and air tracks (“Inclined planes”)

4. Stop watch

5. Ruler  

6. NO PROTRACTORS!!

Procedure: 

Part 1:  Galileo's Experiments (Velocity and Acceleration)

Galileo found that he could not measure motions of falling bodies directly, because they accelerated too quickly. Instead, he did experiments by rolling balls down inclined planes, so that the acceleration was much slower. This is one approach that you will follow in this exercise. However, there are two problems with this technique. The first is friction. A rolling ball is not subject to very much friction, but the friction is not zero. However, there is a more serious issue that Galileo probably did not recognize. As a ball starts to roll down the ramp, some of the gravitational potential energy goes into making the ball spin - and of course the ball will continue to roll when it gets to the end of the ramp. So Galileo could not have gotten the right value for the acceleration of gravity. But he had the right idea.

 Set up a ramp at an angle shallow enough so that you can measure how long it takes to roll down, and not so shallow that friction becomes the dominate force. Record the angle of the ramp and the length of the ramp in your lab notes. With the help of a partner, measure how long it takes an object to go down the ramp. Start with the ball one quarter of the way up from the bottom of the ramp, then one half, then three quarters and finally start with the ball at the top of the ramp. In each position, make several measurements of the time it takes the ball to roll down to the end. Use the above formulas to calculate the final velocity and the acceleration of the ball. Repeat this procedure using a total of three different angles for one ball.  Perform another trial using a ball of a different mass at a previously tested angle.

 Acceleration of Gravity – Air Track Experiment

We can do better than Galileo did, using an air track. The air track is an aluminum bar with holes drilled into it, and an air hose connected to one end. A V-shaped cart fits over the track, and is lifted off the track by the air, so there is almost no friction. There are also no rotating objects to worry about. Set up the air track so that one end is lifted just enough for the cart to begin accelerating smoothly along it. Measure the sine of the angle of inclination of the track to the horizontal. You can do this by measuring the length of the track and distance the top end has been raised. The ratio of those two numbers is of course the sine of the angle. Use the same techniques you used above to measure the velocity and acceleration.  Repeat this procedure using a total of three different angles. 

Data:

Ramp:  3 different angles (with constant mass) + 2 different masses (with constant angle) = 5 scenarios total

Air Track:  3 different angles (with constant mass) + 2 different masses (with constant angle) = 5 scenarios total

Be sure to follow the directions above, with respect to dividing your Ramp and Air Tracks into proportional lengths!!!

Data Table:  Create a data table for all ten scenarios that includes values for mass, angle, average velocity, final velocity, average acceleration, and calculated g for each scenario, plus average g for the ramp, air track, and a combined average.

Graphing Your Results: 

Analysis:

Calculate the actual acceleration of gravity, g, with the data you collected in the lab and the relation

g = a / sin(i) 

where a is your measured acceleration in m/s², and i is the angle of inclination of the air track.

Present all of your data and results for V_a , V_f , a, and g in a properly labeled data table.

 Questions:

1. Is the acceleration in Part 1 constant?  What about the velocity?
2. Why was Galileo unable to accurately directly measure the velocity of falling bodies?
3. What does “Aristotelian” mean?  What four elements did Aristotle think the world was made of?
4. How would Aristotle explain wood burning?  A rock falling?
5. Can you prove mathematically that V_f = 2V_a?
6. How is it possible to determine g, the rate of acceleration due to gravity for a freely falling object, by rolling balls down an inclined plane?  Hint: at what angle does g=a?
7. How does the mass of an object effect it’s rate of acceleration during freefall?

¹Adapted and partially copied verbatim from http://www.bu.edu/astronomy/manuals/AS101/gravity.pdf