Acceleration Down an Incline



Acceleration Down an Incline

There is a well-known story that Galileo dropped two objects of different

weights from the Leaning Tower of Pisa in order to show that all objects

accelerate toward the Earth at the same rate, regardless of their weight

as long as air resistance is negligible. Historians, however, are quite

certain that Galileo never performed such an experiment.

Galileo’s experiments with acceleration involved rolling balls down an inclined plane. He did this out of necessity because of his inability to make precise measurements of the short time intervals needed for measuring the acceleration of objects in free fall. The inclined plane’s angle could be adjusted until the time for the ball to roll to the end was long enough for even the crude time-measuring devices of his day to produce useful results.

In this exercise, you will examine acceleration by measuring the time needed for an object to roll various distances down an inclined plane – much like Galileo did around 400 years ago.

Gathered Data:

• Speed is the distance an object travels per unit of time. Speed can be expressed as kilometers per hour (km/hr), meters per second (m/s), and so on. In most cases, objects don’t travel at a constant speed. Therefore, the average speed is used to describe the motion.

[pic]s = speed, t = time, and d = distance

• Acceleration is the rate at which an object’s speed changes. Acceleration can be expressed as meters per second per second (m/s/s or m/s2). Forces such as gravity, air resistance, and friction can cause an object to decelerate (decrease speed over time). Other forces can cause and object to accelerate (increase speed over time). If the car does not encounter these forces and travels at a constant speed, then it is not changing speed and there is no acceleration or deceleration.

a = acceleration, v = change in velocity or speed, and t = time

[pic]

v = final velocity or speed – initial velocity or speed

Purpose:

1. Examine the acceleration of an object rolling down an inclined plane

2. Determine the shape of a “Distance vs Time” graph for an accelerating object

3. Determine the mathematical relationship between the distance and time an object travels while it is accelerating

Materials:

inclined plane, “Hot Wheels” car, track, stopwatch, meter stick or measuring tape

(Note: marbles may be used if toys cars and track are unavailable)

Hypothesis:

What will be the average speed of a marble rolling down a 20cm tall ramp and traveling 5m?

Will the marble continually accelerate as it travels the 5m? Or will it decelerate?

Vf= a*t when Vi = 0

d = ½ at2 when Vi = 0

     Where Vf  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  

Va= d / t 

In this experiment, you will be able to calculate the average velocity, Va.  The final velocity, Vf, will be twice as large (2Va)

Procedure:

1. Measure and mark from one end of the inclined plane the distances indicated in the data table.

2. Place your inclined plane on something (a book?) so that one end is slightly elevated. Be sure to support the track so that it does not bow.

3. Use the stopwatch to determine how much time is needed for the car (marble) to roll each indicated distance down the incline. Record this time in the data table.

4. Perform two time trials for each distance and average them.

5. Use MS Excel to make a graph of “Distance vs Time.”

6. Use the MS Excel “Add Trendline” function to draw and calculate the best-fit curve to your data points. Place this on your graph.

7. Answer the questions at the end of this activity.

|Distance, meters |Time, seconds | |Average Time, |Acceleration | |

| | | |seconds | | |

|0.10 | | | | | |

| | | | | | |

|0.30 | | | | | |

| | | | | | |

|0.50 | | | | | |

| | | | | | |

|0.70 | | | | | |

| | | | | | |

|0.90 | | | | | |

| | | | | | |

|1.20 | | | | | |

| | | | | | |

|1.60 | | | | | |

| | | | | | |

|2.00 | | | | | |

|2.30 | | | | | |

Questions:

1. How does a “Distance vs Time” graph of accelerated motion compare with a “distance vs time” graph of non-accelerated motion (constant velocity)?

2. How can you tell by looking at a “Distance vs Time” graph whether or not the object has constant or changing speed?

3. What does the shape of your graph and the “best-fit” equation tell us about the mathematical relationship between distance and time for a uniformly accelerating object?

4. When looking at his data, Galileo discovered that an object would travel 4 times as far (22) in twice the time, 9 times as far (32) in triple the time, 16 times as far in (42) in quadruple the time, etc...

Use your graph to find the ….

|time to travel 0.40 m ____ |time to travel 0.10 m ____ |ratio = ____ |

|time to travel 0.60 m ____ |time to travel 0.15 m ____ |ratio = ____ |

|time to travel 0.80 m ____ |time to travel 0.20 m ____ |ratio = ____ |

|time to travel 1.00 m ____ |time to travel 0.25 m ____ |ratio = ____ |

|time to travel 1.20 m ____ |time to travel 0.30 m ____ |ratio = ____ |

|time to travel 1.60 m ____ |time to travel 0.40 m ____ |ratio = ____ |

|time to travel 2.00 m ____ |time to travel 0.50 m ____ |ratio = ____ |

| | | |

|time to travel 0.90 m ____ |time to travel 0.10 m ____ |ratio = ____ |

|time to travel 1.35 m ____ |time to travel 0.15 m ____ |ratio = ____ |

|time to travel 1.53 m ____ |time to travel 0.17 m ____ |ratio = ____ |

|time to travel 1.80 m ____ |time to travel 0.20 m ____ |ratio = ____ |

|time to travel 2.07 m ____ |time to travel 0.23 m ____ |ratio = ____ |

5. Do your results seem to agree with Galileo’s discovery? _____ Why/Why not?

6. What could you do in order to experimentally test whether or not all objects accelerate at the same rate, regardless of their weight?

7. How do you think the angle of incline affects this experiment?

8. What should happen to the time values in your data table if the incline is made steeper?

9. What should happen to the ratios in question #4 if the incline is made steeper?

10. List possible sources of error in this lab.

[pic]

1. Look at your hypothesis. Address each question as whether your guesses were true or false and how close you were.

2. Draw a diagram showing the exact path of each trial. Be detailed as to the exact points the ball might have curved in its path.

3. Did your ball travel at a constant speed? How do you know?

4. How could you change the experiment to make the ball decelerate faster?

5. How could you change the experiment to make the ball accelerate faster?

6. How could you change the experiment to make the ball not accelerate or decelerate for an entire 5m?

7.

a. Is the acceleration in Part 1 constant?  What about the velocity?

b. Why was Galileo unable to accurately directly measure the velocity of falling bodies?

c. How would Aristotle explain wood burning?  A rock falling?

d. Can you prove mathematically that Vf = 2Va?

e. 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?

f. How does the mass of an object effect it’s rate of acceleration during freefall?

g. What are the sources of error in your experiment?

1.

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