Lab 3 - Acceleration of Gravity on an Inclined Plane

Objective: To find the acceleration of gravity by studying the motion of a cart on an incline, while gaining more experience with the tools that will be used during lab.

Procedure: Using the motion detector, aluminum track, and cart we tested the acceleration of gravity.  The steps were pretty simple in this process.  First we leveled the track, with one end elevated.  The motion detector was located at that elevated end to track the cart.  Measurements were taken to calculate the angle of the track, which would be needed later to calculate the gravity.  A few test runs were done to make sure that the motion detector was working, and to give us an idea of how hard to push the cart.  As the cart traveled up the track it would slow to a stop and come back to the bottom of the track.  The motion detector would capture the movement of the cart and the computer would graph it.

Data: For the first set of test runs, block of wood was turned on its side to elevate one side of the track.  The measurements were taken to determine the angle of the track:

 Using the calculator, sin theta = 9.55/228 = 2.40 degrees.

The motion graph for the first set of tests we all similar to this one:

Motion graph at 2.40 degrees

Once these were understood, the testing could begin.  For this height, 3 tests were completed.  The graphs from these tests are shown below:

Test 1

Test 2

Test 3

Once these were completed and everyone felt comfortable with the results, The track was raised and 3 more tests were performed.  Here are the corresponding graphs:

Using the calculator, sin theta = 18.65/228 = 4.69 degrees.

Motion Diagram at 4.69 degrees

Test 4

Test 5

Test 6

Possible sources of error: This lab seemed to be stricken with error.  The first go around one of the linear fits was not completed, and this was not noticed until after the equipment was put away.  This was partially due to the fact that most of the team members were not reading the documentation on how the lab was to be done.  As a result, after half of the team had left, the second half stayed to completely redo the lab.  Most of the team just had to take his word that he did the lab correctly.

Common sources of error are the measurements.  We have measured the best we can with the yardstick that was provided, and the motion detector gets distracted easily and picks up various other movements.  This was the cause for several runs to be completed a second and third time to be able to get data that we could work with, and was closer to the expectations.
 

Questions: For each run, we were expected to calculate the force of gravity using the formula that was provided in the write up.  For each test run, the calculations are illustrated below.

Conclusions:

Lab 2 - Acceleration of Gravity

Objective:  To determine the acceleration of gravity for a free falling object, and to continue to gain experience with the data collecting hardware and computer programs.

Procedure:  Once the hardware is set up and tested, toss a ball into the air and track the position versus time and velocity versus time using the graphing software.  Track this for at least 5 repetitions and average out the data.

Data:  Below are the 5 data captures that were used for this experiment.  Curve fit and line fit were used to determine the best tests to use



Ball Toss Test 1

Ball Toss Test 2

Ball Toss Test 3

Ball Toss Test 4

Ball Toss Test 5

Possible sources of Error:
1. The easy answer to this is that we had different students tossing the ball in different ways.  One student would throw the ball higher than another, there was hesitation and the way the ball was held seem to make a difference as well.

2.  Since the tracking sensor is just that, and sensor, it would sense other movement with the movement of the ball.  For example, several of the test that were not used were due to the movement of the ball thrower, people walking by and other movements that occurred during the testing.

3.  Our own interpretation as a group.  What I mean by this is that if one of us thought that it was a good result, someone else may have wanted to throw it out.  This may have caused us to settle for a less accurate test, or may have given us an improvement.  Hard to say really.

Questions:
1. Why should it be a parabola?  The position versus time graph should be parabolic because gravity = 9.81 m/s^2.  Acceleration is constantly slowing down on the way up, and constantly speeding up on the way down at the same rate.  In relation to this experiment, gravity slowed down the ball on the way up, and sped it up on the way down.  When interpreting to velocity versus time, the line is linear.

2. Why does the slope have a negative slope, and what does the slope of this graph represent? The graph represents gravity, and since gravity is -9.81 the linear graph will slope in the negative direction.

3.  Results from falling body experiment.

Percent error = (measured - actual)/actual * 100

Actual = 9.81

Average from the 5 Tosses

Conclusion: The experiment produced results that were close to what was expected.  The percent error could have been better with a little more time. and more tests.  The results were pretty close to the given force of gravity that was used in the percent error calculation.

In the end, we were able to determine a close proximity to the force of gravity with the experiment that was performed.  Given additional time and practice, I feel confident that we could have come very close to 9.81.