Physics 105

Measuring the Acceleration Due to Gravity

Introduction:

We will study the motion of a freely falling body and, in particular, measure the acceleration due to gravity.  Using the kinematic relationships used in class, you know that if you measure any two of the three kinematic variables velocity, displacement, or time, you can calculate acceleration.

NOTE: For this lab there are two ways of measuring g discussed below: Video Analysis and Galileo's Method. You may choose to perform whichever measurement you  prefer. (You can do both if you really want to, but it is not at all necessary.)

Video Analysis Lab

Equipment

• smartphone or video camera
• object to drop: e.g. ball, shoe, but not a sibling or a feather

Procedure

If you have an iPad or iPhone, you should download the Video Physics app. You can videotape a falling object, and then analyze the video frame by frame, described below. OR you can also video the motion (without Video Physics) and download it to your computer as below.

You can take a video of a falling object, and download or send the video to your computer, and then open it up within LoggerPro, which is available free to students in this course. You can download and install LoggerPro 3.15, instructions can be found at the class Moodle site.

Video analysis is pretty intuitive. The video analysis program will allow you to measure the position vs. time and speed vs. time of a falling object. In video analysis, you will drop an object while videotaping it; you need to have a known distance or measuring instrument in the frame of the video. You do need two poeple: one to hold and drop the object, and the other to take the video. Video the falling object, keeping the camera still, and have a known distance (ruler, person whose height you know, something else with known distance) in the image. Either use an iphone or ipad with Video Physics, or video the falling object and copy the video to a computer, and open it within LoggerPro (in LoggerPro: "Insert - Movie" from menu at top). Using Video Physics or LoggerPro, track the object by clicking on it frame by frame, and be sure to set the scale with the known distance in the image. Copy the data set created into Excel.

At worst, if none of the above will work for you, your instructor may supply you with a video and accompanying dataset that has been captured for you. This will only be used if you have exhausted all other possibilities.

Analysis:

Hints: check out Excel Hints for graphing two columns of data, for trendlines, and statistics of the best fit line (linest or regression).

1. Decide which variables you are going to use to graph which will allow you to determine acceleration. Be careful! Be sure that you choose something to plot that has a linear relationship. In other words, distance vs. time is not expected to be linear, but velocity vs. time is. In addition, distance vs. time^2 has a linear relationship. Verify these claims by checking the kinematics relationships.
2. Create the columns of data that you are going to plot. If the data needs to be manipulated, have Excel do this, don't use your calculator.  If you do not know how to make Excel manipulate data, ask the instructor.

3. Create your graph. Does your graph approximate a straight line as expected? What kinematic variables should the slope and y-intercept represent?

4. Using the linest or regression command, determine the slope AND y-intercept to 90% confidence.  How do they compare to the expected values?

5. To display the best-fit line on the graph you should add a trendline as described in the Excel Hints.  Now you can see how closely the data points lie to the best-fit line. In fact, the scatter of the data points around the best-fit line is due to the presence of random error.

6. If your results are systematically off from the expected value, can you come up with a possible and reasonable reason why?

Galileo's Determination of g Lab

Introduction: Galileo was able to accurately determine the value of g, but he did not have a video camera. How did he do it? He rolled objects down ramps and from distances and times, was able to determine the objects' acceleration due to gravity. We will repeat this experiment using The Ramp PhET. See instructions from the earlier Motion and Error Lab if you forget how to access the PhET simulations.

We will slide an object down the ramp, measure times for successively longer falls, and then analyze the data with the kinematic equations for one dimensional motion in order to find g, the local acceleration due to gravity.

Procedure:

Background

We learned in the statistics labs that when making measurements, we need to take multiple data points (to make the statistics meaningful, at least 5-10). From statistical analyses (see last lab), we can see that if we can vary one variable, and measure another, this will allow for an even better result rather than making the same measurement over and over (in other words, for this lab, we will vary the distance along the ramp rather than leaving the object in one place and making the same measurement 10 times.)

Setup

1. From the web, find and start The Ramp PhET.
2. Choose an object. Does the object matter if it is a frictionless ramp?
3. Check the "Frictionless" box. (Sorry Galileo, we can just clear friction with a check-box.)
4. Choose any starting position greater than 0.0 with the position slider. Note that negative positions are on the flat ground where the object will not accelerate.
5. Choose any ramp angle greater than 0.0 and less than 30 degrees. Any ramp angle works, but do you see how a smaller ramp angle will reduce error?
6. When you are ready to take data, click the "Clear" button (in case you have already inadvertently taken some data), then click the "Go! button.
7. You want to determine the time that it takes your object to accelerate to the end of the ramp. Note the time is displayed in the upper, left corner. NOTE the clock goes on after the object reaches the end of the ramp. So you will need to fool with the pause, playback, and slow motion buttons to do your best to figure out the time that the object reached the end of the ramp.
8. Be sure to record the distance the object slid along the ramp and the time that it took.
9. Repeat steps 4-8 as many times as reasonable for different positions on the ramp. Take data for as many distances as you think will be enough to have the random errors start canceling (this always means at least five data points).  

Data and Analysis:

Hints: check out Excel Hints for graphing two columns of data, for trendlines, and statistics of the best fit line (linest or regression).

1. Decide which variables you are going to use to graph which will allow you to determine acceleration. Be careful! Be sure that you choose something to plot that has a linear relationship, and that may require you to manipulate your data.
2. Create the columns of data that you are going to plot. If the data needs to be manipulated, have Excel do this, don't use your calculator.
3. Create your graph. Does your graph approximate a straight line as expected? What kinematic variables should the slope and y-intercept represent?
4. Using the linest or regression command, determine the slope AND y-intercept to 90% confidence.  How do they compare to the expected values?
5. To display the best-fit line on the graph you should add a trendline as described in the Excel Hints.  Now you can see how closely the data points lie to the best-fit line. In fact, the scatter of the data points around the best-fit line is due to the presence of random error. Since this is a simulation, it is possible to reduce random error significantly, but where does random error come into this measurement?
6. Depending on how far you have gotten into two-dimensional motion, you may know - or you may find out later - that the acceleration due to gravity on a frictionless ramp is a = g * sin(ramp angle). Determine g from your results.

Write-Up

1. If this is a written formal lab (as indicated on the lab syllabus), you will have until the next lab to submit the write up to the appropriate assignment in Moodle. For written formal labs, remember to check the "write-up hints" page to be sure everything is included and check your write-up against the grading rubric.
2. If this is an informal lab, record your results in your lab notebook. Before the next lab you will need to complete the informal lab quiz in Moodle in which you will type in your results and/or answer some questions about the lab.
3. If this is an oral report lab, you will schedule a time to meet with your instructor over GoToMeeting to present your work. You should prepare your results and the answers to any questions in a neat and organized fashion so that you can refer to when necessary during your discussion.
4. Remember to read the next lab and do the pre-lab before the next scheduled lab session. You may work on the pre-lab with others, but each person must submit her or his own work.

Department of Physics