Lab Manual Irina Golub
July 30, 2017
PART ONE: Photographic Analysis of a Falling Object
With the great advances that have been made in digital imaging and analysis, experimental data is often in the form of photographic images. In this experiment, you will make displacement measurements of a tennis ball dropped from a height using photographic data and your computer’s mouse positioning system. From two displacement measurements and the time between these measurements and one of the five kinematic equations that describe one- dimensional motion, the acceleration due to gravity on earth, “g”, will be estimated. Since you know what the correct answer should be (9.8 m/s2) you will be able to calculate the percent error of your estimate.
Neglecting air resistance, a falling object increases its speed 9.8 meters per second every second that it falls on earth. This is “g”, the acceleration due to gravity. Below you will see snapshots taken of a falling tennis ball at equal intervals of time (0.1 second between frames). You can see that the displacement of the tennis ball increases during each successive time interval. This is due to the tennis ball speeding up in each time interval, i.e., the tennis ball is accelerating. Read University Physics Volume 1 Chapter # 3: MOTION ALONG A STRAIGHT LINE
A PC running MS Internet Explorer web browser. (Other web browsers may not work for this experiment.)
The photographic data file shows one composite photo made by splicing six separate images of a tennis ball dropped straight down. Each of the six separate images was taken 0.1 second apart.
Just below the photo in the photographic data file you will see boxes labelled X and Y with numbers that change when you move the mouse over the photo. These numbers are mouse coordinates in what we will call “mouse units.”
You will record the Y-position of the ball in the first and last image (i.e., ball image #1 and ball image #6) (the X-direction is not needed as the object was falling straight down). Since the numbers you record will be in mouse units and not meters, only the difference between these two measurements will be important. You will be able to convert this difference from mouse units into meters because there are two meter sticks joined together vertically in each photo as a reference.
[If you are unable to see the mouse coordinates in your browser and are un- able to get to a BCC lab computer you can measure ruler coordinates instead of mouse coordinates using a plastic ruler held near (but not touching!) the computer display. Substitute the phrase ”ruler coordinates” for ”mouse coordinates” in the procedure and questions. Take your measurements in millimeters. This will not be as accurate as using mouse coordinates which have a higher resolution.]
NOTE: Since mouse units are relative to the top left side of the display, it is important to center the entire photo in your display and not scroll the photo when you take measurements. If you cannot see the entire photo on your monitor without scrolling it, change your display to 800 x 600 by clicking the “Start” button, then “Control Pane’, then “Display”, then “Settings”, and adjusting the Screen Resolution to 800 x 600.
1. Determine the conversion factor between mouse units and meters as follows. In each
photo, two meter sticks are joined together vertically. Read the mouse’s y-coordinate at the top of the upper meter stick by clicking on that point. Read the mouse’s y- coordinate at the bottom end of the lower meter stick by clicking on that point. The difference between these measurements represents 2 meters.
For example, if the top of the top meter stick is at y=50 and the bottom of the bottom meter stick is at y=650, then 650-50 = 600 mouse units = 2 meters. Therefore, one (1) mouse unit would equal 2 meters/600 mouse units = 0.0033 meters [This calculation was just an example of how to perform the calculation. Do not use 0.0033 meters per mouse unit as the conversion between mouse units and millimeters. Measure and perform your own calculation]
2. Open the photographic data file. Measure the y-position (i.e., y-coordinate) of the ball (in mouse units) for the first image and the last (i.e., 6th) image five times. Measure from the same place on the ball in each photograph (e.g., the top of the ball)., and record these values on your data table.
3. Calculate the difference in the y-coordinates (mouse units) of the ball from the first image to the last image. For example, if the y-coordinate of the ball in image #1 was 1369 mouse units and 1748 for the ball in image #2, then the difference would be 1748- 1369 or 379 mouse units.
4. Multiply the difference you found in step #3 by the meters/mouse unit conversion you found in step #2. For example, if you found a difference of 379 mouse units between image #1 and image #6 and a meters/mouse unit conversion of 0.0033 in step #2, the result would be 379 mouse units x 0.0033 meters/mouse unit = 1.25 meters.
5. Using y=0.5 gt2, solve for g where y is the result you found in step #4 (in meters) and t is the time difference between the 1st and 6th photos (0.5 seconds). For example, using 1.25 meters for y and 0.5 sec for t, g is calculated to be 10 m/s2.
6. Compute the percent error between the value for “g” you calculated com- pared to the actual value of “g”.
PART TWO: ESTIMATING REACTION TIME
After you see the rear brake lights on the car in front of you, how much time does it take for you to step on your brake pedal? This time interval is one measure of your reaction time. Reaction time complicates many time measurements because it introduces a time lag between an event and the manual recording of the event (e.g., with a stop watch). Automated measurements employ sensors that have very short response times. Read the Free Falling Object with Air Resistance. 1. Neglecting air resistance, an object in free fall moves through a distance, in meters, given by 0.5gt2.
2. Count the air resistance, an object in free fall moves through a distance, in meters, given by
𝑇𝑇 = �2 𝑦𝑦 𝑔𝑔
(1 + 𝑘𝑘𝑦𝑦 6𝑚𝑚
Where k is the constant of proportionality; the numerical value of k depends upon the shape of the object being dropped and the density of the atmosphere. Use the approximal value of the 𝑘𝑘 = 3.46 ∗ 10−3 𝑘𝑘𝑔𝑔
By measuring the distance an object falls between two events, the time interval between the events can be calculated. In this experiment, you will estimate the reaction time for your hand using one-dimensional kinematics and free fall.
EQUIPMENT Yardstick with metric rulings (i.e., a meter stick) The assistance of another person PROCEDURE 1. Your assistant should hold a meter stick vertically. The top of your outstretched hand should line up with the bottom of the meter stick. Your fingers and thumb should form a “V” around the bottom of the meter stick. Your hand should neither be too open or too closed for best results. 2. At a time chosen by your assistant, your assistant will drop the meter stick through your outstretched hand and you will safely grab the meter stick. 3. After grabbing the meter stick, record the position of the top of your hand on the meter stick in centimeters. 4. Perform five trials of the experiment and record your results into the data table.
5. Determine the weight of the meter stick. 6. Convert the displacements from centimeters to meters. CALCULATIONS 1. Calculate the average displacement for the five trials. Calculate the relative error of your measurement of the displacement. 2. Calculate your average reaction time using the average displacement. If neglecting air resistance using the formula:
3. Calculate your average reaction time using the average displacement count the air resistance using the formula:
𝑇𝑇 = �2 𝑦𝑦 𝑔𝑔
(1 + 𝑘𝑘𝑦𝑦 6𝑚𝑚
4. Compere your results.
4. Find in the internet the average reaction time of a human.
5. Calculate the percent error between your results and the theoretical data from the internet.
3. Would you expect the reaction time to move a leg (e.g., pressing the brake pedal in response to a visual stimulus) is greater, the same, or less, than the hand reaction time measured in this experiment? Why?